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.