GMAT Verbal Set 5

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to

(give) credit

2^(1/2)

1.41

to (appeal to)

A group of South Tampa homeowners filed a legal appeal ___ block construction of a WiFi tower

Allow ___

Allow to

to (affect to)

As per the market experts there won't be any immediate affect ___ the market due to the recent buy out

to (allergy to)

As strange as it sounds, it's possible to have an allergy ___ cold temperatures.

Associate ___

Associate with

At least as ... ___

At least as ... as

Attribute ___

Attribute to

If r + s > 2t, is r > t ? (1) t > s (2) r > s

COMBINE INEQUALITIES!!!!!!! Answer is D. Try it. Do it now. Now.

Disguised Positives & Negative Questions

Generally Speaking, whenever you see inequalities with zero on either side of the inequality, you should consider testing positive/negative cases to help solve the problem

like

Her coat is just __ mine.

Number is a multiple of 3 and 2

How to check whether a number is a multiple of 6

In danger ___

In danger of

Likely __

Likely to

Model ___

Model after

Not only ... ___ ___ ...

Not only ... but also ...

Not so ... ____

Not so ... as

FORBID

RIGHT: The law FORBIDS any citizen TO VOTE twice. WRONG: The law FORBIDS any citizen FROM VOTING twice.

INSTEAD OF

RIGHT: He wrote with pencils RATHER THAN with pens. SUSPECT: He wrote with pencils INSTEAD OFpens. Note: The GMAT seems to avoid INSTEAD OF even when it is correct. He wrote with pencils, BUT NOT pens. WRONG: He wrote with pencils INSTEAD OF with pens.

ISOLATED

RIGHT: The culture was ISOLATED FROM outside CONTACT. SUSPECT: The culture was IN ISOLATION WRONG: The culture was IN ISOLATION FROM outside CONTACT.

Range from ... ____ ...

Range from ... to ...

sum = (average)(number of terms)

Sum of consecutive numbers

with

concur (person)

We can count __John's to compete the project

count on

for

craving

to

credit (give money)

The thief has escaped ___ the prison

escape from

that

indicate

to

prior

x als etwas betrachten

to think of x as y

of ...에 대해 관대한.

tolerant

to

train

Consider

"I consider you a very good friend"

appear (appear to)

'Milk drops' under the tongue a___ to treat milk allergies

**John's working style is a contrast to Jacob's

'a contrast to' - contrast is used as noun; mainly used to show the dissimilarities between two things

**John is contrasting his working style with that of Jacob

'contrast with' - contrast is used as verb; denotes the actual act of contrasting two things

While on a straight road, Car X and Car Y are traveling at different constant rates. If car X is now 1 mile ahead of Car Y, how many minutes from now will Car X be 2 miles ahead of Car Y? (1) Car X is traveling 50 mph; Car Y is traveling 40 mph. (2) 3 minutes ago Car X was 1/2 mile ahead of Car Y.

(1) Shrinking distance problem: 50-40 = 10 mph*t=1 (2) We are told that 3 minutes ago Car X was 1/2 mile ahead of Car Y. Therefore, Car X took 3 minutes to get 1/2 mile ahead, or r3=1/2 --> r = 6 mph 6t = 1 mile --> t = 1/6 of an hour or 6 minutes THEREFORE, D. Growing distance you subtract the rates. Word translations.

1/16

(1/4)^2

How many multiples of 7 are there between 100 and 150?

(147 - 105)/7+1 = 7

(2 + 5)^3=

(7)^3 (NOT 2^3 + 5^3)

All

(Both, All) of the letters received before January 15 went into the drawing for the $10 million prize.

If Kelly received 1/3 more votes than Mike in a student election, which of the following could have been the total number of votes cast for the two candidates. (A) 12 ; (B) 13; (C) 14; (D) 15; (E) 16

(C) 14

Each

(Each, Both) of the doctors had his own speciality.

Both

(Each, Both) of the women went to Bryn Mawr for their undergraduate degrees.

For an evenly spaced set, the mean and median of the set are equal to the average of the...

(First + Last) /2

The sum of consecutive integers =

(The Number of Items in the Set) X "Middle Number" Or Median

If

(Whether, If) Eduardo comes to the party, eh will bring a bottle of wine.

for

(get) credit

12 is divisible by 3 can be said in many different ways...

* 12 is a multiple of 3 * 12/3 is an integer *12 = 3n, where n is an integer *12 can be shared among 3 people so that each person has the same number of items *3 is a divisor of 12, or 3 is a factor of 12 *12/3 yields a remainder of 0 *3 "goes into" 12 evenly

If the problem states or assumes that a number is an integer, you may need to use prime factorization to solve the problem.

* determining whether one number is divisible by another number * Determining the greatest common factor of two numbers * Reducing fractions * Finding the least common multiple of two (or more) numbers * Simplifying square roots * Determining the exponent on one side of an equation with integrer constraints

What are factors and multiples?

*A number is a FACTOR of another numbers if it can be divided evenly into that number *A number x is considered to be a multiple of another number y, if y times an integer = x *Example - 15 is a multiple of 3 (3x5)

List divisibility rules

*Div by 2 if units digit can be evenly div by 2 *Div by 3 if sum of digits can evenly be div by 3 *Div by 4 if sum of last 2 digits can be div by 4 *Div by 5 if final digit is 0 or 5 *Div by 6 if div by 2 and 3 *Division by zero is undefined *Zero in numerator is fine; it equals zero

All evenly spaced sets are fully defined if the following are known...

*The smallest (first) or largest (last) number in the set *The increment (always 1 for consecutive integers) *The number of items in the set.

What are digits?

*There are 10 digits 0-9 *ALL integers are made up of digits *The digits can be different units in decimals; ones, tens, tenths, hundredths

Perfect Squares, Cubes, etc..

- All perfect squares have an odd total number of factors - The prime factorization of a perfect suqare contains only even powers of primes (Also true that any number whose prime factorization contains only even powers of primes must be a prime number) - If a numbers prime factorization contains any odd powers of primes, then the number is not a perfect square

-er ___

-er than

Fewer Factors, More Multiples.

...

For any set of consecutive integers with an EVEN number of items, the sum of all the integers is NEVER a multiple of the number of items.

...

For any set of consecutive integers with an ODD number of items, the sum of all the integers is ALWAYS a multiple of the number of items.

...

If you add or subtract two multiples N, you get another multiple of N

...

In general, the divisor (y in this case) will always be greater than the remainder. To illustrate this concept, let's look at a few examples: 15/4 gives 3 remainder 3 (the divisor 4 is greater than the remainder 3) 25/3 gives 8 remainder 1 (the divisor 3 is greater than the remainder 1) 46/7 gives 6 remainder 4 (the divisor 7 is greater than the remainder 4)

...

Interest = Principal x (1 + rate/accrual per year)^(accruals per year x years)

...

The product of k consecutive integers is always divisible by k!.

...

The sum of n consecutive integers id divisible by n if n is odd, but it is not divisible by n if n is even.

...

Two data sufficient statements always provide TRUE information

...

Yes/No data sufficiency problem, YES is a sufficient answer and NO is a sufficient answer. MAYBE is not a sufficient answer.

...

You can separate or combine the product or quotient of two roots

...

a^x + a^x + a^x = 3a^x

...

targeted

... at

Consider...

...(blank)

Discussion...

...about

Between...

...and

As many...

...as

Define...

...as

Saw...

...as

Think of...

...as

Not only...

...but also

Intend to provide...

...for

Discourage...

...from

Relieved...

...of

Argument...

...over

Less...

...than

More...

...than

So...

...that

Addicted...

...to

From...

...to

The right to plead...

...to

Believed...

...to be

Thought...

...to be

Credited...

...with

((.000064)^1/3)^1/2

.02

1

0! = ?

Boomtown urban planners expect the city's population to increase by 10% per year over the next two years. If that projection were to come true, the population two years from now would be exactly double the population of one year ago. Which of the following is closest to the percent population increase in Boomtown over the last year? 20% 40% 50% 65% 75%

1 Year Before Now --> 100 1 Year After --> 110 2 Years After --> 121

It takes an elevator four seconds to go up one floor. How many floors will the elevator rise in two minutes?

1 floor/4 seconds or .24 floors/second (NOT 4 seconds per floor --> this is a frequent error)

Divisibility & Addition/Subtraction

1) if you add a multiple of N to a non multiple of N, the restult is a non multiple of N 2) If you add two non multiples o fN, the result couldbe either a multiple of N or a non multiple of N

Testing Odd & Even Cases

1. Ask yourself: how do any given constraints limit the possible scenarios 2. Create a table to keep track of the allowable scenarios, given any constraints in the problem. (If unsure how to limit the scenarios, write out all possibilities and then eliminate the ones that dont fit the constraints.)

3^(1/2)

1.73

16.6%

1/6 = what %

1/8 = 3/8 = 7/8 = 1/6 = 5/6 =

1/8 = .125 3/8 = .375 7/8 =87.5 1/6 = .167 5/6 = 83

12.5%

1/8 = what %

Taking the reciprocals and flipping the sign: x < y and x > 0; y > 0 then you know....

1/x > 1/y

Square of Numbers

11=121, 12=144, 13=169, 14=196, 15=225, 16=256, 17=289, 18=324, 19=361, 20=400, 21=441, 22=484, 23=529, 24=576, 25=625

The population of locusts in a certain swarm doubles every two hours. If 4 hours ago there were 1,000 locusts in the swarm, in approximately how many hours will the swarm population exceed 250,000 locusts? 6 8 10 12 14

12. Remember 4 hours ago, then 2 hours ago, then now...

The probability of event A occurring is the number of outcomes that result in A divided by the total number of possible outcomes.

1st Rule of Probability: Basic Rule is what?

Combinatorics

2!=2, 3!=6, 4!=24, 5!=120, 6!=720, 7!=5040, 8!=40320 nc2=nc(n-2)=n(n-1)/2 When picking balls or jelly beans take worst case scenario.

What are the first 10 prime factors?

2, 3, 5, 7, 11, 13, 17, 19, 23 and 29

Prime Numbers up to 100. 25 in number

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

(216)^(1/3) = ...

216 = 3 x 3 x 3 x 2 x 2 x 2 = 6^3

Quick Cubes

2=8, 3=27, 4=64, 5=125, 6=216, 7=343, 8=512, 9=729

a^x * b^x = (ab)^x

2^4 * 3^4 = 6^4

Odd

2n+1, 2n+3, 2n+5

Even

2n, 2n+2, 2n+4

The probability of an event occurring plus the probability of the event not occurring = 1

2nd Rule of Probability: P(E) = 1 - P(not E)

Right Angle Triangle Combinations

3,4,5 (multiples too) || 5,12,13 (X2 multiple) || 7,24,25 || 8,15,17

x(sq. rt 3), x, 2x

30-60-90 triangle basic lengths of sides

12^3

3^3 x 4^3 = ?

the probability of event A AND event B occurring is the probability of event A times the probability of event B, given that A has already occurred.

3rd Rule of Probability: Conditional Probability

x, x, x(sq. rt 2)

45-45-90 triangle basic lengths of sides

The probability of event A OR B occurring is the probability of event A occurring plus the probability of event B occurring minus the probability of both events occurring. P(A or B) = P(A) +P(B) - P(A and B)

4th rule of Probability

83.3%

5/6 = what %

5^3 = 6^3 = 7^3 = 8^3 = 9^3 =

5^3 = 125 6^3 = 216 7^3 = 343 8^3 =512 9^3 =729

What number is 150% greater than 60?

60 (1 + 150/100) = 60*2.5 = 150

If x is a positive integer, is x! + (x + 1) a prime number? (1) x < 10 (2) x is even

7!+ 6 --> divisible by 1 to 7 7! + 11 --> prime 7! + 13 --> prime 6! + 11 --> prime

Is 27 a factor of 72?

72 Prime Factors = 2, 2, 2, 3, 3; 27 Prime Factors = 3, 3, 3. 72 has only two 3's and 27 has three 3's; therefore, 27 is not a factor of 72.

Units Digits

7= 7,9,3,1 & 3=3,9,7,1

(2 x 5)^3 =

= (10)^3

Sum of the number of consecutive integers =

= (Last - First + 1)

Sum of the number of consecutive multiples =

= (Last - First)/(Increment) + 1

y percent more than z

= z + z (y/100)

y percent less than z

= z - z(y/100)

8k8 + k88 1,6p6 If k and p represent non-zero digits within the integers above, what is p? 6 7 8 9 17

A

Gerund

A gerund is the -ing form of a verb acting as a noun, in any of the "noun roles" possible in a sentence. A gerund can be the subject, the direct object, or the object of a prepositional phrase.

What is a multiple?

A multiple of an integer is formed by multiplying that integer by any integer, so 8, 16, 24 and 32 are some of the multiples of 8.

What are prime numbers?

A positive integer that can be divided evenly only by 2 numbers; itself and one. *Two is the smallest and ONLY even prime number. One and zero are NOT primes. *ALL prime numbers are positive.

Car A is chasing Car B. How long does it take for Car A to catch up to Car B?

A's distance = a mph x t B's distance = b mph x t A - B distance = a - b mph x t

Car A and Car B start driving towards each other at the same time. Eventually they crash into each other. Or, Car A and B start driving away from each other at the same time.

A's distance = a mph x t hours B's distance = b mph x t hours A + B distance = a + b mph x t hours (ADD) (ADD) (SAME)

k,m, t are > 0. k/6 + m/4 = t/12. Do t and 12 have common factors > 1? (1) k is a multiple of 3 (2) m is a multiple of 3

A. 2k + 3m = t (1) 2k + 3m = t --> 2k has the factors 2 and 3 --> 3m has a factor of 3 and something else. Therefore, there is a GCF greater than 1. (2) 2k + 3m = t --> 3m already has 3 as a factor --> 2k does not tell us anything

Cheese is AS GREAT AS people say.

AS...AS RIGHT

Cheese is NOT AS great AS people say.

AS...AS RIGHT

He wins frequently, AS MUCH because he plays SO hard AS because he cheats.

AS...AS RIGHT

His knowledge springs AS MUCH from experience AS from schooling.

AS...AS RIGHT

His knowledge springs NOT SO MUCH from experience AS from schooling.

AS...AS RIGHT

We have AS MANY apples AS need to be cooked.

AS...AS RIGHT

We have AT LEAST AS MANY apples AS you.

AS...AS RIGHT

We have THREE TIMES AS MANY pears AS you.

AS...AS RIGHT

We have ten apples, ABOUT AS MANY AS we picked yesterday.

AS...AS RIGHT

Although (Although X Y)

A___ he had slept at 7 and woke up at 10, he was still sleepy

Ability ___

Ability to

Able ___; Ability ___

Able to; Ability to

If the length of side AB is 17, is triangle ABC a right triangle? (1) The length of side BC is 144. (2) The length of side AC is 145.

According to the Pythagorean Theorem, in a right triangle a2 + b2 = c2. (1) INSUFFICIENT: With only two sides of the triangle, it is impossible to determine whether a2 + b2 = c2. (2) INSUFFICIENT: With only two sides of the triangle, it is impossible to determine whether a2 + b2 = c2. (1) AND (2) SUFFICIENT: With all three side lengths, we can determine if a2 + b2 = c2. It turns out that 172 + 1442 = 1452, so this is a right triangle. However, even if it were not a right triangle, this formula would still be sufficient, so it is unnecessary to finish the calculation. The correct answer is C.

to (acquiesced to)

After a hard-fought battle, the retailers finally acquiesced ___ the draft regulations

(After/ Following) the gold rush, the mining town collapsed

After is better

with (analogy with)

Alexander first studied the vortex tube by making an analogy ___ a concentric-pipe

of (ask of)

All I ask ___ you is one thing, please don't be cynical

Consecutive Multiples?

All the values in the set are multiples of the increment {12, 16, 20, 24}

of (afraid of)

Although he is not afraid ___ the dark he cannot continue without his flashlight

Similar triangles

Angles are equal; areas proportional

Prime Factor?

Any number that is divisible by 1 and itself

(nothing)

Art historians consider __ the Mona Lisa one of the greatest works of art.

(nothing)

Art historians consider the Mona List __ one of the greatest works of art.

as

Art historians regard the Mona Lisa __ one of the greatest works of art.

as

Art historians regard the Mona Lista __ one of the greatest works of art.

As... ___

As ... as

As ... __ ...

As ... as ...

(As an adolescent/ while in adolescence) , John suffered from tonsillites

As an adolescent/ a teenager/ a child

so (as X so Y)

As interest rates are rising, ___ have consumer and producer prices

What are the associative and distributive laws?

Associative - when adding or multiplying you can group or regroup numbers the way you like *Example - 2+3+4 is the same as 3+2+4 Distributive - when multiplying you can regroup numbers *Example - a(b+c) is the same as ab + ac

(total A) / (total B)

Average Rate: Average A per B

(total distance) / (total time)

Average Rate: Average speed

If n is a non-negative integer such that 12^n is a divisor of 3,176,793, what is the value of n^12 - 12^n ? - 11 - 1 0 1 11

B

What is the median value of the set R, if for every term in the set, Rn = Rn-1 + 3? (1) The first term of set R is 15. (2) The mean of set R is 36.

B

x/y < 1 and y > 0 then you know...

B/c y is positive you can multiple y: x < 1(y) --> x < y

1. Focus on the question stem - thinking about the information needed to answer the question. 2. Look at each stem separately. 3. If neither statement was sufficient alone, look at both statements together. 4. Half of the DS answers on GMAT come down to step 3.

Basic DS Strategy

nor

Because Jenny was grounded, she could neither leave the house __ use the telephone.

Immediately write out the DS problem type (value, range, yes/no) on your scratch pad.

Before you begin strategy.

to

Before you enter the house you are required __ take off your hat.

Believe ___

Believe that, Believe to be.

Believe ___

Believe to be

Between ... ___ ...

Between ... and ...

Both ... ___ ...

Both ... and ...

Both John __ Jack are coming for dinner

Both X and Y

If w, x, y and z are integers and w + x = y, is y divisble by z? (1) w and x have a remainder of 1 when divided by z (2) z = 2

C

If n is an integer and n^3 is between 1 and 100, inclusive, what is the value of n? (1) n = 2k + 1, where k is an integer (2) n is a prime number

C.

Car A and B are driving directly toward each other.

Car A --> a Car B --> b shrinking distance b/w a + b; If Car A is going 30 mph and Car B is going 40 mph, then the distance b/w them is shrinking at 70 mph.

Car A is chasing Car B and falling behind

Car A --> a mph Car B --> b mph growing distance between is a - b

as (*as..)

Chocolate tastes as good ___ ice cream

(n-1)!

Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?

to (alternative to)

Clay-based hydrogels could be green alternative ___ polymers

P(E)P(F)

Combined Events: E and F

P(E) + P(F) - P(E and F)

Combined Events: E or F

1 - P(E)

Combined Events: Not E = P(not E) = ?

The team is composed (from/ of) people (of/ from) every department

Composed of

Principal (1 + interest/number times compounded)^(t)(n)

Compound interest formula

Find simple interest then look for the answer that is a little bigger

Compound interest rule

Connection ___

Connection between

Consequence ___

Consequence of

Continue ___

Continue to

Contrast ___

Contrast with

Credit ___

Credit with

Cindy has her eye on a sundress but thinks it is too expensive. It goes on sale for 15% less than the original price. Before Cindy can buy the dress, however, the store raises the new price by 25%. If the dress cost $68 after it went on sale for 15% off, what is the difference between the original price and the final price? $0.00 $1.00 $3.40 $5.00 $6.80

D

A basketball coach will select the members of a five-player team from among 9 players, including John and Peter. If the five players are chosen at random, what is the probability that the coach chooses a team that includes both John and Peter? 1/9 1/6 2/9 5/18 1/3

D Teams with John and Peter = (1)(1)(7!)/((4!)(3!)) Total = (9!)/(5!3!)

If x is a positive integer, is x^3 - 3x^2 + 2x divisible by 4? (1) x = 4y + 4, y = integer (2) x = 2z + 2, z = integer

D. Both 1 and 2 are sufficient

Small standard deviation

Data points are clustered

Large standard deviation

Data points are spread apart

Debate ___

Debate over

Decide ___

Decide to

Define ___

Define as

from

Democrats are not so different __ Republicans in the United States.

If the outcome of one event affects the outcome of the other event.

Dependent events: When are two events said to be dependent events?

Different ___

Different from

Difficult ___

Difficult to

Dispute ___

Dispute over

Distinguish ... ___ ...

Distinguish ... from ...

Distinguish ___ ... and ...

Distinguish between ... and ...

to (ability to)

Donkeys have the ability ___ communicate with one another via sonar

to (access to)

Due to patient privacy acts, access ___ medical records requires explicit consent by the patient

Add or subtract 2 odd numbers, and the result is...

EVEN

Sum of any two primes above 2 is ...

EVEN

When you multiply integers, and any of the integers are even, the result is...

EVEN

by (accompanied by)

Each Quantitative and Verbal lesson is accompanied ___ a reinforcement quiz

whether

Eduardo wasn't sure (whether, if) he could make it to the party.

Either ... ___ ...

Either ... or ...

Estimate __ ____

Estimate to be

Even +- Even =

Even

Odd X Even =

Even

Odd+- Odd =

Even

Even x Even =

Even (and divisible by 4)

Remainder 0

Even integers

What are odd and even numbers?

Even numbers are integers that can be divided by 2; Odd numbers are integers that cannot be divided by 2. *ZERO IS EVEN Rules: *even x even = even *odd x odd = odd *even x odd = even *even + even = even *odd + odd = even *even + odd = odd

Extent __ ____

Extent to which

What is a factor?

Factor is a positive integer that divides evenly into an integer (1,2,4 and 8 are all factors (also called divisors of 8).

apply (apply to)

Feb 1st was not the last day to a___ to college

with (argue with)

Few people would argue ___ the premise that the quality of CD players has improved over the years

Calculate out the first DS questions to make sure they are correct. It is important to start out the section strong.

First DS questions...

1. If you have as many distinct linear equations as you have variables, you can answer ANY question about the system. 2. If you are only asked to solve for part of the system, you don't necessarily need all n equations. 3. If you are asked to solve for a relationship instead of the value of variables, you don't necessarily need all n equations.

For a system with n variables..?

Skip statements that you do not understand. Eliminate as much as possible.

For hard questions do the following..

Forbid ___

Forbid to

Group 1 + Group 2 + Neither - Both = Total

Formula for Mixed Group problems (involving Both/Neither)

(sum of bases)(height) / 2

Formula for area of a Trapezoid

From ... ___ ...

From ... to ...

GCF & LCM

GCF : lowest power of SHARED prime factors LCM: Highest factor of ALL prime factors

the total amount before any deductions

Gross

Gross Profit = Selling Price - Cost

Gross Profit formula

as

He did not vote for the Libertarian Party (as, like) I did.

as

He is not so much smart __ cunning.

as

He walks to work, just __ I do.

by (affected by)

He was deeply affected ___ the themes in the play

from

He was prohibited __ entering the public library after he accidentally set the dictionaryt on fire with a magnifying glass.

that

He was so late __ he missed the main course.

like

Her coat is just (as, like) mine.

to be

His friends do not believe the ring he bought at the auction __ __ Jackie O's; they all thing he was tricked.

of (approve/disapprove of)

His mother-in-law did not approve ___ his slovenly manner

for (adapted for)

How can health promotion interventions be adapted ___ minority ethnic communities

multiply or divide the numbers outside the radical signs, then the numbers inside the radical signs

How do you multiply roots together.

Absolute Value?

How far away is the number from 0 on the number line?

14 liters

How many liters of a solution that is 10% alcohol by volume must be added to 2 liters of a solution that is 50% alcohol by volume to create a solution that is 15% alcohol by volume?

0.15n + 0.08(5) = 0.1(n+5)

How many liters of a solution that is 15% salt must be added to 5 liters of a solution that is 8% salt so that the resulting mixture is 10% salt?

about 1/2 of the time

How often do you have to look at both statements combined?

Check each prime number up to the approximate square root of the number. If you haven't found a number less than or equal to the square root of the number, then the number is prime.

How to check for a prime number.

Sum of digits is multiple of 3, last two digits multiple of 4.

How to check whether a number is a multiple of 12.

Sum of digits is multiple of 3

How to check whether a number is a multiple of 3.

Last two digits are multiple of 4 or the number can be divided by 2 twice.

How to check whether a number is a multiple of 4.

Sum of digits is multiple of 9

How to check whether number is multiple of 9

Find all prime factors

How to find all divisors of a number

y2 - y1 / x2 - x1

How to find the slope.

for (allows for)

Hybrid motherboard allows ___ two complete systems on one board

to (ask X to Y)

I asked her ___ baby-sit for my child

and

I can distinguish between black __ white.

from

I can't distinguish day __ night.

from

I can't distinquish day __ night.

to

I don't permit my children __ play with knives in the living room.

to

I forbid you __ call me before noon.

or

I must have either chocolate ice cream __ carrot cake to complete a great meal.

with (agree with)

I tend to agree ___ everything you have said

at (angry at)

I was so angry ___ myself, and wanted to give up there and then

Which of the following would result in a remainder of 7 when divided by 12? I. 151 II. 3,443 III. 5,995 I only I and II I and III II and III I, II and III

I. TRUE: 151 - 7 = 144. 44 is divisible by 4, and the sum of the digits of 144 is 9, which is divisible by 3. II. FALSE: 3,443 - 7 = 3,436. Because 36 is divisible by 4, the number 3,436 must also be divisible by 4. However, the sum of digits of 3,436 is 16, and 16 is not divisible by 3. III. TRUE: 5,995 - 7 = 5,988. 88 is divisible by 4, and the sum of the digits of 5,988 is 30, which is divisible by 3. The correct answer is C.

$11, 025

If $10,000 is invested at 10% annual interest, compounded semi-annually, what is the balance after 1 year?

Disguised Postive & Negative Example

If (a-b) / c < 0, is a>b ? 1) c> 0 2) a+b < 0 The fact that (a-b)/ c < 0 tells you that a-b and c have different signs. Thus one expression is positve and the other is negative. Stmt 1: tells you that c is negative, therefore a- b must be positive. Sufficent Stmt 2: Says that sum of a and b is negative. doesnt tell you weather a is lager than b. Insufficent.

Stick Separator Method (same gifts or items)

If 16 oranges are distributed among 4 children such that each gets at least 3 oranges, the number of ways of distributing them is a. 30 b. 210 c. 15 d. 35 e. 40 Number of grouping simply becomes number of ways to arrange remaining 4 oranges and 3 separators between themselves = (4 + 3)!/(4!*3!) = 35

Factor Foundation Rule

If a is a factor b, and b is a factor of c, then a is a factor of c. Or, any integer is divisible by all of its factors and it is also divisible by all all the factors of its factors.

What is a remainder?

If a number cannot be evenly divided by another number, the number left over at the end of the division is called the remainder.

Non-terminating Decimals

If in a fraction, the denominator is factor of a number other than 2 or 5, the decimal will be non terminating. Also if denominator gives 10 multiple after deducting one, the denominator can be 9,99,999 and hence non terminating

What are distinct numbers?

If two numbers are distinct, they cannot be equal.

Percent Change

If two precent changes are the same in a profit like relationship, then the third change will be equal to the other two.

Wes works at a science lab that conducts experiments on bacteria. The population of the bacteria multiplies at a constant rate, and his job is to notate the population of a certain group of bacteria each hour. At 1 p.m. on a certain day, he noted that the population was 2,000 and then he left the lab. He returned in time to take a reading at 4 p.m., by which point the population had grown to 250,000. Now he has to fill in the missing data for 2 p.m. and 3 p.m. What was the population at 3 p.m.? 50,000 62,500 65,000 86,666 125,000

If we decide to find a constant multiple by the hour, then we can say that the population was multiplied by a certain number three times from 1 p.m. to 4 p.m.: once from 1 to 2 p.m., again from 2 to 3 p.m., and finally from 3 to 4 p.m. Let's call the constant multiple x. 2,000(x)(x)(x) = 250,000 2,000(x3) = 250,000 x3 = 250,000/2,000 = 125 x = 5 Therefore, the population gets five times bigger each hour.At 3 p.m., there were 2,000(5)(5) = 50,000 bacteria. The correct answer is A.

Like vs. Such as

If you are given a choice on the GMAT, choose such as. The GMAT writers prefer such as to like when what follows are examples; to these writers, like means "similar to"

If vs. Whether

If you are given a choice on the GMAT, choose whether. On the GMAT, if is reserved for conditional if-then statements.

D or E

If you have to guess in a problem, which ones should you guess? Especially if you have to plug numbers.

to

If you take the GMAT enough times, you might develop the ability __ choose the credited responses without reading the questions.

to

If you take the GMAT enough times, you might develop the ability __ chose the credited responses without reading the questions.

about

If you worry too much __ the GMAT, you'll develop an ulcer.

Each other vs. One another

In GMAT English, each other is used to refer to two things, and one another is used for three or more.

Geometry

In a square. If length of the diagonal is sqrt(52). Hence the length of each side of the square = sqrt(26)

Critical Reasoning - assumption question

In an assumption question, the key thing to realize is that you are not looking for the answer choice that does the most for the stimulus when added - you are looking for the answer choice that hurts the most when taken away. The correct answer to an assumption question is something that is "necessary" to the argument. For example, taking the GMAT is necessary for acceptance into most MBA programs. If you take the GMAT away, then the conclusion - being accepted into a MBA program - is harmed. An assumption is not something that has to really strengthen the conclusion when added. For example, just taking the GMAT does not guarantee admission into an MBA program.

at least 3 steps

In general, difficult questions require how many steps to solve?

2 steps

In general, medium questions require how many steps to solve?

To find the number of distinct permutations of a set of items with indistinguishable ("repeat") items, divide the factorial of the items in the set by the product of the factorials of the number of indistinguishable elements.

Indistinguishable events how to find the number of permutations

Minor arc = 2(inscribed angle)

Inscribed Angle, Minor Arc

What are consecutive integers?

Integers listed in order of increasing size without any integers in between

Diagnoles of rhombus

Intersect at midpoints and are perpendicular bisectors

| A union B| = |A| + |B| - |A intersect B|

Intersecting Sets

to (ask + person + infinitive)

Ireland has asked Fifa ___ let them be an extra team in next year's World Cup

widely (widely anticipated that)

It is w___ anticipated that the Securities Act will be brought into force by 2012

John and Mary were each paid x dollars in advance to do a certain job together. J worked on the job for 10 hours and Mary worked for 2 hours less than John. If Mary gave John y dollars of her payment so that they would have received the same hourly wage, what was the dollar amount, in terms of y, that John was paid in advance?

J --> 10 hours M --> 8 hours J --> x+y M--> x -y Hourly Wage = $/hr (x+y)/10=(x-y)/8 --> 9y

Joey runs a race 30 seconds faster than Tommy

Joey --> t - 30 Tommy --> t

John demands (that he be given a raise/ for a raise)

John demands that he be given a raise

as (as... so too)

Just __ the French like their wine, so (too) the English like their beer

Just as ... __ ___ ....

Just as ... so too ...

so too

Just as I crossed over to the dark side __ __ will you, my son.

Just as Katy is a champion swimmer, __ is Angie

Just as X, so Y (to point similarities)

Kelly received 1/3 more votes than mike

Kelly received M + 1/3(M)

with (acquaint with)

Let me acquaint you ___ my family

Lie vs. Lay

Lie - To recline or be located. PT lay PPT lain Lay - to put, place or put down. PT Laid Laid

Link ___

Link to

1. Start by writing each number as a product of primes. 2. Write so that each new prime factor begins in the same place. 3. Lowest common multiple is found by multiplying all factors in either list.

Lowest Common Multiple 60: 2 x 2 x 3 x 5 72: 2 x 2 x 2 x 3 x 3 LCM: 2 x 2 x 2 x 3 x 3 x 5

Ratio of men to women in a room is 3 : 4. If there are 56 people in the room, how many of the people are men?

M men/W women = 3/4 and M + W = 56 OR 3x + 4x = 56 x = 8 M = 3 * 8 = 24 NEVER HAVE TWO UNKNOWN MULTIPLIERS IN A PROBLEM

If there is an evenly spaced set...

MEAN = MEDIAN!!!!!

to (accede to)

Management was not willing to accede ___ labor's initial demands

to

Many amusing quips are attributed __ Dorothy Parker.

such as

Many of my favorite ice cream flavors, (like, such as) chocolate chip and strawberry, are also available as frozen yogurt.

such as

Many of my favorite ice cream flavors, __ __ chocolate chip and strawberry, are also available as frozen yogurt.

with

Many people credit Christopher Columbus __ the discovery of America, but Native Americans were here first.

as

Many people see euthanasia __ an escape from pain.

as (acclaimed as)

Martha Graham was acclaimed ___ the greatest dancer of her times

of

Mel Gibson is a native __ Australia.

as

Memorizing idioms is not as fun __ playing bingo.

to (to aid + person / thing)

Merkel makes public case for Germany ___ aid Greece‎

for (account for)

Micorosft announced that China will account ___ a larger share of company's revenue in 2010

as

Mom and Dad gave the same punsihment to me __ to you.

More ___

More than

with

Most politicians prefer not to be associated__ the Mafia.

Much as Lola needed the car, she had no refuse

Much as

Quick Division & Multiplication

Multiple by 2 & Divide by 10. AB=2A*(1/2B). Example: 3.5*22=2*3.5*(22/2)=7*11=77

1. Find total number of possible outcomes. 2. Find the number of desired outcomes.

Multiple event probability

3, 6, 9, 12

Multiples of 3

Consecutive Numbers Product

Multiplication of K consecutive integers is always divisible by K

as

My GMAT teacher defines the conclusion __ the main point of the argument.

with

My father likes to contrast my grades __ my borther's.

to

My pasta sauce is far superior __ my mother-in-law's.

to (amount to)

NHTSA says Toyota's violations could amount ___ $13.8 billion

Mel Gibson was a native ____ Australia.

Native of (noun) Mel Gibson was a native of Australia.

The kangaroo is native ____ Australia.

Native to (adjective) The kangaroo is native to Australia.

Neither ... ___ ...

Neither ... nor ... What follows nor determines whether the verb is singular or plural

the amount after deductions

Net

Not ... ___ ...

Not ... but [rather, merely] ...

Not so much ... ___ ...

Not so much ... as ...

Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

Number added or deleted

347

Number of integers from A to B inclusive = B - A + 1 How many consecutive integers are there from 73 through 419, inclusive?

Add or subtract an odd with an even, and the result is...

ODD

Sum of 2 and any other prime is...

ODD

When you multiply integers, and none of the integers are even, the result is...

ODD

Odd +- Even =

Odd

Odd x Odd =

Odd

odd numbers only have odd factors

Odd Factors

Remainder 1

Odd Integers (5/2 --> R = 1; 3/2 --> R =1)

Any multiplication involving an even number creates an even product.

Odd and Even rule.

Critical Reasoning - assumption question

On GMAT assumption questions, choices that RESTATE or CONTRADICT stated evidence are automatically incorrect.

1. Don't choose E if you have to guess. 2. Pick between A or C if you can eliminate B. 3. Historically, A is slightly more common as the right answer.

On harder DS questions, choices tend to be more sufficient than they appear...

Compare to vs. Compare with

On the GMAT, compare with is the generally preferred form. Use compare to to point out an abstract or figurative likeness, and compare with to consider likenesses and differences in general.

Double vs. Twice

On the GMAT, double is only used as a verb; when making a comparison, the preferred form is twice. He promised to double the company's profits in less than a year. I ate twice as much as you did.

Opposition ___

Opposition to

P is X percent of Q

P = x/100*q

Perceive ___

Perceive as

p/100 = is/of

Percent Formula

(amount of change) / (original amount)

Percent increase = ?

n! / (n - r)!

Permutations: Order Matters

What is the arithmetic order of operation?

Please excuse my dear aunt sally *Parenthesis, exponents, multiplication, division, addition, subtraction

What are positive and negative numbers?

Positive numbers are to the right of zero, Negative numbers are to the left of zero. Rules: *pos x pos = pos *pos x neg = neg *neg x neg = pos *pos + neg = subtraction of neg number *neg + neg = neg

1. Start by writing each number as product of primes. 2. Write so that each new prime factor begins in the same place. 3. Greatest Common Factor is found by multiplying all factors appearing in BOTH lists

Prime Factorization to find Greatest Common Factor

If a point is chosen at random within a space with an area, volume, or length of Y and a space with a respective area, volume, or length of X lies within Y, the probability of choosing a random point within Y is the area, volume, or length of X divided by the area, volume, or length of Y.

Probability and Geometry.

1. A and B < A or B 2. A or B > Individual probabilities of A, B 3. P(A and B) = P(A) x P(B) <-- "fewer options" 4. P(A or B) = P(A) + P(B) <-- "more options"

Probability of multiple events rules.

with (associate X with Y)

Programmers associate the website ___ certain file types present in the Windows registry

Prohibit ___

Prohibit from

Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

Properties of 0

to (ask +infinitive)

Prosecutors ask ___ close case against von Brunn

Remainders

Q: If a/b yields a remainder of 5, c/d yields a remainder of 8, and a,b,c and d are all integers, what is the smallest possible value for b+d? A: Since the remainder must be smaller than the divisor, 5 must be smaller than 5 b. b must be an integer, so be is at least 6. Similarly, 8 must be smaller than d and d must be an interger so d must be atleast 9.Therefore, smallest possible value for b+d is 6+9=15 ** Remainder cannot be greater than divsor or negative, must adjust for excess by taking out the divisor from the remainder or adding the divisor to the remainder (when is negative)

-b +- sq. rt(b^2 - 4ac) / 2a

Quadratic formula

AS PART OF the arrangement, he received severance.

RIGHT

BECAUSE OF the sun, plants grow.

RIGHT

BECAUSE the sun SHINES, plant grow.

RIGHT

BEING infected does not make you sick.

RIGHT

BY SHINING, the sun makes plants grow.

RIGHT

My first job was an apprenticeship AS a sketch artist.

RIGHT

Plant grow BECAUSE the sun SHINES.

RIGHT

The judges saw the horses BEING led to the stables.

RIGHT

We are concerned about the forests AND the oceans.

RIGHT

We are concerned about the forests, the oceans, AND the mountains.

RIGHT

Plants grow, FOR the sun shines.

RIGHT (gramatically correct, but very formal)

AS the president of the company, she works hard.

RIGHT = In the role of

AS we did last year, we will win this year

RIGHT = In the same way

JUST AS we did last year, we will win this year.

RIGHT = In the same way

AS a child, I delivered newspapers.

RIGHT = In the stage of being

AS I had already paid, I was unconcerned

RIGHT = because, since

AS I walked, I became more nervous

RIGHT = during

Maria WAS ALLOWED TO WATCH the movie

RIGHT Allowed to = Permitted

The demolition of the old buidling ALLOWS FOR new construction

RIGHT Allows for = permits the existence of

The holiday ALLOWS Maria TO WATCH the movie today.

RIGHT Allows to = Permits

I value my ABILITY TO SING

RIGHT Note: I CAN SING is preferred to I HAVE THE ABILITY TO SING.

NUMBER

RIGHT: A NUMBER OF dogs ARE barking. THE NUMBER OF dogs IS large. THE NUMBER OF dogs HAS FALLEN, but THE NUMBER OF cats HAS RISEN. The grey oyster nearly vanished, but ITS NUMBERS have rebounded. SUSPECT: There HAS BEEN A DECLINE IN THE NUMBER OF dogs. WRONG: THE NUMBERS OF dogs HAVEfallen. Dogs HAVE FALLEN IN NUMBER, but cats HAVE RISEN IN NUMBER.

JUST AS SO

RIGHT: AS you practice, SO shall you play. (= in the same way or manner) JUST AS you practice, SO shall you play. (= in the same way or manner) JUST AS you practice piano regularly, you should study regularly. (= in the same way; the situations are analogous) WRONG: You practice, SO shall you play. JUST LIKE you practice, SO shall you play.

EVERY

RIGHT: FOR EVERYdollar SAVED,THREE dollars ARE WASTED. SUSPECT: FOR EVERY dollar SAVED, you WASTE THREE dollars. WRONG: FOR EVERY dollar SAVED WASTES THREE dollars.

ENSURE

RIGHT: He ENSURES THAT deadlines ARE met (or WILL BE met). WRONG: He ENSURES THAT deadlines MUST BE met (or SHOULD BE met).

HELP

RIGHT: He HELPS RAKE the leaves. He HELPS TO RAKE the leaves. He HELPS me RAKE the leaves. He HELPS me TO RAKE the leaves. His HELP IN RAKING the leaves has been welcome. WRONG: He HELPS me IN RAKING the leaves. I need him AS HELP TO RAKE the leaves.

**ONLY

RIGHT: Her performance is exceeded ONLY by theirs. (modifies by theirs) WRONG: Her performance is ONLY exceededby theirs. (technically modifies exceeded) Note: ONLY should be placed just before the words it is meant to modify. In both speech and writing, we often place ONLY before the verb, but this placement is generally wrong, according to the GMAT, since we rarely mean that the verb is the only action ever performed by the subject.

INFLUENCE

RIGHT: His example INFLUENCED me. SUSPECT: His example IDtS INFLUENTIAL TO me (orAN INFLUENCE ON me). WRONG: His example IDtS INFLUENTIAL ON me.

INSPIRE

RIGHT: His example INSPIRED me. SUSPECT: His example WAS INSPIRATIONAL TO me (or AN INSPIRATION TO me).

EVEN

RIGHT: I am EVEN RICHER THAN a prince. I earn AS MUCH money AS EVEN the wealthiest king. WRONG: I am RICHER EVEN THAN a prince. I earn EVEN AS MUCH money AS the wealthiest king.

OR

RIGHT: I do NOT want water OR milk. SUSPECT: I do NOT want water AND milk. (implies the combination):

LOSS

RIGHT: I have suffered a LOSS OF strengrh. (= decline of a quality) They have suffered a LOSS IN the euro. (= decline of an investment). WRONG: I have suffered a LOSS IN strength.

INTENT

RIGHT: I went with the INTENT (or INTENTION) OF LEAVING soon. I went with the INTENT TO LEAVE soon. SUSPECT: I went with the INTENT THAT I WOULD LEAVE soon.

**LIKE

RIGHT: LIKE his sister, Matt drives fast cars. (= borh drive fast cars) Matt drives fast cars LIKE his sister. (= borh drive fast cars, OR both drive fast cars in the same way) Matt drives fast cars LIKE his sister's. (= borh drive similar cars; he does NOT drive his sister's car) WRONG: Matt drives fast cars LIKE his sister does. LIKE his sister,SO Matt drives fast cars.

MEANS

RIGHT: Music education is A MEANS TO improved cognition. WRONG: Music education is A MEANS OF improved cognition. Music education is A MEANS FOR improved cognition.

LET

RIGHT: My doctor LETS me SWIM in the ocean. WRONG: My doctor LEAVES me SWIM in the ocean. The surgery WILL LEAVE me TO SWIM in the ocean.

**LIKELY

RIGHT: My friend IS LIKELY TO EAT worms. IT IS LIKELY THAT my friend WILL EAT worms. My friend is MORE LIKELY THAN my enemy [is] TO EAT worms. My friend is TWICE AS LIKELY AS my enemy [is] TO EAT worms. MORE THAN LIKELY, my friend WILL EAT worms. WRONG: My friend IS LIKELY THAT he WILL EAT worms. RATHER THAN my enemy, myfriend is THE MORE LIKELY to EAT worms.

DOUBLE

RIGHT: Naomi wrote ten letters, DOUBLE THE NUMBER THAT Sara wrote. Naomi's income DOUBLED in three years. Naomi DOUBLED her income in three years. WRONG: Naomi wrote DOUBLE THE LETTERS THAT Sara did.

MOST

RIGHT: OF ALL the Greek gods, Zeus was THE MOST powerful. (superlative) He was THE SECOND MOST attractive AND THE MOST powerful. WRONG: OF ALL the Greek gods, Zeus was THE MORE powerful. He was THE SECOND MOST attractive AND MOST powerful

LACK

RIGHT: Old gadgets ARE LACKING IN features. Old gadgets LACK features. The LACK OF features is upsetting. SUSPECT: There is A LACK OF engineers TO BUILD new gadgets. WRONG: Old gadgets LACK OF features. It is hard to build bridges LACKING engineers.

LIE

RIGHT: Our strength LIES IN numbers. (= resides in) Yesterday,our strength LAY IN numbers. (= resided in) Tomorrow, our strength WILL LIE IN numbers. I lose my books whenever I LAY them down (present tense of different verb). WRONG: Tomorrow,our strength WILL LAY IN numbers.

FOR (conjunction)

RIGHT: Plants grow, FOR the sun shines. (grammatically correct but very formal). BECAUSE the sun SHINES, plants grow. Plants grow BECAUSE the sun SHINES. BECAUSE OF the sun, plants grow. BY SHINING, the sun makes plants grow

ESTIMATE

RIGHT: She ESTIMATES the cost TO BE ten dollars. The cost IS ESTIMATED TO BE ten dollars. WRONG: She ESTIMATES the cost AT ten dollars. She ESTIMATES the costAT ten dollars.

HEAR

RIGHT: She HEARD THAT her investment HAD PAID off. WRONG: She HEARD OF her investment PAYING off.

INVEST

RIGHT: She INVESTED funds IN research TO STUDY cancer. WRONG: She INVESTED funds INTO or FOR research TO STUDY cancer. She INVESTED funds IN research FOR STUDYING cancer.

** IN ORDER TO

RIGHT: She drank coffee IN ORDER TO STAY awake. She drank coffee TO STAY awake (infinitive TO STAY indicates purpose). SUSPECT: She drank coffee IN ORDER THAT or SO THAT she MIGHT stay awake. She drank coffee SO AS TO STAY awake . WRONG: She drank coffee FOR STAYING awake. Coffee was drunk by her IN ORDER TO STAY awake or TO STAY awake. Note: the subject COFFEE is not trying TO STAY awake.

GOAL

RIGHT: The GOAL IS TO EXPAND the company. SUSPECT: The GOAL IS EXPANSION OF the company. WRONG: The GOAL IS EXPANDING the company.

INTERACTION

RIGHT: The INTERACTION OF two nuclei COLLIDING releases energy. WRONG: SUSPECT: The INTERACTION BETWEEN two nuclei COLLIDING releases energy. WRONG: The INTERACTION WHERE two nuclei COLLIDE releases energy.

FAULT

RIGHT: The criminals ARE AT FAULT FOR BREAKING the law. SUSPECT: BREAKING the law IS THE FAULT OF the criminals. WRONG: THAT the criminals BROKE the law IS AT FAULT. IT IS THE FAULT OF the criminals WHO BROKE the law.

DUE TO

RIGHT: The deficit IS DUE TO overspending.(= results from) Our policy will not cover damage DUE TO fire. (= resulting from) BECAUSE politicians SPEND money, we have a deficit. WRONG: DUE TO politicians SPENDING money, we have a deficit. DUE TO THE FACT THAT politicians SPEND money, we have a deficit.

EVER

RIGHT: The economy is MORE fragile THAN EVER BEFORE. WRONG: The economy is MORE fragile THAN NEVER BEFORE. The economy is MORE fragile AS NEVER BEFORE. The economy is MORE THAN EVER BEFORE fragile.

NATIVE

RIGHT: The kangaroo is NATIVE TO Australia. (said of animals, plants) My friend is A NATIVE OF Australia. (said of people) WRONG: The kangaroo is NATIVE IN Australia.

HOLD

RIGHT: The law HOLDS THAT jay walking is illegal. SUSPECT: The law HOLDS jay walking TO BE illegal WRONG: The law HOLDS jay walking is illegal

MAKE

RIGHT: The leader MADE the resistance POSSIBLE. The leader MADE IT POSSIBLE TO RESIST oppression. The leader MADE IT POSSIBLE FOR us TO RESIST oppression. (Note: The IT properly refers to rhe infinitive TO RESIST.) Windshields ARE MADE resistant to impact . SUSPECT: The leader MADE POSSIBLE the resistance. Windshields ARE MADE TO BE resistant to impact. WRONG: The leader MADE POSSIBLE TO RESIST oppression.

FROM ... TO

RIGHT: The price fell FROM 10 euros TO 3 euros. The price fellTO 3 euros FROM 10 euros. WRONG: The price fell FROM 10 euros DOWN TO 3 euros. The price roseFROM 3 euros UP TO 10 euros.

MASS

RIGHT: The truck HAS ten TIMES THE MASS of a small car. WRONG: The truck IS ten TIMES THE MASS of a small car.

INTERACT

RIGHT: These groups often INTERACT WITH ONE ANOTHER (or EACH OTHER). WRONG: These groups often INTERACT AMONG ONE ANOTHER These groups often INTERACT WITH THEMSELVES.

EQUIPPED

RIGHT: They are EQUIPPED TO FIGHT on any terrain. WRONG: They are EQUIPPED FOR FIGHTING on any terrain.

INSTEAD

RIGHT: They avoided the arcade and INSTEAD went to a movie. WRONG: They avoided the arcade and RATHER went to a movie. They avoided the arcade, RATHER going to a movie.

MAYBE

RIGHT: This situation IS PROBABLY as bad as it can get. This situation MAYBE as bad as it can get. (less certain than PROBABLY) PERHAPS (or MAYBE) this situation IS as bad as it can get. SUSPECT: IT MAY BE THAT this situation IS as bad as it can get. WRONG: This situation IS MAYBE as bad as it can get.

DOUBT

RIGHT: We DO NOT DOUBT THAT the apples are ripe. We HAVE NO DOUBT THAT the apples are ripe. She DOUTS WHETHER Jan will arrive on time. SUSPECT: She DOUBTS THAT Jan will arrive on time (The GMAT claimsthat DOUBT, used in a positive statement without NOT or NO, should be followed by WHETHER or IF,not THAT) WRONG: We DO NOT DOUBT WHETHER the apples are ripe. We HAVE NO DOUBTWHETHER the apples are ripe.

KNOW

RIGHT: We KNOW her TO BE brilliant. She is KNOWN TO BE brilliant. We KNOW him AS "Reggie." He is KNOWN AS "Reggie." WRONG: We KNOW her AS brilliant. (KNOW AS = named)

OBJECT

RIGHT: We OBJECT TO these proceedings. SUSPECT: we HAVE AN OBJECTION TO these proceedings.

INSTANCE

RIGHT: We eat out often; FOR INSTANCE, last week we ate out every night. WRONG: We eat out often; AS AN INSTANCE, last week we ate out every night.

ONCE

RIGHT: We might ONCE have seen that band . WRONG: We might AT ONE TIME have seen that band.

MORE

RIGHT: We observed A 10% INCREASE IN robberies last month. MORE AND MORE we have observed violent robberies on weekends. INCREASINGLY we have observed violent robberies on weekends. SUSPECT: We observed 10% MORE robberies last month.

DISCOVERY

RIGHT: love the DISCOVERY THAT carbon CAN form soccer-ball molecules. SUSPECT: I love the DISCOVERY OF carbon's ABILITY TO form soccer-ball molecules. WRONG: I love the DISCOVERY OF carbon BEING ABLE TO form soccer-ballmolecules.

**INDICATE

RIGHT: A report INDICATES THAT unique bacteria LIVE on our skin. SUSPECT: A report INDICATES the presence of unique bacteria on our skin. (Note: this correct form seems to be avoided in right answers.) A report IS INDICATIVE OF the presence of unique bacteria on our skin. WRONG: A report INDICATES unique bacteriaLIVE on our skin. (THAT is needed.) A report IS INDICATIVE THAT unique bacteria LIVE on our skin. A report INDICATES unique bacteria AS present on our skin. A report INDICATES unique bacteriaTO LIVE on our skin.

EXCEPT

RIGHT: EXCEPT FOR a final skirmish, the war was over. SUSPECT: BESIDES a final skirmish, the war was over. WITH THE EXCEPTION OF a final skirmish, the war was over. EXCEPTING a final skirmish, the war was over.

DO

RIGHT: I did not eat the cheese, but my mother DID (or DID SO) WRONG: I did not eat the cheese, but my mother DID IT (or DID THIS).

EITHER ... OR

RIGHT: I will take EITHER the subway OR the bus. WRONG: I will take EITHER the subway AND the bus.

FACT THAT

RIGHT: It is important to recognize THAT our strategy is working. We have succeeded BECAUSE we work hard. SUSPECT: It is important to recognizeTHE FACT THAT our strategy is working. THE FACT THAT our strategy is working is important to recognize. WRONG: We have succeeded DUE TO THE FACT THAT we work hard.

DIFFER / DIFFERENT

RIGHT: My opinion DIFFERS FROM yours. My opinion IS DIFFERENT FROM yours. WRONG: My opinion IS DIFFERENT IN COMPARISON TO yours. Note: The form DIFFERENT THAN does not appear in the 10th, 11th, or 12th Editions of the Official Guide. According to other style guides, you should use DIFFERENT FROM, rather than DIFFERENT THAN, when you are comparing nouns.

MISTAKE

RIGHT: My spouse HAS MISTAKEN me FOR a wealthier person. WRONG: My spouse HAS MISTAKEN me AS a wealthier person. My spouse HAS MISTAKEN me TO a wealthier person.

LESS

RIGHT: Our utilities add up to LESS THAN 10% of our income. WRONG: Our utilities add up to LOWER THAN 10% of our income.

**NOT ... BUT

RIGHT: She DID NOT EAT mangoes BUT ATE other kinds of fruit. She DID NOT EAT mangoes BUT LIKED other kinds of fruit AND later BEGAN to like kiwis, too. A tomato is NOT a vegetable BUT a fruit. A tomato is NOT a vegetable BUT RATHER a fruit. The agency is NOT a fully independent entity BUT INSTEAD derives its authority from Congress. (note that the verbs IS and DERIVES are parallel) She DID NOT EAT mangoes; INSTEAD, she ate other kinds of fruit. WRONG: She DID NOT EAT mangoes BUT other kinds of fruit. She DID NOT EAT mangoes; RATHER other kinds offruit.

ELECT

RIGHT: She ELECTED TO WITHDRAW her money early. SUSPECT: She ELECTED early WITHDRAWAL OF her money. WRONG: She ELECTED WITHDRAWING her money early.

** ENOUGH

RIGHT: The book was SHORT ENOUGH TO READ in a night. The book was SHORT ENOUGH FOR me TO READ in a night. SUSPECT: The power plant has found a way to generate energy at an unprecedented scale, ENOUGH FOR powering and entire city. WRONG: The book was SHORT ENOUGH THAT I could read it in a night. The book was SHORT ENOUGH FOR IT TO BE read in a night. The book was SHORT ENOUGH SO THAT I could read it in a night. The book was SHORT ENOUGH AS TO BE read in a night.

MANDATE

RIGHT: The general MANDATED THAT a trench BE dug. (subjunctive) SUSPECT: We HAVE A MANDATE TO CALL an election soon. (= have authority) WRONG: The general MANDATED a trench TO BE dug. The general MANDATES THAT a trench WILL BE dug. We HAVE A MANDATE FOR an election in the nearfuture.

DISTINGUISH / DISTINCTION

RIGHT: The investor DISTINGUISHED BETWEEN trends AND fads. There is a DISTINCTION BETWEEN trends AND fads. SUSPECT: The investor DISTINGUISHED trends FROM fads. WRONG: The investor DISTINGUISHED trends AND fads. The investor DISTINGUISHED BETWEEN trends FROM fads. There is a DISTINCTION BETWEEN trends WITH fads. There is a DISTINCTION OF trends TO fads. Trends HAVE a DISTINCTION FROM fads.

EFFECT

RIGHT: The new rules will AFFECT our performance . SUSPECT: The new rules will HAVE AN EFFECT ON our performance. (wordier) WRONG: The new rules will CAUSE AN EFFECT ON our performance.

ECONOMIC

RIGHT: The rise in gasoline prices has an ECONOMIC impact on consumers. Our new car is more ECONOMICAL than our last. (= efficient) WRONG: The risein gasolineprices has an ECONOMICAL impact on consumers.

FIND

RIGHT: The scientist FOUND THAT the reaction WAS unusual. SUSPECT: The scientist FOUND the reaction TO BE unusual. WRONG: The scientist FOUND the reaction WAS unusual

DIFFERENCE

RIGHT: There is a DIFFERENCE IN ability BETWEEN us. There is a DIFFERENCE BETWEEN what you can do AND what I can do. There are DIFFERENCES IN what you and I can do. WRONG: There are DIFFERENCES BETWEEN what you and I can do.

**EXPECT

RIGHT: We EXPECT the price TO FALL. The price IS EXPECTED TO FALL. We EXPECT THAT the price WILL FALL. IT IS EXPECTED THAT the price WILL FALL. Inflation rose more than we EXPECTED. There IS an EXPECTATION THAT the price will fall. SUSPECT: There IS an EXPECTATION the price WILL FALL. There IS an EXPECTATION OF the price FALLING. Inflation rose more than we EXPECTED IT TO. Inflation rose more than we EXPECTED IT WOULD. WRONG: The price IS EXPECTED FOR IT TO FALL. IT IS EXPECTED THAT the price SHOULD FALL.

EXPEND

RIGHT: We EXPEND energy ON neighborhood development. WRONG: We EXPEND energy FOR neighborhood development.

EXTENT

RIGHT: We enjoyed the film TO some EXTENT. "Thumbs part up" is the EXTENT TO WHICH we enjoyed the film WRONG: "Thumbs part up" is the EXTENT THAT we enjoyed the film.

** NOT ONLY ... BUT ALSO

RIGHT: We wore NOT ONLY boots BUT ALSO sandals. We wore NOT ONLY boots, BUT ALSO sandals. (comma is optional) We wore NOT JUST boots BUT ALSO sandals. SUSPECT: We wore NOT ONLY boots BUT sandals. Note: The GMAT has used this construction in correct answers. We wore NOT ONLY boots BUT sandals AS WELL. We wore boots AND ALSO sandals WRONG: We wore NOT ONLY boots AND ALSO sandals. we wore NOT ONLY boots BUT, AS WELL, sandals.

DISINCLINED

RIGHT: She DISINCLINED TO WRITE to herparents. WRONG: She HAS A DISINCLINATION TO WRITE to her parents. There IS A DISINCLINATION ON HER PART TO WRITE to her parents. Her busy schedule BRINGS OUT A DISINCLINATION IN HER TO WRITE to herparents.

We work all night, AND we sleep all day.

RIGT Note the comma before AND.

at (aim at)

RIM takes aim ___ consumer market with new BlackBerry OS 6.0

with (afflicted with)

Recently, software engineers have become a group afflicted ___ the disease

Regard ___

Regard as

View separately

Remember not to fall in the trap

If p is an integer, is p/18 an integer? (1) 5p/18 is an integer. (2) 6P/18 is an integer.

Rephrase to ask are there two 3's and and a 2 in the prime box of p?

A good data sufficiency strategy is to rephrase the information in a question.

Rephrase.

Require ___

Require to

to (account to)

Researchers took these factors into account ___ see if they made a difference

Resistance ___

Resistance to

AS A PART OF the arrangement, he received severance.

SUSPECT

Being an advocate of reform, I would like to make a different proposal.

SUSPECT

We are concerned about the forests AND ALSO the oceans.

SUSPECT

Cheese is NOT SO great AS people say.

SUSPECT Should be: Cheese is NOT AS great AS people say.

We have AS MANY apples AS THERE need to be cooked.

SUSPECT Should be: We have AS MANY apples AS need to be cooked.

We have AS MANY apples AS OR MORE apples THAN you.

SUSPECT Should be: We have AT LEAST AS MANY apples AS you.

We work all night AND we sleep all day.

SUSPECT The GMAT usually links two clauses with comma + AND.

Plants are amazing IN THAT they grow in the sun.

SUSPECT Correct but wordy

The growth of plants IS EXPLAINED BY THE FACT THAT the sun shines.

SUSPECT Correct but wordy

Plants grow BECAUSE OF the sun, WHICH SHINES.

SUSPECT Should be: Plant grow BECAUSE the sun SHINES.

He wins frequently, AS MUCH because he plays AS hard AS because he cheats.

SUSPECT Should be: He wins frequently, AS MUCH because he plays SO hard AS because he cheats.

lot (a lot)

Sad movies always make her cry a ___

Same ___

Same as

to

Scores on the GMAT range from 200 __ 800.

IF

See also WHETHER. RIGHT: Inflation can hurt profits IF costs increase. (IF = condition) I can eat ice cream, PROVIDED THAT my doctor approves. (= ONLY IF) SUSPECT: Inflation can hurt profits WHEN costs increase. (WHEN = time period) WRONG: I can eat ice cream, PROVIDED my doctor approves. (requires THAT)

Seem ___

Seem to

(x-n(n)y-n)

Set Problems formula

but also

She is not only beautiful, __ __ smart.

as to be

She is so beautiful __ __ __ exquisite.

A = P(1 + r) ^n

Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)

principle (interest rate - in decimal form) (time - in years)

Simple Interest formula (remember this is only the interest earned, not the total amount of money present in the bank after interest earned)

(# of favorable outcomes) / (# of possible outcomes)

Simple probability

For a fixed distance, the average speed is inversely related to the amount of time required to make the trip.

Since Mieko's average speed was 3/4 of Chan's, her time was 4/3 as long.

A necklace is made by stringing N individual beads together in the repeating patter red, green, white, blue and yellow. If the necklace design begins with a red bead and ends with a white bead, then N could equal? 16 32 41 54 68

Since the pattern repeats every five beads.. RGWBY 5, 15, 20 is a yellow bead. Remainder 1 = Red, 2 = Green = 2, White = 3, Blue = 4, Yellow = 0. Therefore, which answer choice has a remainder of 3, since it ends on W.

So ... __ __ __ ...

So ... as to be... My new computer game is so entertaining as to be genuinely addictive

So ... ___

So ... that. In fact, it's so addictive that I spend several hours playing it.

Soap, Alcohol, Water: 2, 50, 100 Soap to Alcohol is doubled? Soap to Water is halved? What is the new ratio?

Soap to Alcohol = 2*2 to 50 = 4 to 50 Soap to Water = 1/2*2 to 100 = 1 to 100 Soap, Alcohol, Water: 2, 50, 100 New Soap to Alcohol: 4, 50 New Soap to Water: 1 100 Soap, Alcohol, Water: 4, 50, 400

Organize into a grid.

Some GMAT word problems involve groups with distinct "either/or" categories (male/female, blue collar/white collar, etc.) The key is to do what with the information?

with (affinity with)

Some people have a natural affinity ___ children

Terminating or Non Terminating Decimals

Steps for finding no. of either zero digits or non zero digits: Make 10 pairs and multiple individual left overs.

Sue left her office at the same time as Tara left her. They met some time later.

Sue --> t Tara --> t

Sue left the office 1 hour after Tara, but they met on the road.

Sue --> t - 1 Tara --> t

Sue and Tara left at the same time, but Sue arrived home 1 hour before Tara did.

Sue --> t -1 Tara --> t

If the statement answers Yes OR No, the statement is sufficient. MAYBE is when the statement is insufficient.

Sufficiency in "Y/N" question types

Superior ___

Superior to

Target ___

Target at

If the inflation index between '89 and '70 is 3.56 and price of Model K mixer was 102.40 more in 1989 then 1970. What is the price of Model K in 1970?

The 1989 price (3.56x) minus the 1970 price (x) = 2.56x. 2.56x = 102.40.

22

The average of 5 numbers is 2. After one number is deleted, the new average is -3. What number was deleted?

The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

The average of consecutive numbers

than

The chimpanzee is much more intelligent __ the orangutan.

at

The commercials were obviously targeted __ teenage boys.

Remainders contd...

The decimal of a quiotent is the remanider and must be an integer. Moreover, the decmial part of the quiotent can be multipled by the divisor to get the intger remainder. Ex: 7/5 = 1.4.... (.4)*5=2.0 (2 is the integer version of the remainder)!

If (x # y) represents the remainder that results when the positive integer x is divided by the positive integer y, what is the sum of all the possible values of y such that (16 # y) = 1? 8 9 16 23 24

The definition given tells us that when x is divided by y a remainder of (x # y) results. Consequently, when 16 is divided by y a remainder of (16 # y) results. Since (16 # y) = 1, we can conclude that when 16 is divided by y a remainder of 1 results. Therefore, in determining the possible values of y, we must find all the integers that will divide into 16 and leave a remainder of 1. These integers are 3 , 5, and 15. The sum of these integers is 23. The correct answer is D.

in (aid in + gerund)

The explorers needed aid ___ finding drinking water

that

The hypothesis __ aspartame causes brain tumors has not been proven yet.

to

The kangaroo is native __ Australia.

with (*associate with)

The left wants the Republicans to closely associate ___ the Tea Party movement

What is the arithmetic mean (average) of a evenly spaced set?

The median or middle number (or average of middle number).

over

The men had a dispute __ money.

closer

The more you ignore me, the (closest, closer) I get.

like

The mule __ the donkey, is a close relative of the horse.

like

The mule, (like, such as) the donkey, is a close relative of the horse.

the number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

The number of ways independent events can occur together.

of (accuse of)

The politician was accused ___ being economical with the truth

Bill runs a hot dog stand, and at the end of the day he has collected an assortment of $1, $5, and $10 bills. He discovers that the number of $1, $5, and $10 bills that he has is in the ratio of 10 : 5 : 1, respectively. How many $10 bills does he have? (1) The dollar value of his $1 bills equals the dollar value of his $10 bills. (2) Bill has a total of $225.

The question stem tells us that Bill has a stack of $1, $5, and $10 bills in the ratio of 10 : 5 : 1 respectively. We're trying to find the number of $10 bills. (1) INSUFFICIENT: Since the ratio of the number of $1 bills to $10 bills is 10 : 1, the dollar value of the $1 and $10 bills must be equal. Therefore statement (1) gives us no new information, and we cannot find the number of $10 bills. (2) SUFFICIENT: The problem states that the number of $1, $5, and $10 bills is in the ratio of 10 : 5 : 1, so let's use an unknown multiplier x to solve the problem. Using x, we can see that there are 10x $1 bills with a value of $10x. Furthermore, there are 5x $5 bills with a value of $25x. Finally, there are 1x $10 bills with a value of $10x. Statement (2) says that the total amount he has is $225, so we can set up an equation as follows: $10x + $25x + $10x = $225 $45x = $225 x = 5 Since there are 1x $10 bills this means that there are 5 $10 bills. The correct answer is B.

to (according to)

The questions in an adaptive test are weighted according ___ their difficulty

but

The review was not mean-spirited __ merly flippant.

Sum of two primes

The sum of any two primes will be even ("add two odds"), unless one of those primes is the number 2. So if you see the sum of two primes that is odd, one of those primes must be the number 2

to be

The time he has spend impersonating Elvis is estimated __ __ longer than the time Elvis himself spent performing.

Subjunctive

The verb which follows the subjunctive indicator, infinitive form is used without the to.

Division

There are no guaranteed outcomes in division because the division of two integers may not yield an integer result ** rember that 3/4 is deemed to have a remainder of 3, 0 is an integer** Divided = Quotient * Divisor + Remainder

What is an integer?

They are numbers that: *can be negative or positive *they do NOT include fractions *zero is also an integer; it is not positive or negative

Balancing

Think of averages as what? The average of 3, 4, 5, and x is 5. What is x? 3 is 2 less than 5 4 is 1 less than 5 5 is the average x = 5 + 3 = 8

as

Think of it more __ a promise than a threat.

3-4-5, 5-12-13, 9-12-15

Three triangle length patterns

Figure out the probability for each individual event. Multiply the individual probabilities together.

To determine multiple-event probability where each individual event must occur in a certain way.

What is the units digit of 7^2*9^2*3^3?

To find the units digit of a product or a sum of integers, only pay attention to the units digit of the numbers you are working with. Drop any other digits.

To boldly go...or...to go boldly

To go boldly

to (able +infinitive)

Tom is able ___ play the guitar with his toes

P(event NOT occurring) = 1 - P(event occurring)

Trial Problems: look at the probability of NOT OCCURRING

Exterior angle d is equal to the sum of the two remote interior angles a and b

Triangle abc with d on the outside with a line. What does d = ?

to

Try __ stay awake during the essay section of the test.

Try ___

Try to

on (agree on + noun / gerund)

UN officials agree ___ major downsizing in peacekeeping force

to (allocated to)

Under the new constitution, a fixed number of seats are allocated ___ the military and to civilians

Unlike John, (Tom wrote a good essay/ Tom's essay was good)

Unlike X, Y

Amount vs. Number

Use amount when referring to an uncountable quantity, like soup or live, and number when referring to countable things, like jelly beans or people

Use ___

Use as

Among vs. Between

Use between when referring to two items or groups, among when referring to three or more

Both vs. Each

Use both when pointing out similarities; use each when pointing out differences. Note that each is always singular.

Fewer vs. Less

Use fewer to describe countable things, like jelly beans or people, and less to describe an uncountable quantity, like soup or love.

As vs. Like

Use like to compare nouns; use as to compare actions- in other words, use as when what follows is a clause

Native ___

Use native to meaning "indigenous to" when discussing plants, animals, and the like. Use a native of when discussing people and where they were born.

Idioms

Verbs + infinitives: allow A to do X choose to do X decide to do X forbid A to do X persuade A to do X try to do X to prohibit A from doing X

View ___

View as

4/3 TT r ^3

Volume of a sphere

AS BEING a child, I delivered newspapers.

WRONG

BEING THAT the sun shines, plants grow.

WRONG

My first job was an apprenticeship OF a sketch artist.

WRONG

The ABILITY OF plants TO grow IS BECAUSE the sun shines.

WRONG

The growth of plants IS EXPLAINED BECAUSE OF the shining of the sun.

WRONG

The growth of plants IS EXPLAINED BECAUSE the sun shines.

WRONG

WHILE BEING a child, I delivered newspapers.

WRONG

WHILE IN childhood, I delivered newspapers.

WRONG

We are concerned about the forests, ALSO the oceans.

WRONG

I value my ABILITY FOR SINGING

WRONG It should be: I value my ABILITY TO SING.

I value my ABILITY OF SINGING

WRONG It should be: I value my ABILITY TO SING.

I value the ABILITY FOR me TO SING

WRONG It should be: I value my ABILITY TO SING.

Homework is ALLOWED FOR DOING BY Maria.

WRONG It should be: Maria is ALLOWED TO DO homework.

The ALLOWING OF shopping TO DO (or TO BE DONE).

WRONG It should be: Shopping IS ALLOWED.

The holiday ALLOWED FOR Maria TO WATCH the movie.

WRONG It should be: The holiday ALLOWS Maria TO WATCH the movie today.

The holiday ALLOWED Maria the WATCHING OF the movie

WRONG It should be: The holiday ALLOWS Maria TO WATCH the movie today.

The holiday ALLOWS THAT homework BE done (or CAN BE done).

WRONG It should be: The holiday ALLOWS homework TO BE done.

Cheese is AS great THAT people say.

WRONG Should be: Cheese is AS GREAT AS people say.

Cheese is SO great AS people say.

WRONG Should be: Cheese is AS GREAT AS people say.

Cheese is SO great THAT people say.

WRONG Should be: Cheese is AS GREAT AS people say.

His knowledhe springs NOT from experience AS from schooling.

WRONG Should be: His knowledge springs NOT SO MUCH from experience AS from schooling.

We have AS MANY apples THAN you.

WRONG Should be: We have AS MANY apples AS you.

We have SO MANY apples AS you.

WRONG Should be: We have AS MANY apples AS you.

We have AS MANY OR MORE apples THAN you.

WRONG Should be: We have AT LEAST AS MANY apples AS you.

We have THREE TIMES AS MANY MORE pears AS you.

WRONG Should be: We have THREE TIMES AS MANY pears AS you.

We have ten apples, ABOUT EQUIVALENT TO what we picked yesterday.

WRONG Should be: We have ten apples, ABOUT AS MANY AS we picked yesterday.

They worked AS a sketch artist.

WRONG Need to agree in number

BECAUSE OF SHINING, the sun makes plants grow.

WRONG Should be: BY SHINING, the sun makes plants grow.

BECAUSE the sun SHINES IS the REASON that plants grow.

WRONG Should be: BY SHINING, the sun makes plants grow.

ON ACCOUNT OF SHINING or ITS SHINING, the sun makes plants grow.

WRONG Should be: BY SHINING, the sun makes plants grow.

Plants grow AS A RESULT OF the sun SHINING.

WRONG Should be: Plant grow BECAUSE the sun SHINES.

Plants grow BECAUSE OF the sun SHINING.

WRONG Should be: Should be: Plant grow BECAUSE the sun SHINES.

to (as X to Y)

We are puzzled as ___ how it happened

Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 30 white marbles. How many red marbles could be in bag A? 1 3 4 6 8

We are told that bag B contains red and white marbles in the ration 1:4. This implies that WB, the number of white marbles in bag B, must be a multiple of 4. What can we say about WA, the number of white marbles in bag A? We are given two ratios involving the white marbles in bag A. The fact that the ratio of red to white marbles in bag A is 1:3 implies that WA must be a multiple of 3. The fact that the ratio of white to blue marbles in bag A is 2:3 implies that WA must be a multiple of 2. Since WA is both a multiple of 2 and a multiple of 3, it must be a multiple of 6. We are told that WA + WB = 30. We have already figured out that WA must be a multiple of 6 and that WB must be a multiple of 4. So all we need to do now is to test each candidate value of WA (i.e. 6, 12, 18, and 24) to see whether, when plugged into WA + WB = 30, it yields a value for WB that is a multiple of 4. It turns out that WA = 6 and WA = 18 are the only values that meet this criterion. Recall that the ratio of red to white marbles in bag A is 1:3. If there are 6 white marbles in bag A, there are 2 red marbles. If there are 18 white marbles in bag A, there are 6 red marbles. Thus, the number of red marbles in bag A is either 2 or 6. Only one answer choice matches either of these numbers. The correct answer is D.

If 72 cupcakes must be divided equally among the students in a certain class, how many students are in the class? (1) If the number of students is reduced by one-third, each student will receive 3 more cupcakes. (2) If the number of cupcakes is doubled, each student will receive 12 cupcakes.

We can begin by rephrasing the question; because we know that the 72 cupcakes must be shared equally among the students, we must have the following relationship: We can pick variables to represent both the number of students and the number of cupcakes each student will get: let s represent the number of students, and let p represent the number of cupcakes per student. Thus, we have the following equation: The original question asked for the value of s. Solving for s, we can rephrase this question as "what is 72/p?" Thus if we can determine the value of s directly or p we have sufficient data to answer the question. (1) SUFFICIENT: If the number of students is reduced by one-third, then two-thirds of the students will remain; the new number of students would therefore be (2/3)s. In this scenario, each student would then receive 3 more cupcakes, or p + 3 cupcakes each. Translating the general equation from the stem using this new information yields the following equation: Substituting the equation, p = 72/s, from the stem into the equation from statement (1) yields: (2) SUFFICIENT: If there are twice as many cupcakes, then there are 144 cupcakes and each student will receive twelve of them, so we know p = 12. Translating the statement yields the following equation: # of cupcakes = (# of students) × (# of cupcakes per student) 144 = s(12) s = 12 The correct answer is D.

of (on account of)

We canceled the beach picnic on account ___ the bad weather forecast

What is the sum of the digits of the positive integer n where n < 99? 1) n is divisible by the square of the prime number y. 2) y4 is a two-digit odd integer.

We cannot rephrase the given question so we will proceed directly to the statements. (1) INSUFFICIENT: n could be divisible by any square of a prime number, e.g. 4 (22), 9 (32), 25 (52), etc. (2) INSUFFICIENT: This gives us no information about n. It is not established that y is an integer, so n could be many different values. (1) AND (2) SUFFICIENT: We know that y is a prime number. We also know that y4 is a two-digit odd number. The only prime number that yields a two-digit odd integer when raised to the fourth power is 3: 34 = 81. Thus y = 3. We also know that n is divisible by the square of y or 9. So n is divisible by 9 and is less than 99, so n could be 18, 27, 36, 45, 54, 63, 72, 81, or 90. We do not know which number n is but we do know that all of these two-digit numbers have digits that sum to 9. The correct answer is C.

to (analogous to)

We don't believe that 802.11a will prove analogous ___ Betamax

to (adapted to)

We fail to understand how human ancestors adapted ___ previous periods of climate change

Wendy walks 1 mile per hour more slowly than Maurice

Wendy --> r -1 miles per hour Maurice --> r miles per hour

1. Value 2. y/n 3. a range of numbers

What are the three DS question types?

180(n-2)

What does the Sum of the angles in a Regular Polygon formula look like?

Representing Even's and Odd's Algebraically

What is the remainder when "a" is divided by 4? 1) a is the square of an odd integer 2) a is a multiple of 3 Stmt 1: An arbirtary odd inter can be writter as 2n+1, where n is a integer. Therefore stmt 1 is (2n+1)^2 = 4n^2 + 4n + 1. The 1st two terms are multiples of 4 and thus have a remainder of 0. The "+1" would give the term a remainder of 1. Sufficent Stmt 2: Can be proven by picking examples. When 3/4 rmainder is 3, when 6/4 the remainder is 2

Immediately try factoring/simplifying when possible

What to do with equations that have fractions

and

When given the choice, I choose both ice cream __ cake.

Add/SUB

When we add or subtract two numbers the only way the answer will be even is if BOTH numbers or even or odd, otherwise, result will be odd

Odds & Evens

When you multiply integers, if ANY of the integers is even, the result is EVEN - If ther eare TWO even integers in a set of integers being multiplied together, the result will be divisible by 4 ( 2*5*6 = 60 (divisible by 4) - If there are THREE even integers in a set of integers being multiplied together, the result will be divisible by 8 (2*5*6*10 = 600 (divisible by 8)

Immediately UNFACTOR or vice versa

When you see an equation in factored form in a question?

Consider work done in one hour. Inverse of the time it takes everyone working together = Sum of the inverse of the times it would take each person working individually.

Work problem rule

Worry ___

Worry about

I will have tea ____ coffee

X instead of Y

The CEO has attributed the loss ___the economic recession earlier in the year

X is attributed to Y

You are to your parents what I am to mine

X is to Y what W is to Z

If x is an even integer, is x(x +1)(x+2) divisible by 4?

Yes. Setup prime boxes.

Is 456 divisible by 8?

Yes; because 456 is divisible by 2 three times. (456/2 = 228, 228/2 = 114; 114/2 = 57). Always check the last three digits of a larger number.

Is 48 divisible by 6?

Yes; because it is divisible by 2 (it ends with an 8, which is even) AND by 3 (4+8, which is divisble by 3).

Is 4,185 divisible by 9?

Yes; because the sum of the digits is divisible by 9 ((4+1+8+5 = 18)/9 = 2)

Is 28 divisible by 4?

Yes; because you can divide it by 2 twice. Or, when the last two digits are divisible by 4.

Is 72 divisible by 3?

Yes; the sum of its digits are 9, which is divisible by 3.

to (agree to)

You agree ___ pay to us the reasonable cost of re-delivering the goods to you

for

You are responsible __ the child.

to

You have a responsibility __ take care of the child.

For some people, laptops are just a means __ an end

a means to

of

a native

to

ability

Cats have the ability (to see /of seeing) in the dark

ability to see Cats can see.... is better

to

able

to

accede

to

access

The editor has access __ the entire manuscript

access to

as

acclaimed

by

accompanied

to

according

for

account (explaining something)

to

account (receiving blame or credit)

of

accuse

John has been (accused of/ accused with/ accused to have committed ) theft

accused of

with 을 숙지시키다.

acquaint

in

acquiesce

in 묵인하다

acquiesce

Modern mobile phones can (act as/ act like) cameras

act as - function

Please stop (acting like/ acting as) a kid

acting like - metaphorical comparison

for

adapted

When we multiply terms with the same base, we ___ the exponents.

add

to

affect

with

affinity

with친밀감

affinity

with

afflicted

with ...으로 고통받아

afflicted

of

afraid

His behavior (aggravated/ was aggravating to) the problem

aggravated - made worse is aggravating - annoying

to

agree (not noun/gerund/person)

on

agree (noun/gerund but not person)

with

agree (person)

John and Tina agree (on/ with) the need to hire a trainer

agree on = agree upon

I agree (to/ with) your proposal of buyout

agree to

I agree ____ your demands

agree to (a contract; implies concession or settlement) I agree to your demands.

Lets try to agree (upon/ with) a date for the vacation

agree upon = agree on

Paris agrees ____ me.

agree with (a person, a place; implies harmony) Paris agrees with me.

Your analysis (agrees with/ agree to) mine

agrees with

in

aid (gerund)

The motorist need aid (in finding/ to find) their way out

aid in finding

at

aim

to

allergy

to

allocated

We allowed room __ improvement when we wrote this book

allowed for

for

allows

to

alternative

always try to factor

always try to factor

John cant decide (among/ between) a laptop, a mobile phone and a media player

among

to

amount

Zahl von x

amount of x

to

analogous

with

analogy

at

angry

Bob is angry ____ the demonstration.

angry about (an event, idea, etc.) Bob is angry about the demonstration.

Wanda is angry ____ me.

angry at (a person) Wanda is angry at me.

Max is angry ____ me.

angry with (a person; more confrontational than angry at) Max is angry with me

that

anticipated

to

appeal

to

appear

This dish appears __ undercooked

appear to be

to

apply

of

approve

The chairman approves __ the new marketing plan

approves of

with

argue (someone)

over

argue (topic)

For an evenly spaced set, the sum of the elements in the set equals

arithmetic mean (average) X the number of elements

Ein Mittel um

as a means to

als Ergebnis

as a result of

The match has been posponed as a result of rain

as a result of = because of

The landlord owes me an apology - he as good as coled me a thief.

as good as = nearly

Is the novel as great as is being reported in the media?

as great as

so viele wie (zählbar)

as many ... as

wie x

as x as

of

ask

to

ask (person)

The child asked __a glass of water

asked for

He is asking __ trouble

asking for

with

associate

John always associates coke (with/ to) pizza

associate X with Y

Jacol likes to associate (with/ among) honest people

associate with

to be

assume

that

assure

as

at least as

to

attempt

to

attend

Tim is attending __ his sick mother

attend to

by

attended

to

attention

to

attest

to

attribute

We attribute our success (to/ from) good fortune

attribute to

Fügt x an y

attributes x to y

on

authority

to

available

to

averse

that

aware (independent clause)

of

aware (something)

from

away

on

base

on

based

This movie is base __ a true story

based on

of

be oblivious

of

because

to

begin

in

belief

I believe John's version (as/ to be) the truth

believe to be

from

benefit

than

better

No city seems better served by a motorway beltways than Madrid

better served by X than by Y

lieber von x als von y bedient

better served by x than by y

My car is better (than/ from) yours

better than

He had to choose between yoga (and/ or) dance

between x and y

in

boom

x und y zusammen

both x and y

to

bring

by

built

x^a * x^b = x^(a+b)

c^3 * c^5 = c^8

for

call

of

capable

Jerry is capable (for/ of) great feats of strength

capable of

about

care

John cares a lot (of / for/ about) his family

cares about = cares for

upon

center

on

centers

The conversation ceters (around/ on) Mozart's contribution to music

centers on

of

chance (something)

to

chance (verb)

of

choice

to

choose

I chose an interesting gift __ anniversary

choose X for Y

We choose him (as/ to be) our representative

chosee as

Walter claimes __ he can run backwards

claims that

with

collaborate

with ...와 협동하다.

collaborate

with

collide

with ~와 충돌하다

collide

on

comment

with

compare (differences)

to

compare (similarities)

You can compare my copy ____ the original.

compare to (to show similarity) You can compare my copy to the original.

John is comparing a BMW (with/ to) Mercedes

compare with

His work can't compare ____ mine.

compare with (to show difference and similarity) His work can't compare with mine.

In Argentina, Maradona is often compared (to/with) God

compared to

for

compensate

for 보상하다, 보충하다

compensate

with

comply

of

composed

of

comprise

about

concern (consider)

in

concern (relevant)

for

concern (worried)

I am concerned (with/ about) my brother's health

concerned about = worried about

This topic is concerned (with/ about) the use of DNA sequencing

concerned with

I can't concieve of you (to be/ as) a scientist

concieve of X as

that

conclude

in

concur (opinion)

to

conductive

to (열・전기 등을) 전도하는, 전도성의

conductive

John is confirming the plan __Jack

confirm with

to 집단의 다른 구성원들과 행동[생각]을 같이 하다; (관습 등에) 따르다[순응하다]

conform

Does my dress conform (with/ to) your regulation?

conform to

with

conformity

There is no connection between Tim and Larry

connection between X and Y

All sets of consecutive integers are sets of...

consecutive multiples.

of

consequence

Rising temperatures is a consequence (of/ for) global warming

consequence of = result of

(nothing)

consider

I consider myself (none/ as/ to be) a close firend of the rockstar

consider X Y

of

consist

Success consists ____ valuing hard work.

consist in (to mean reside or inhere) Success consists in valuing hard work.

My meal consists ____ bread and jam.

consist of (to mean composed of) My meal consists of bread and jam.

with

consistent

that

contend

Jack is contending (that/ with) Jerry for the award

contend with - compete with someone

John contends (with/ that) his friend is innocent

contends that - claim/ state

to

continue

Tim has been asked to continue __ his training

continue with

to

contrary

Jenna is contrasting her casual jeans (with/ to) a formal top

contrasing with

to

contrast

with

contrast

to

contribute

to

convert

The facts dont correlate (to/ with) her story

correlate with

with

correspond (not to)

to

correspond (not with)

The results of the experiment correspond ____ the predictions.

correspond to (to mean match; be in agreement) The results of the experiment correspond to the predictions.

The lovers corresponded ____ each other while one of them was on location in Paris.

correspond with (to mean exchange letters) The lovers corresponded with each other while one of them was on location in Paris.

The costs associated (to/ wtih) setting up a factory are prohibitive

costs associated with

with

credit (not money)

Telenet gave Tim a credit (of / for) $100 because of an interruption in service

credit for

The team credits its own success (to/ with) good fortune

credit to

Newton is credited (with the discovery of/ as discovering / to having discovered/ for discovering the laws of) gravity

credited with

of

danger

Rampant cutting of trees is a danger to ecology

danger to + noun

from

date

These CDs date (from/ on/ at) the early 70s

date from - to have existence that extends from a particular time

The document has been dated (at being/ at/ as being) 100 years old

dated at

with

deal

over

debate

The MPs debate (about/ over/ on/ for) the bill tomorrow

debate about/ on/ over - discuss in detail

to

decide (action)

on

decide (something)

Let's decide ____ a place to eat.

decide on (a noun) Let's decide on a place to eat.

Tina decided ___ the chocolate flavored ice-cream

decide on - select

Let's decide ____ have some fun.

decide to (do something) Let's decide to have some fun.

Monarch declared all fundamental rights (none/ as/ to be) unconstitutional

declared (takes nothing)

in

decline

against

defend

as

defined

Evaporation is defined (as/ in/ to be) the process in which water changes into vapor

defined as

by

delighted

I'm delighted (to/ at) make your acquaintance

delighted to = glad to

that

demand

that

demonstrate

on

depend

The team's success is dependent (upon/ on) him

dependent on

darauf ankommend ob x

depends on whether x

as

depict

The director depicted the actor (as/ to be) a mutant

depicted as

from

descend

of

descendant

of

desirous

Language structure is partly determined (by/ from) social structure

determined by

from

differ

Hats differ ____ shoes.

differ from(to mean unlike) Hats differ from shoes.

I differ ____ him politically.

differ with (to mean disagree) I differ with him politically.

from

different

Hats are different ____ shoes.

different from (not than) Hats are different from shoes.

Myopia differs from hypermetropia I am very different from my twin sister Her hobbies are different than mine

differs/ different from

to

difficult

with

disagree

I disagree ___ you on this subject

disagree with (person/ idea) - same as agree with

of

disapprove

I disaprove __ the use of cheating to pass the test

disapprove of

to

disclose

Please disclose the details to me at once

disclose to - reveal

from

discourage

I discouraged them (from filing/ to file ) a complaint

discourage from

of

disdain

of

disdain 업신여김, 무시

with

disgust

of

dispose

whether

dispute

There is a dispute ___ the new name of the city

dispute over

Unterschiede zwischen x und y

distinctions between x and y

distinctions (zwischen x und y)

distinctions between x and y

Criminals cannot distinguish right from wrong Criminals cannot distinguish between right and wrong

distinguish X from Y distinguish between X and Y

unterscheide zwischen

distinguish between x and y

from

divergent

from

divergent 분기하는 갈라지는

that

doubt

I doubt (that/ whether) his venture will succeed

doubt that

on

draw (take out)

Could I draw attention (to/ at) this slide?

draw attention to

to

drawn

Jerry was drawn (to/ at) the sports car

drawn to - attracted to

By the end of the contest the boxer had drawn (on/ upon/ at/ to) all the energy he had

drawn upon - used up

All the time I dream (about/ of) football

dream about

to

due

from

dwindle

Her will power is starting to dwindle away

dwindle away - become less or smaller

to

easy

to

effort

or

either

I will have either ice-cream or pastry

either X or Y

entweder x oder y

either x or y

Tom was elected (to/ for) the office by the party members

elect to

Freddie was elected (as/ to be/ to act as ) the president of our club

elected as

by

embarrassed

the weakest candidate emerged (as/ to be) the winner

emerged as

from

emerges

The donation will enable the college __ buy a new projector

enable X to Y

with

enamored

to

encourage

We encouraged Mary __ her singing career

encourage in

by

encouraged

We encouraged Mary __ develop her singing talents

encouraged X to Y

... enough ____

enough to

The boy was not tall enough to reach the window The boy was short enough not to reach the window

enough to

The temperature outside is high enough to cause a heat stroke

enough to

with

entrusted

of

envious

to

equal

from

escape

I think my earlier request escaped your notice

escape notice - to go unnoticed

to

essential

Oxygen is essential (to/ for) life

essential to

to be

estimate

The worth of the sculpture was estimated ___ Madrid

estimated at - used to denote place where the estimation was done

** The sculpture was estimated (to be/ at) worth much more than the base price.

estimated to be

All sets of consecutive multiples are ...

evenly spaced sets.

The house is beautiful and perfect except __ one thing - the price

except for

Ausgenommen (+)

except for + noun

for

exchange

to

expect

I am expecting parcel __ my brother

expect from - to be waiting for something from someone

I expected better __ John

expected X of Y - to anticipate that someone will do something

The ruler is expected (to/ that he should) protect his people

expected to

** Don't expend too much effort (at/ on) this document

expend on - spend on

ausweiten (+)

expended on

to

explain

You can't explain ___ all your mistakes

explain away - to explain something so that it is no longer a problem

to

expose

Do not expose the film__ direct sunlight

expose to

to

extend

The man failed ____ his efforts.

fail in (an attempt) The man failed in his efforts.

I hope I do not fail (in/ on) the test

fail in - you will fail in something

The teacher failed half of the class (in/ on) the test

fail on - somebody will fail you on something

The man failed ____ finish his painting.

fail to (do something) The man failed to finish his painting.

with

familiar

by

fascinated

John is fascinated (by/ with) his boss

fascinated by

that

fear

from

flee

The dogs fled ___ their cruel master

flee from - run away

The dogs fled __ their kennel

flee to

in

fluctuations

on

focus

Tom is trying to focus (on/ at) the problem at had

focus on

to

forbid

John forbid his driver (to enter/ from entering) the house

forbid to

of

frequency

to

from

I am travelling from New York to London

from X to Y

for

give credit

for

grounds

A plant grows ___ a seed

grow from

The child grew (into/ to be/ as) tall handsome teenager

grow into

for

guilty

by

hindered

about 1/3

how many DS questions are Y/N?

that

hypothesize

with

identical (not to)

to

identical (not with)

**My problem is identical (with /to) yours

identical with

with (무엇의 규칙)에 따르는[맞춘]

in conformity

to

in contrast

Im Vergleich mit X ist y

in contrast with x, y; in contrast to x, y

in Gefahr

in danger of

in danger

in danger of

John is in danger of contracting malaria

in danger of verb +ing

to

in order

Jack works out everyday (so as to/ in order to) build his stamina

in order to

She began taking classes in order (to/ that she could) learn French

in order to

to

inclined

of

independent (not from)

from

independent (not of)

The children have been independent (to/ of) their parents since childhood

independent from

His reasoning was flawed, and appeared to be independent (to/of) any logic

independent of

Studies indicate___women actually live longer than men

indicate that

Fred indicated his assent to me

indicate to

towards

indifferent

Can you make yourself indifferent _____ someone you love?

indifferent towards

with

infected

from

inherit

Jeanne has inherited her complexion ___ her mother

inherited from

that

insist

The members insisted ___ the speaker be removed from his post

insisted that

of

instance

This is a real life instnace__ plagiarism

instance of

of

instead

in

instill

to

intent

of

interaction

to

introduce

in

invest

John has invested 6 weeks __ preparing for the test

invested in

The agreement invests the vice-chairman __ the authority to act on the chairman's behalf in certain conditions

invests with

from

isolate

We isolated the chemicals___the source of the leak

isolated from

isoliert von

isolated from

to credit x with (Deutsch)

jdm. etw. zuschreiben

of

jealous

by

judge

so

just as

x wie auch y

just as x, so y

Even as a young boy he was (known to/ known as wanting to) explore different ways of doing things

known to

to

lead

The police led the criminal ___ from the other accused.

lead away

A life of sin will inevitably lead ___ suffering

lead to

than

less

My problem is less serious than yours

less X than Y

less successful (ale)

less successful than

weniger erfolgreich als

less successful than

The CEO is likely___arrested today

likely to be

to

liken

in

localized

Are international charities becoming more localized ___the economic crisis?

localized in

to

manage

The college has been asked to manage __the funds that it has

manage with

that

mandate

The rules of war mandate ___ no prisoner be tortured for information

mandate that

I have got as (many/ much) books as you can

many

Jerry mad me as (many/ much) as fifteen mistakes in the test

many

with

meet

for

mistake

John mistook a Ferrari (as/ for/ to be) a Lamborghini

mistake X for Y

after

modeled

The Indian constitution is modeled ____ the British constitution

modeled after

than

more

I am more clever than my brother

more... than

if a first object may be chosen in m ways and a second object may be chosen in n ways, then there are mn ways of choosing both objects

multiplication principle

Pay $10 per CD for the first 2 CDs, then $7 per additional CD

n = # of CDs bought T = total amt. paid ($) T = $10 x 2 + 7 x (n - 2) (assuming n > 2)

Permutations -- Order Matters

n!/(n-k!)

combinatorics -- order does not matter

n!/(n-k!)k!

to

native

John is a native (of/to) the US

native of - use for human

The Royal Bengal Tiger is native (of/to) the Sunderbans

native to - use for plants or animal species

The CEO deemed it necessary ___ask the employee to resign

necessary to

for

need

to

need

nor

neither

We could neither walk (nor/ or) drive to the venue

neither X nor Y

My achievement is no less than his achievement

no less ... than

but

not

I would have not tea ____ coffee

not X but rather Y

nicht nur wegen v, sonder wegen y

not just because of x, but because of y

not just because of x ... (aber y)

not just because of x, but because of y

but also

not only

Not only is he very intelligent, ____ very humble

not only X but also Y

nicht nur x aber auch y

not only x ... but also y

I am not so much sad ___perplexed

not so much X as Y

Nicht x aber y

not x, but rather y

nicht nur x sonder auch y

not x, but rather y

The scientists noted ___ the aspect ratio remained unchanged

noted that

to

oblivious

of

on account

John has very strong opinions (on/ about) censorship

opinions on

to

opposed

of

opposite

to

order

x vorschreiben y zu

order x to be y

in

originate

Some of our customs originate (in/ from) past belief

originate from

All his troubles originate (in/ from) his mind

originate in

of

partake

in

participate

as

perceive

to

permit

Can you permit me ___ the door please

permit (someone) through

John permitted his son __ drive to college

permit X to Y

She would permit not permit me up the ladder

permit up

to

persuade

I persuaded Tim ___ complete my assignment

persuade X to Y

to

potential (not for)

for

potential (not to)

The coach thinks Jack has the potential __ play at the national level

potential to

I have practiced ____ my recital.I am practicing ____ be an actor.

practice for/to (when practice is a verb) I have practiced for my recital.I am practicing to be an actor.

The practice ____ red-lining is heinous.

practice of (when practice is a noun) The practice of red-lining is heinous.

to

predisposed

to ...성향이 있는.

predisposed

to

prefer

Jack prefers tea (to/over) coffee

prefer X to Y

to

preferable

against

prejudiced

against ...에 대해서 편견을 갖게 하다, ...에게 해를 끼치다.

prejudiced

The country's mind is preoccupied ___ soccer

preoccupied with

to

pressure

from

prevent

Purchase price

price purchased for by wholesaler

market value

price sold for by retailer (after markup)

by

prized

He prized his only child ____ everything else in the world

prized above

Designer corals have been prized ___ jewelry ___nearly 5000 years

prized as, prized for

Gold jewelry has been prized ___ thousands of years

prized for

by

profit

from

prohibit

The landlord has prohibited John ___ coming late in the night

prohibit X from Y

x y verbieten

prohibit x from doing y

to

promise

Is this shirt promised __ anyone?

promise to

against

protect

with

provide

whether

question

The students' marks range ___ good ___ average

range from X to Y

Schwank von x nach y

range from x to y

These trees range ____ a very large territory

range over

of

rate

for

rates

John enquired the rates ___ apple

rates for

than

rather

to

receptive (not of)

of

receptive (not to)

He was reconciled ____ his sad fate.

reconcile to (to mean accept hardship) He was reconciled to his sad fate.

After the fight, Pinky reconciled ____ Gomez.

reconcile with (a person) After the fight, Pinky reconciled with Gomez.

to

refer

Evaporation refers ___ a scientific term

refer to

My friend referred me ___ a specialist

refer to

as

regard

I have always regarded you ___ my brother

regard as

of

regardless

to

related

with

relations

The child was reluctant (to attend / about attending) the class

reluctant to

of

repent

of 뉘우치다, 회개[후회]하다

repent

with

replace

The job requires John (to/ none) supervise the entire operations of the assembly line

require X to

John was required to supervise the entire operations of the assembly line

require to

benötigt x um y zu machen

require x to do y

John wants to know what is required (of/for) him in this job

required of

The job requires that John (to/ none) supervise the entire operations of the assembly line

requires that X

for

requisition

into

research

This resembles chocolate ice cream ___ flavor, but not in consistency

resemble in

to

resistance

to

respond

to

responsibility

It is the CEO's responsibility ___ meet the assigned targets

responsibility to

for

responsible

The CEO is responsible ___ meeting the assigned targets

responsible for

The US has imposed restrictions ___ the licensing of firearms

restrictions on

Verboten

restrictions on x

Bad temper results ____ lack of sleep.

result from (when result is a verb) Bad temper results from lack of sleep.

I hope that this will result ___ the police finding your car

result in

Lack of sleep results ____ bad temper.

result in (when result is a verb) Lack of sleep results in bad temper.

Bad temper is a result ____ lack of sleep.

result of (when result is a noun) Bad temper is a result of lack of sleep.

It will be interesting to see what results ___ the police's efforts

results from

of

rid

for

rival

between

rivalry

Rivalität zwischen x und y

rivalry between x and y

s/t = 64.12...what is the remainder?

s = 64t + .12t

Would you sacrifice your job for a chance to go to Europe?

sacrifice X for Y

I sacrificed a lot for money __ visit Europe

sacrifice to

The police continue to seek ___ the thief who stole John's car

seek after

The prisoner seeks pardon ___ the victim

seek from

Jenny sought ____ a helper for her mother

seek out

seem +

seem + infinitive

The boss seemed ___ a nice person when I met him

seem like

The accused seemed (to be/ like) hiding something

seem to be

to

send

of

sensible

to

sensitive

from

separate

of

sequence

John narrated the entire sequence __events to the cops

sequence of

to

similar

My house is similar ___ yours

similar to

John's grades are so poor (as to/ in order to) lead to his expulsion from the school

so X as to Y - denote cause and effect cannot replace "in order to"

Jerry is so soft-spoken ___ one can barely hear him speak

so X that Y

I am looking at him ____ I am studying his jacket

so much as - can mean 'but rather'

There was not _____ a speck of dust in the house

so much as = even

so x

so x that y

x wie y

so x that y

of

solicitous

of ...을 염려하는.

solicitous

than

sooner

of

sparing

The company's astounding profits speak ___ themselves

speak for

Sheena wants to speak ___ for the rights of the homeless

speak up

I will speak ___ John about this problem

speak with

The chairman claimed that he was speaking ___ his experience

speaking from

on

spend

1.4

sq. rt(2)

1.7

sq. rt(3)

Unsquaring and inequality: x < y and x&y > 0

sqrt(x) < sqrt (y)

I do not subscribe ___ the view that John is guilty

subscribe to

When we divide the terms with the same base, we ___ the exponents.

subtract

This group includes such cars ___ BMW ____ Audi

such X as Y and Z

from

suffer

to

superior

of

suspicious

with

sympathize

I have sympathy ____ Bob.

sympathy for (to mean have compassion for) I have sympathy for Bob.

I have sympathy ____ your position.I am in sympathy ____ your position.

sympathy with (to mean agreement; sharing of feelings) I have sympathy with your position.I am in sympathy with your position.

of

take advantage

with

tamper

The new ad for lawnmower is targeted ___ gardeners

target at

the -er ... ___ ___ ...

the -er ... the -er ..

die Fähigkeit etwas zu machen

the ability ... to

Greatest Common Factor (GCF)

the largest divisor of two more integers

The more the price rise, the ____ the demand increases

the more/ greater X, the more/ greater Y

steigende Kosten

the rising cost

This color looks the same to me ___ it would ___ anyone else

the same to X as to Y

das Selbe an x wie y

the same to x as to y

Least Common Multiple

the smallest multiple of two or more integers

kein Zweifel daran dass

there is no doubt that

John thinks ___ Jack ___ is best friend

think of X as Y

to

threaten

with

tinker

with ...을 만지작거리다.

tinker

estimate

to be

to consider

to consider x y

to credit x (+)

to credit x with

Divide 4999 by 15 => 333 integers

to determine the number of integers less than 5000 that are evenly divisible by 15...?

x für y halten

to mistake x for y

He was trained (to become/ as) an athlete ever since he was a child

trained to

to

transit

to

transmit

to

try

John said the would (try to come/ try and come) on time

try to

A satellite is composed of 30 modular units, each of which is equipped with a set of sensors, some of which have been upgraded. Each unit contains the same number of non-upgraded sensors. If the number of non-upgraded sensors on one unit is 1/5 the total number of upgraded senors on the entire satellite, what fraction of the sensors on the satellite have been upgraded?

u = upgraded across satellite n = non-upgraded per module u/(30n + u) n/u = 1/5 --> 5n = u

anders als x ist y

unlike x, y

For centuries, people have been using herbs ___ remedies for the different diseases

used X as Y

X für y nutzen

used x as y

as

view

The management views the problem (as/ to be) an opportunity

view X as Y

of

violation

to

way

John is unable to decide whether__ go to Harvard or Stanford

whether to

Jerry is training for six hours with the aim of winning the marathon

with the aim of 'verb'ing

mit dem Ziel

with the aim of + (verb)ing

Gedanken machen +

worried about

I am worried ___ my parents

worried about

about

worry

x^3 < x^2. Describe the possible values of x.

x < 1 (except 0)

dogs to cats is 2 to 3

x dogs to y cats = 2 dogs to 3 cats or x dogs/y cats = 2/3

x wird auf z Jahre geschätzt

x is dated at z years old

x>y

x is more than y

X ist zu Y wie w zu z

x is to y what w is to z

x ist fas so schnell wie y gestiegen

x rose almost as fast as y

Is .4x > .3x? And you know x>0 then you know...

x's cancel out and the question is .4 > .3?

Squaring inequalities: x < y and x & y > 0 then you know....

x^2

Squaring inequalities: x > y and x > 0; y > 0 then you know....

x^2 < y^2

x/y < y/x and x and y > 0 then you know...

x^2 < y^2

s Sq. rt (x^r)

x^r/s = ?

Multiplying two inequalities: x < y; z < w and x,y,z,w > 0 then you know....

xz < yw (you can multiple two inequalities but NOT divide them)

To perform in a certain youth dance group, girls must be between 4 feet tall and 4 feet 6 inches, inclusive. If x represents a girl's height, in inches, write an absolute value equation for the heights of girls who are eligible to perform.

|x - 51| <= 3.


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