GMAT Paul

elliptical construction

Ellipses, i.e., leaving out a word or phrase because that exact word or phrase appears elsewhere in the sentence, can be identified any time a phrase is left incomplete: Ex. Joe's is an especially well constructed house. ('house'-omitted) Ex. Joe's shoes are nicer than Bob's. ('shoes'- omitted) Ex. Joe is taller than Bob. ('is'- omitted) Ex. Joe's house is better constructed than Bob's. ('is constructed'-omitted)

pnc geometry formula

# sides, # points formula

Probability of choosing RR (red, red) vs RW (red, white or white, red)

#R/total X #R-1/total-1 vs #R/total X #W/Total-1 x 2(b/c wr, rw can happen 2 ways)

consective multiples, counting # in a sequence

(Last-First)/increment then +1

Work Rate: identical machine formula

(old#)*(time)=(new #)*(time) since the same rate, rate cancels out 4R1(9hours)=3R1(t hours) R1 cancels out 4(9)=3(T T=12

always remember x^2-y^2=

(x+y)(x-y)

FANBOYS

, FANBOY is a reset

see a comma

, modifer

present participle

-ing , actively doing action

adverbial modifier

-ly ing , sparkling with rain (modifies dog ran) (modifies the noun verb)

x was dated..

..at (not as being, or to be)

Integers

0 is an integer but NOT + or - it is EVEN, it is NOT prime

a perfect square will have

1 odd # factors 2 Yes. A perfect square will always be able to be expressed as the product of an even number of prime factors because a perfect square is formed by taking an integer and squaring it. Therefore, the result will have exactly double its prime factors.

Take Notes in RC

1. Main Idea 2. Each paragraphs structure

choosiing smart numbers

1. recognize you can choose smart numbers 2. choose smart number (avoid 1,0) 3. solve using your numbers 4. find a match in the answers

quadratic problem: figuring out roots

1. using sign of B can eliminate answers 2. doing quick factoring using common quadratic forms can eliminate answers

combined work

1/9, 1/5 2.5<time together<4.5 can guess if they give answers between or outside this range

1/9

11.1%

1/8

12.5%, .125

5/4

125%, 1.25

4/3

133%, 1.3

Q 45 m

14-15q

1/6

16.7%, 16 2/3, .1667

if the sum of 2 primes = even

2 is not one of the primes

1/50

2%, 0.02

units digit table

2,8 are important

Q 30 m

21-22q

Q 15 m

28-29q

double a rate in ratios

2:3 doubled is 4:3

relative rates, try and think of time and distance as weighted averages

2x the rate means they go 2/3 if the other person travels at 1r.

use among when ___

3 things

3/8

37.5%, .375

27^2

3^6

factor 87

3x9, 87X1

1/25

4%, 0.04

ratio: remember to use the equation unit = ratioxmultipl

4oz=12x solve for x

5/8

62.5%. .625

6/8

75%, .75

Q 60 m

8-10q

5/6

83.3%

7/8

87.5%, .875

odd/2

= decimal

recalculate average

A N S chart

Subordinator

Although, after, because, before, if, until, since, so that, that, unless, when, while

Ratios:

Part - part 3:4 m:w Part - whole 3:7 men:employee

Played vs Playing

Played cannot act as a noun (ing forms can be a noun, ed cannot) Playing soccer is fun - playing is a noun Played soccer - incorrect

Argument

Premise--> conclusion ( the two parts) because/since are key words (idea at the begining is a premise, second part is the support Given this evidence How can I argue the opposite of the conclusion

relative clause

Relative pronoun as subject (in red): I like the person. The person was nice to me. I like the person who was nice to me. I hate the dog. The dog bit me. I hate the dog that bit me. I am moving to Louisville, KY. It is home to the Muhammad Ali Museum. I am moving to Louisville, KY, which is home to the Muhammad Ali Museum. Relative pronoun as object (in red): I like the bike. My father gave me the bike. I like the bike that my father gave me.

Using since

Since 1989, no one HAS broken that world record. WRONG Since 1989, no one Broke breaks.

CR question family

Structure Assumption Evidence

working verb THAT

THAT acts as a reset and a new subj-verb-obj will follow: ex the teacher is confident THAT her students mastered the lesson.

position of modifiers, essential vs non essenctial

The box of nails, which is nearly full, belongs to Jean. essential: of nails non essential, which is nearly full essential should be placed as close to the noun as possible.

noun modifier

The dog ran down the street sparkling with rain. (street sparkling with rain) (modifies the noun)

proof that

Use relative clause that after proof

CR: Fill in the blank

Usually an strengthen category. Can be Inference: If X it should be expected Y, if X it must be shown that Y

linking verb is parallel marker

WAS , IS nomination IS a step forward

Conditional tense: simple present + simple future

add WILL + base form.

Conditional tense: past tense + Conditional

add WOULD + base form of verb WOULD provide

inequalities:

add them to sovle a question

subordinate markers

after, so that, although, Before, if, since, so that, that, unless, until, when, while

sum of consecutive integers

also n(n+1)/2= sum of consecutive integers

counterpoint

although, though, however, yet, but

3-4 item list

always an AND on the last item NEVER 2 ANDS.

background

always fact based

Paralleism markers OPEN think about the X and Y on either side of the marker

and, or , rather apples AND pears

v-ing acting as a verb form present participle

another verb will be immediately before it. stayed playing

modifiers

answer who what when where why

Active and passive can be parallel

as long as tense is maintained

Idiom w built in parallel structure

between x and y, distiguish x from y, think of x as y, consider xy, estimate x to be y, view x as y, in contrast to x,y, mistake x for y, whether x or y

CR: intermediate conclusion

both a claim and a premise; supports the final conclusion

Parallelism markers CLOSED think about X and Y after the marker

both/and, either/or, not/but, not only/but also, From/to

cost splitting

c/3 3 people , c/3-c/4=15 when price drops $15/pp or 4(x-15)=3x

SC pronouns: it, that, or those

can be used to make a copy of the subject, ex: the money spent is less than THAT spend by her children. ( different money) the money spend by her parents is more than IT was expected to be. (same money) Make sure the copy pronoun matches in quantity Her company is outperforming the (not those) companies of her competitors .

where

can modify a place

whose

can mondify a place, french region WHOSE

SC Pronouns their

careful: plural always

Conclusion words

change flaw to error, gap, mistake, defect, fault, imperfection

decreased vs less

change vs comparison

overlapping set with fractions

choose a common denominator for total

average rate for round trip if individual rates are given

choose a distance, it will always work out.

educated guess rather than , instead of

choose rather than

educated guess like vs such as

choose such as

remainder 2 equations

common solution set, 1st common solution is the common remainder. quotient is the lcm of the 2 quotients

exponents

comparing exponents

X more than Y

comparison

x, Like Y

comparison using , like

exponents in denominator

conjugate the denominator

convinced of

convinced of + noun (not convinced of subj + v)

convinced that

convinced that subj + verb (not convinced that noun)

CR: premise

core to argument supports authors conclusion because, since, result of

7/9 larger than 4/5?

cross multiply. place answers by the corresponding numerator . NOT denominator 35<36, 4/5 is greater

rules of 3, divisibility by 3, cyclicity

cyclicity 3,9,7,1 digits add up to 9 ^1 3 ^2 9 ^3 7 ^4 1 i.e 3^21 = 21/4 = R 1= units digit is 3

rules of 4, divisibility, cyclicity

cyclicity 4,6 divided by 2 twice, OR if last 2 digits are divsible by 4. i.e. 23456 is , 56/4 =14. ^1 4 ^2 6 ^3 4 ^4 6

rules of 7

cyclicity 7,9,3,1 divisibility is Remove the last digit, double it, subtract it from the truncated original number and continue doing this until only one digit remains. If this is 0 or 7, then the original number is divisible by 7. Example: 1603 -> 160-2(3)=154 -> 15-2(4)=7, so 1603 is divisible by 7.

rules of 8

cyclicity 8,4,2,6 can be divided by 2, three times. OR last 3 digits are DIV by 8

rules of 9

cyclicity 9,1 sum of digits is DIV by 9

DRT diverging

d1+d2= d total

Teeter-totter for weighted average

distance between the two numbers can help you determine the weight. ex: 80, 92, 100. 92 is 12 away. there is 20 between 100-80. 12/20 = 60% weight to 100.

rules of 6, divisibility, cyclicity

divisible by 2 BOTH 2 and 3. i.e.: 48 1. ends in even #, DIV by 2 2. add 4+8 = 12, DIV by 3 cyclicity: always 6 in units digit

compound inequality

do equivalent action to each side of the equation

ratio: when adding or subtracting to get new ratios

dont need the multiplier in some equations

Rate work: if then - if some object had travelled at some rate, it would have save t time.

end up with a quadratic

rules of 5, divisibility, cyclicity

ends in 0, 5 units always end in 5 at any power

explained as

equate two things ex: a yawn can be explained as

arithemtic sequence

evenly spaced set

1 is a factor of

every integer, one is NOT prime

expectations that

expectations that .... would .... (needs a would)

Fewer factors, more multiples

factors are smaller than integer, multiples are larger than integer

Rate work: catch up and pass. or make up and catchup and pass

faster dist = slower dist + (make up + pass dist)

you can connect a past participle AND present participle in parallel or different tenses of the verb

fatigued AND dreaming, eats AND drank

coordinate geometery

find point that intersects a line

remainder: common problem, x/6 r 4, x/5 r 3 what is r when x/30

find the common solution in the set

not only __ but__

first blank it expected, second is surprise.

FANBOYS

for, and, nor, but, or, yet, so

Passive voice

form of TO BE ( has been, was) + past participle

1/2<2/3<11/12 as you get larger n/d you get closer to one as you add 9/9 or 1000/1000

fraction < 1 1/2<2/3<11/12

3/2>4/3 as you add

fraction >1 , 3/2>4/3>13/12>1013/1012

explain by

give a reason for something. ex: doctors yawn explained by...

past perfect

had played (EARLIER PAST Moment) = HAD + past participle had played by the time we ARRIVED (later past) needs: a simple past tense verb or a time marker that occurred in the past but later than the past perfect action

past perfect

had... earlier action and simple past for the later action you had considered a GRE class, but you signed up for the GMAT

present perfect

has played =HAVE/HAS + past participle

past perfect passive

have been - ed

present perfect

have/has... for the past few weeks, you have been taking a class starts in the past continues in the future

who substitutes

he, she, we, they (subject nouns/pronouns)

absolute: remember to establish the conditions, then interpret the equations, then plug in the right equations based on the conditions.

here 0<x<1 (equations with the roots - 1 would be +, roots with 1 would be -.

consecutive integer rule

highest- lowest < n terms being subtracted

whom substitutes

him, her, us, them (object noun/pronoun)

as vs to be

hired AS no hired to be

whose substitues

his, hers, our, their (posessive nouns/pronouns)

transition expression

however, therefore, in addition, needs a semicolon

simplify inequalities

http://www.veritasprep.com/blog/2011/01/quarter-wit-quarter-wisdom-do-what-dumbledore-did/

use less with weights and measure

i weigh less than 200 lb. even though it is specific, its the overall amount that youre talkiong about so USE Less.

CR approach

identify the question deconstruct the argument pause and state the goal work from wrong to right

even though

idiom not even with

rules of 2, Divisible by 2, AND 2 ^x units:

if integer is EVEN only EVEN PRIME, First PRIME Units digit cyclicity ^1 2 ^2 4 ^3 8 ^4 6 i.e. 2^21, take 21/4: R1, so units digit will be 2 (#1 spot in cyclicity)

number properties

if n is a product of 2,3, and a 2 digit prime how many factors are > 6 4. multiply 6, 1,2,3 by 11: 66,11,22,33

Rearrange an argument cheatsheet

if premise, conclusion, background, intermediate conclusion are jumbled REARRANGE to create a BEACUSE A THEREFORE B - this will be your premise--> conclusion

Nonessential modifier

if you remove the modifier the sentence still makes sense. usually a ,which (comma which) sentence. ex: the large dog, which has black fur, is a Labrador

if vs whether

if: specify conditions or hypothetical whether: choice about an uncertainty, do not need the whether or NOT.

GCF

ignore non shared factors

v-ing, to v (inf form)

implies intent, When an infinitive verb is used right after a conjugated (or tensed) verb, the implication is that intent is involved. ex:You began studying (in order) to get a good GMAT score

incresaed vs greater

increased is a change, greater is a comparison

if you change a sequence by multiplying, the SD

increases or decreases by that multiple. Meaning if you adjust the SD by .8, then SD decreases by multiplying SD by .8

2nd-4th paragraph : flaws ESSAY

introduce one flaw (don't repeat the exact language from the prompt) explain why it is a flaw (how does this make the conclusion less likely to be true?) suggest ways to fix the flaw (you're fixing the flaw, not changing the conclusion; what could the author do to strengthen his/her argument?)

v-ing by itself

is not a working verb,it is a present particple

that of

is redundant

pronouns are scary

it, they. Figure out what pronoun refers to ex: it = what, is it missing a THE, ex: made it. need it to be made the x it, its, they, them, their,

sequence :: elements in an even subset

k-1/2

MULTIPLE

larger integers created by multiplying that integer by any integer

Rate work: converging / different time

later is "t", earlier is "t+time earlier"

dollars

less than 20 dollars works.

DRT problem : converging diff times

let T = object that left later, let T + additional time be for the object that left first

DRT problem: converging diff speed

let r = slower, let r+ additional speed = faster key is that rate * t = distance. The sum of d1 and d2 have to add up to the total distance.

Frank's, Like

like his brother's , like that of his brothers, ALL WORK

, + conj can connect two independent clauses to create a compound sentence

lin drove to work, but Greg rode his bike.

___ and ____ ____as well as____

look for V tense 1 before and and verb tense 2 after

SC: when you see a pronoun

look for its antecedent NOUN, then replace the noun for the pronoun, does it make sense? (principle of the meaning)

when you see more or increase

look for the other to cause redundancy

Odd # algebraically

m=2K+1 , K is an integer

RC approach

main idea purpose

, but is a reset

make sure the modifier after but modifies the correct subj

quadratics rule

make sure you DONT cancel the x out. WRONG

superficial parallelism vs actual parallelism

make sure you determine the meaning of the sentence

absolute value problem

make sure you test both sides of the absolute

made = verb

making = modifier

countable modifier

many, few, fewer, fewest, number, numerous

so that

means cause and effect

absolute value situation

mod A< mod B

Essential Modifier

modifier is necessary to understand the sentence ex: the job that she started last week is much harder than her previous job. (no comma that sentence)

, which (NOUN modifier)

modifies the noun before the comma

, ing modifier (ADVERBIAL modifier)

modifies the subj/verb

uncountable modifier

much, little, less, least,amount,great

linear equation:

must know

sum of consecutive integers

n, n+1, n+2... sum of first 3 integers is 3n+3. sum of last 4 integers in a 7 consec integers: 4n+18 aka: 4n + 3+4+5+6

;

need two complete ideas on either side of the semicolon

,who

needs to modify the right noun before the ,

absolute value; find condition, then solve each mod for the condition to determine the sign and then interpret the equations based on those conditions

neg mod = opposite of the equation pos mod = same sign of the equation

, which

never which,

absolute checking solutions, when there is a absolute= neg

no need to solve when absolute = neg

CR: background

not core provides context

be verb + verb-ing

now verb-ing is a verb. was running

Powers 9

odd = 9 even = 1

pos neg

odd coeff shows something, even coeff hide answer

prepositional phrase

of noun, cannot be the subject of a sentence

at a time when/ that

ok, not where or which

Equation traps #2 swiss chocolate example

one equation can solve for 2 variables

x+y>0

one of them has to be pos. neg neg case ruled out

Equation traps #5 equation has 3 solutions, or only one real solution

one real solution x^2+4=0 has no solution

x^3<x^2

only works when x<1,

CR: counterpremise

opposes conclusion, sets up trap answers although, yet, however, but

no only ___ but also ___

paralellism trigger, look for s/v agreement

Both THOSE who are popular and THOSE who are not ....

parallel after both/and

____ or _____

parallelism trigger, look for s/v agreement

ratio: adjust part to part vs part to total ratio

part to part add or subtract only from the item needing adjustment. part to total, add or subtract item from both part and total.

verb-ing

participle

present tense ... future (will)

past tense... conditional (would)

which cannot modify

people

whose can modify

people/things

percent, what, is , of

percent x/100 of = multiply is = equals what = x

simple past

played

Simple present

plays

root phrase

portion before a list starts...all that follow should be parallell to the other members in the list. the company's...pay, conditions, and shortage of... if that they had shortages was in the three - that woould be wrong

in which

prepositional modifier of which without a ,

types of warmups and middlemen

prepositional phrase : of, in, to, for, with, on, by, at, from dependent clause: begin with who or because

OF noun after another nouns

prepositional, throw it out when determining tense of following verb ex: the recent string OF burglaries (use the singular tense of string NOT plural of burglaries in the verb)

Divisibility

prime box

Time left 55 min quant /V 56min

q 10

Time left 35 min/V 37 min

q 20

Time left 15 min/V 19 min

q 30

fractions: higher level

reduce the fractions

themself

reflexive #1 they made macaroni for themselves reflexive #2 they ate the macaroni themselves after the kids binged on candy. themself should not refer back to a specific noun. It should refer to a pronoun

figuring out roots, equation trap - forgetting "0", I get this wrong.

remember to look for "0"

, and

reset

, and , but , or

reset button, new subj and verb after the comma

Rhombus facts:

rhombus is divided by the diagonals into four right triangles, rhombus area = multiply diag/2

If you see: Although,

ride out the although until you find the subject being modified by the although

comma splice

run on sentence

percent profit

sale-cost/cost* 100 = % p

Equation traps #1

same equation

coordinate: how to find shared point on 2 lines

set each equation = to each other (third vertex in this example)

remainder: when remainders are =

set the equations = to each other

Backsolving

set up a chart, use b and d, then pick

odd.even problems

set up a table and test scenarios. Overlapping sets will satisfy both statement 1 and 2, determine if all are in agreement.

complicated inequality/quadratic/absolute problem

shows all the techniques

noun that....

signals a noun modifier

SC Pronouns it/its

singular

Rate work: converging/ different speeds

slow is r, faster is "r + difference in speed"

Rate work: converging/ relative rates

slow is r, faster is "xr"

FACTORS

smaller integers that divide evenly into an integer

quadratic: using x^2-y^2

sneaky use of formula

testing absolute value solutions

solve then test solutions

when linear equation is an inequality

solve with a (Total-x) solution

top CR questions

strengthne, weaken, assumption, evaluation, inference, explain discrepency

them

strict plural pronoun: object: refers back to an earlier pronoun (She made macroni for them)

that followed by a verb, that

sub- v-that-subj - v- object

noun followed by that signals a more complex sentence structure

subj verb THAT subj verb obj

exponents ( quadratic in numerator and denominator)

subtract them

like vs such as

such as is preferred. sometimes SUCH will be separated from AS

quadratic formulas

sum and product of roots

Rate work: diverging

sum dist = total dist. add speeds together

premise

supports authors argument, can be fact or opinion, data, comparison signaled by because, since, due to, as a result of, after all

hard absolute problem

t-q has to be positive because it is = to 2 absolute values which can never be neg. s has to be in the middle for t-q to = sum of the distance of t-s, s-q

converging rate

t? r1T + r2T= D rates are additive d? Td-d1/r2= d1/r2 time is equal

triangle circmscribed in circle, when the diameter is the hypotenuse of the circle

the angle is a 90 degree angle

Good starts to the flaw paragraphs 2-4

the authors evidence also falls short... the author fails to consider the author does not consdier alternative causes the author does not predict unforseen consequences the authors evidence is faulty

Percent change

the original # is 100%

If the sum of 2 primes = odd

then one of the primes is 2.

conclusion

therfore, thus, so , consequently CAN be a prediction, judgement, statement of causality, outcome of a plan

the words before and after

they are time markers that are so clear that they make using the past perfect unnecessary

formula/move/property/

things to evaluate when reviewing missed problem

which or whom can follow prepositions

through which, for whom

DRT catch up

time = Change dist/change rate or person A behind has to make up the (distance + what the other person B) catch up and pass: Person A has to travel (distance behind + what B traveled + pass distance)

verb tense

time frame # actions sequence of actions meaning voice mood

work problem

time together = product (hours)/ sum (hours)

Linking verbs

to be (is, are, was, were, am, been, be, being) appear become Feel Grow Look Remain Represent Resemble Seem Smell Taste Turn

not only but also

two ideas that reinforce each other Check the two parts after the not only X , but also Y by usng the verb subj and verb before the not only. ex: it is not only man-made but also designed by humans it is man made. it is designed..

use between only with ___ things

two things or people

percent profit

use %c in the p=r-c formula ++ = 1+%inc --=1-%dec

Rate work: catch up and pass SIMPLIFIED

use Time = change in dist/change in rate

do not use less with countable items

use fewer ex: 10 items or fewer

NO use LESSS with countable items

use fewer, ex: 10 fewer

backsolve - math

use prettiest answer, (usually middle, BCE) try some math, see if it works

DRT: variable rates

use r , 2r for 2x as fast

when within or since or in the last...

use the present perfect when the action is still occurring

The word NUMBERS

use: greater than, do not use: more than its numbers are to be much greater than before.

but also

used for two contrasting ideas

Flaw CR question prompt

uses the word flaw, it will not have IF TRUE would indicate a FLAW. Weaken question will say IF TRUE

WRONG compound sentance

using a , without conjunction : called a run on sentence

past participle

verb conjugation with -ed, indicating an action is completed

participles

verb forms that can act as two work classes, adjective or verb. past participle finished structure. adj finished modifies structure. he finished. verb present participle swimming swan, adj swam swimming in the lake, verb

were to be v -ed

were to be occupied language. This verb tense can be used to indicate something that took place at a later point in the past than some other event

mixture problems

wet vs dry

Prime Box

when figuring out divisible by questions, take all the numbers and figure out their prime box i.e. If N is div by 8 and 15, is N div by 12. 8 Prime box: 2,2,2 15 Prime box: 3,5 From the set you can make 12: 2x2x3 YES However, if j is DIV by 12 and 10, is it DIV by 24. NO 12: 2,2,3 10:2,5 There are not 3 twos to make 8 in either 12 or 10.

use in which, not where

when it is a condition , situation , case, circumstance, or arrangement. i.e. we had an arrangement in which he cooked and I cleaned.

relative pronouns

who for people can substitute for subject nouns/pronouns (he, she, we, they) whom for people can substitute for object nouns/pronouns (him, her, us, them) whose for people can substitute for possessive nouns/pronouns (his, hers, our, their) that for people or things can be either subject or object can only be used in restrictive relative clauses (see below) which for things can be either subject or object can be used in non-restrictive relative clauses can also be used in restrictive relative clauses, though some people don't like this use

relative clause

who, which, what, when, where, that

interrogative pronoun

whom, who, what, which, whose

simple future WHEN, use present perfect to clarify timing

will pay when you ASK (simple perfect) - pay at the same time will pay when you HAVE TAKEN out the garbage - pay after you do something

simple future

will play

warmup

words before the subject

middlemen

words between subj and verb

approach to finding the gcf

work backwards from the smallest number in the set

x/y = Q + r/y

x = Qy +r

absolute value

x is closer to -5 than to 7 means |x−(−5)|<|x−7||x−(−5)|<|x−7| --> |x+5|<|x−7||x+5|<|x−7|. Both sides are non-negative, thus we can safely square: x2+10x+25<x2−14x+49x2+10x+25<x2−14x+49 --> x<1x<1. So, we have that for x to be closer to -5 than it is to 7, x must be less than 1. Only the third option gives the values of x all of which are less than 1. Answer: C (III only). _________________

unlike x, y

x,y should be similar items

CR 4 forms

Argument Plan of action Paradox Statement

As can have a clause follow it

As her brother did, ava aced the test. OK to have did.

CR wrong answer types

Assumption Q: No tie to the argument, No tie to the conclusion Assumption and Evidence Q: Reverse Logic Assumption Q: Irrelevant Distinction (comparison between things that are not necessary to compare) Inference Q: Real World Distraction Switching terms Structure/Explain a Discrepency Q: One word off, or Half Right

probability

At least : use the 1-x (x is probability of desired outcome NOT happening )

crisscross the ratio on the teeter-totter

B_________9______x__|_____7____________G X is middle and if | is skewed towards girls that mean G:B 9:7

capable __

Capable of

CR: Classify information in argument

Cause and Effect: therefore, so, consequently, for this reason, it follows that, as a result Concession: Eventhough, although, though, whereas, despite, while it is true that Premise: because, since, for, after all Contrast: however, but, nevertheless, even so

nouns in prepositional phrases cannot be subjects

Citizens of many countries are expressing concern about the environmental damage caused by the widespread release of greenhouse gases maybe impossible to reverse (About the envirnmental damage cannot =be a subject

interest compounded

FV=P(1+r/n)^nt

Rate work: if asked to find total distance in a round trip problem?

Figure out one trip distance and then double

First Paragraph ESSAY

First Paragraph summarize the issue state a thesis acknowledge that the other side does have some merit introduce your examples 3 to 5 sentences total

angles of x , acute,right,obtuse

For a right triangle: a2+b2=c2 For an acute (a triangle that has all angles less than 90°) triangle: a2+b2>c2 For an obtuse (a triangle that has an angle greater than 90°) triangle: a2+b2<c2

Paradox

Given fact 1, how can it be that fact 2

reducing a relative clause

I like the paintings that hang in the SASB North lobby. I like the paintings hanging in the SASB North lobby.

probability equation

In total, there are 8 red marbles, y white marbles, and 8 + y total marbles in the jar. The probability of obtaining two red marbles is given by: P(Red AND Red) = 8 8 + y × 7 7 + y = 56 (8 + y) × (7 + y) The probability of obtaining one red marble and one white marble is given by: P(Red AND White) = 8 8 + y × y 7 + y × 2 = 16y (8 + y) × (7 + y) Note the multiplier of 2 in the second expression. That is because there are TWO different ways Joan could obtain a Red and a White marble if Joan pulls out two marbles sequentially: Red THEN White White THEN Red By contrast, there is only one way that Joan could obtain two Red marbles: Red THEN Red. Based on these calculations, the question can be rephrased as: 56 (8 + y) × (7 + y) > 16y (8 + y) × (7 + y) ? 56 > 16y ? 3.5 > y ? Therefore mathematically, if y is less than 3.5 (i.e., 3 or less), the answer to the question will be "YES." Otherwise, the answer is "NO." (1) INSUFFICIENT: All we know is that y is less than or equal to 8. It could be greater than 3 or less than 3. (2) SUFFICIENT: We know that y is NOT less than 3 (in other words, y is at LEAST 4). The correct answer is B.

Like vs as

Like - compare nouns AS- compare phrases and verbs

ASN

Make a chart for Average, n, Sum to figure out changes in averages.

IR Parts

Multi Source Reasoning 3 questions, one a multiple choice, 2 opposite ans question yes/no, true false yes/no, true false Table prompt single opposite ans question yes/no, true false Graphical Interpretation - drop downs questions Two Part Analysis

Parallelism 5

Neither X nor Y

Like should be followed by a noun or pronoun or noun phrase,

Never a clause or a verb, However it can be followed by a gerund - like skiing, swimming is. OK

Plan of Action

PLan--> goal Look for in order Given this plan, How can I argue plan wont reach goal

These, those vs them

Them cannot be a subject or a modifier (adj) EX: WRONG Them are broken. WRONG them books. These can be used as obj and subject or modifier These are broken... Subj These books... Mod I did see these. Obj

SC Pronouns: This, those, these, that

They can be used as adjectives, ex: those things, these materials

Parallelism 6

Unlike X, Y ( rare use of comma in parallelism)

Rate work: Average rate out and back trick

Use any distance as #, prefer common multiple

IR: types of questions

Would (not) help explain Yes no. If the statement can be proven true

Parallelism 1

X and Y

Parellelism 3

X but Y

Parallelism 8

X more than Y

Parallelism 2

X or Y

Paralellism 4

X rather than Y

Parallelism 7

X,Y, and Z

ZONEF

Zero One Negative Extremes Fraction

where cannot modify

a condition, situation, case WRONG :we had an arrangement where he cooked RIGHT: we had and arrangement IN WHICH he cooked.

as well as

a modifier

inequality hard

x3<16xx3<16x --> x3−16x<0x3−16x<0 --> x(x2−16)<0x(x2−16)<0 --> x(x+4)(x−4)<0x(x+4)(x−4)<0. Roots are -4, 0, and 4. This gives us 4 ranges: x<−4x<−4, −4<x<0−4<x<0, 0<x<40<x<4, and x>4x>4. Now, test some extreme value: for example if xx is very large number then the whole expression is positive. Here comes the trick: since in the fourth range, when x>4x>4, the expression is positive, then in third range it'll be negative, in the second positive, and in the first range it'l be negative again: -+-+. Thus, the ranges when the expression is negative are: x<−4x<−4 and 0<x<40<x<4. Only answer choice D does not include values of x that are not the solutions of given inequality.

cubic equation can be factored out when:

x^3-X^1-81x+81

coordinate geometry: Multiple triangles

xc3 - collinear/diaganol

X^2 + y^2 = odd

y and x have to be odd / even , or even/odd

y^x<0

y is neg, x is odd

coordinate geo: equation of a line that passes through a point

y-y1=m(x-x1)

use of semicolon

you can combine 2 independent clauses with a ; no conjunction needed. ex: earl walked to school;he later ate his lunch.