GMAT Verbal Set 5
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.
