GMAT Overview

Analysis of an Issue topc = 30 mins

Analysis of an Argument topic = 30 mins

5 mins break

Quantitavie Section = Data Sufficiency + Problems = 37qs & 75 mins

5 mins break

Verbal Section = Reading Comp + Sentence Correction + CR = 41qs & 75 mins

Kaplan DS practice test, Oct 30

8 correct

16 incorrect

2 mins per question; 25% of questions are experimental

spend the most time on the first 15 questions

Bin 3 Princeton Quant, Nov 10

17 correct

9 incorrect

Verbal Section

Critical Reasoning = 12 qs

Reading Comp = 14 qs

Sentence Correction = 15 qs

Quantitative Section

Problem Solving = 22 qs

Data Sufficiency = 15 qs

Arithmetic 50%, Algebra 25%, Geometry 15%, Logic, Graphs

Practice Tests

Kaplan CR practice test, Oct 30

13 correct

7 incorrect

Kaplan SC practice test, Oct 30

17 correct

11 incorrect

Kaplan RC practice test, Oct 30

12 correct

1 incorrect

Kaplan PS practice test, Oct 30

21 correct

4 incorrect

Bin 3 Princeton Verbal, Nov 10

18 correct

8 incorrect

Bin 4 Princeton Quant, Nov 10

17 correct

9 incorrect

Cambridge Arco, Nov 5

Total = 660 to 700

GMATPrep 1, Nov 18

Quantitative = 44 (9 incorrect)

Verbal = 37 (12 incorrect)

Total = 660

Kaplan 1, Nov 19

Quantitative = 36

Verbal = 38

Total = 620

Princeton Online, Nov 23

Quantitative = 42 (11 incorrect)

Verbal = 33 (10 incorrect)

Total = 610

PowerPrep 1, Nov 24

Quantitative = 47 (86%)

Verbal = 41 (93%)

Total = 710 (95%)

Princeton 1, Nov 25

Quantitative = 40 (10 incorrect)

Verbal = 45 (10 incorrect)

Total = 690

Kaplan 2, Nov 26

Quantitative = 37 (12 incorrect)

Verbal = 30 (12 incorrect)

Total = 560

Princeton 2, Dec 2

Quantitative = 46 (7 incorrect)

Verbal = 37 (11 incorrect)

Total = 670

OG 11 RC Review = 24 questions (141 total)

2; 4; 6; 11; 16; 18i; 25; 33; 47; 51; 61; 76; 78; 86; 102; 110; 113; 114; 119; 127; 130; 132; 133; 140

OG 11 CR Review = 17 questions (124 total)

3; 6; 15; 16; 22i; 43; 51; 53; 57i; 77i; 82; 85; 89; 98; 99; 116i; 123

OG 11 SC Review = 26 questions (138 total)

3i; 4i; 14; 27i; 31; 37; 59i; 60; 62i; 69; 73i; 75; 80i; 81i; 88; 92; 97; 105; 112i; 116; 117; 121; 127; 132; 133; 136

OG11 DS Eval, Dec 19

Excellent (22 correct, 2 incorrect)

OG11 RC Eval, Dec 19

Excellent (16 correct, 1 incorrect)

OG11 CR Eval, Dec 19

Above Avg (11 correct, 6 incorrect)

OG11 SC Eval, Dec 19

Excellent (16 correct, 2 incorrect)

Kaplan Paper, Dec 3

Quantitative = 42 (6 incorrect) 88%

Verbal = 39 (9 incorrect) 89%

Total = 660 (90%)

GMATPrep 2, Dec 23

Quantitative = 48 (12 incorrect, 1 incomplete)

Verbal = 37 (14 incorrect)

Total = 690

Kaplan 3, Dec 9

Quantitative = 35 (11 incorrect)

Verbal = 34 (13 incorrect)

Total = 570 (67%)

GMATPrep 1 again, Dec 24

Quantitative = 47 (15 incorrect)

Verbal = 40 (11 incorrect)

Total = 710

Kaplan 4, Dec 10

Quantitative = 38 (8 incorrect)

Verbal = 31 (14 incorrect)

Total = 570 (67%)

PowerPrep 2, Dec 26

Quantitative = 49 (93%) 4 incorr

Verbal = 44 (97%) 3 incorrect

Total = 750 (99%)

Princeton 3, Dec 16

Quantitative = 45 (8 incorrect)

Verbal = 35 (10 incorrect)

Total = 650

Princeton 4, Dec 17

Index out of range :-)

KEY QUESTIONS

OG 11 PS Review = 39 questions (249 total)

5; 9i; 22; 53; 63; 68; 85i; 88; 95; 99; 105; 113i; 116i; 126; 127; 129; 137; 175; 176; 180i; 181i; 191; 195i; 204i; 207; 208; 209i; 216; 217; 218; 220i; 225; 228i; 234; 239; 240; 241; 248

OG 11 DS Review = 29 questions (155 total)

4; 9; 56; 65i; 69i; 80; 82i; 83i; 101; 102i; 104i; 110i; 114; 119i; 120; 124; 125; 131i; 132; 137; 138; 139; 140; 141; 145; 146; 147; 150; 154

OG11 PS Eval, Dec 18

Excellent (20 correct, 4 incorrect)

Critical Reasoning Approach

Passage is divided into: Conclusion + Premises + Assumptions

Assumptions usually aren't stated, the Conclu. And Premises are

Structure = prem+prem+prem+conclu or conclu+prem+prem+prem

8 CR question types

1) Assumption Qs - hit the conclusion

2) Strengthen the Argument Qs - hit the conclusion

The best strengthen answers provide new information

3) Weaken the Argument Qs - hit the conclusion

4) Inference Qs - hit the premise

very basic, very narrow and have little to do with conclusion

5) Parallel the Reasoning Qs

A then B, if not A then not B, if always A then always B

6) Resolve-Explain Qs

7) Evaluate the Argument Qs

8) Identify the Reasoning Qs

2) and 3) ask to find the unstated premise and support or

weaken the conclusion

3 types of Assumption Questions

1) Causal Assumption - is there another reason

2) Analogy Assumption - are these situations comparable

3) Statistical Assump - are the stats representative

Assumptions aren't stated, if an answer is stated it's not correct

If negating an assumption doesn't kill the argument, it's not assumption

Ad hominem - to the man flaws of argument

7 basic principles of Critical Reasoning

1. Understand the structure of the argument

conclusion + evidence (support for conclusion)

because, for, since precede evidence

therefore, hence, thus precede conclusion

2. Preview the Q before reading the stimulus

3. Paraphrase the author's point

4. Judge the argument's persuasiveness, be an active reader

5. Answer the Q being asked - be very specific

6. Try to prephase the answer

7. Focus on the scope of the argument

watch out for all, always, never, none - they are rarely accurate

zero in on usually, probably, sometimes - they are often accurate

CR Question Types

1. Assumption Qs - a piece of support is required for the conclusion

to remain valid. Deny or negate the statement and see if the argument

falls apart. Use the Denial Test

2. Strengthen/Weaken Qs - reveal the author's assumption to be

unreasonable. The most common on the GMAT. Weaken doesn't

mean disprove

3. Inference Qs - the conclusion doesn't depend on the inference

but on the assumption. Something that must be true if the

conclusion is true. This is an extension of the argument, not a

part of it. The Denial Test works here also.

Sentence Correction Approach

Never read choice A

Scan all answers for differences

Eliminate an answer as soon as you see 1 error in it

Don't worry about punctuation

Don't read the directions

Make sure verbs agree

a modifier should be as close as possible to the word

it modifies

the - present. Using only when action is continuing

Only animate objects are "able" to do anything

20% of the SC choices are fine the way they are

1) Pronoun errors

2) Misplaced modifiers - should immediately follow

3) Parallel Construction

4) Parallel Comparision

5) Tense

6) Subject verb agreement

7) Idioms

8) Quant. Words

SC Examples

Neither this nor that IS

Majority + audience = is

This ... in addition to = is

This … as well as that HAS

hopefully = NEVER USE

Sweden is but one of a number

of nations that ARE accepting

Unlike Tom and his program…

Mark didn't = NO; Unlike Tom

whose program… Mark didn't

= YES

Of the people who did this, the

best known IS (not one) Mary

Still harvest as they HAVE DONE

(not did)

The reason … was because = WILL

NEVER BE CORRECT

I provide you with a fuller picture

than DOES she

Very unique = BIG NO NO

Try to fix - it could be said

they, as a rule, are = NO NO

they are, as a rule, .. = yes

Mary and I told him

he told Mary and ME

whether this … or whether that

just as he can… so he can

strong grounds for opposing of the…

generate growth in industries like = no

generate growth in industries such as = YES

who might once have died in childhood

in spite of his arm crippled, he… = no

his arm being crippled, he = YES

this is a hazard for the Romans, as it is

SC Idioms

Regard AS

Consider a threat

Prefer TO

Just as… SO …

Discourage FROM

Convict AGAINST

Closer THAN

As close AS

Don't know how to do this…OR how to do that

No man but would give…

As though I WERE = when describing mood

Not only…but also..

no so much … as

defined as

regard as

modeled after

based on

as a result of

agree with

choose from

depend on

instead of

see…as

distinguish between..and..

to result in

a debate over

a dispute over

responsibility to

responsible for

different from

consequence of

so…as to be…

appear to

conclude that

due to

worry about

target as

distinguish from

so (adject) that

depicted as

as great as

better than

attributed to

credited WITH

according to

because of

contribute to

in order to

think of…as

prohibit from

so large…as to…

preference FOR

geared towards

not only ON but also ON

advances met WITH

so much THAT… AS THAT…

SC Examples - part 2

diabetes, together with X, RANKS…

The number of citizens declaring blah JUMPED = OK

The # of citizens who declared blah HAS JUMPED = NOT OK

With no predators and expanses of green = NOT OK

With no predators and WITH expanses of green = OK

In addition to her work, Mary contributed through her discovery and through her

documentation = OK

In addition to her work, Mary's contributions include her discoveries and

documentation = NOT OK

The population numbered about 20, 10 times the estimated population of 1 = OK

The population numbered about 20, 10 x that of their population of 1 = NO

To have 5 times the mass of = OK

To be 5 times Jupiter's mass = NOT OK

The symptoms that girls experience are more lively than are those that boys

experience = OK

The symptoms that girls experience are more lively than symptoms of boys

=NOT OK

That no less than a breakthrough is necessary = NO!

That a breakthrough is necessary = YES

Surpassed only by = YES

Only surpasses by = NO

Requires that pay be the same for jobs historically held by women as for jobs

requiring comparable skill that are usually held by men = OK

Requires to pay as much for jobs historically held by women as for a job(!!!)

demanding comparable skills usually held by men (!!!) = NO!

Claim to be able, from 1 page, to assess = OK

Claim the ability, from 1 page, of assessing = NO!

it has and will continue to do = NO

it has continued to do = YES

it leaves some unmoved, while overcoming..

In danger of contracting = YES

in danger to contract = NO!

that are now = YES

now that are = NO!

Reading Comp Approach

Identify the topic and scope = topic is large, scope is niche

Identify the author's purpose and structure

Identify the author's voice

Get the gist of each paragraph

Look for the main idea = HUGE

4 types of questions

Global; Inference; Logic; Explicit Detail

Don't memorize details

Structure questions = hypothesis stated & analyzed; proposal

evaluated & alternatives explored; viewpoint set forth and defended

Logic questions = answers discussing content or detail are wrong

Best Method

Attack opening paragraph

Create mental roadmap

Stop to sum up

Attack the questions

3 Passage Types

Social Passage

Science Passage

Business Passage

The answer that is vague and indisputable is usually the correct one

Respect for professionals

Pro US

Moderate emotion answers are usually accurate

Negative tones to diversity are usually inaccurate

GMAT passages rarely resolve anything - be careful

Essay Words to use

For example

Furthermore

Moreover

Surely

Truly

Most important

Certainly

Consequently

I like red gum VS While the majority

of people lean to blue gum,

I firmly believe that red gum

is better

Essays Approach

Human grader grades 30 essays per hour, 2 mins per essay

Use first, therefore, because, for example

5 mins develop; 20 mins compose; 5 mins proofread

limit the use of there is, there are, in my opinion

always outline essay prior to beginning

always provide insightful examples and support, don't just say because…

write as much as you can and @ least 4 paragraphs

digest the issue

select the points you will make

organize and lead in with the better argument

finish strongly

Analysis of an Issue

The issue of …is a controversial one. On the one hand…on the other hand… However,

in the final analysis it is clear that…

One reason for my belief is that…

A chief reson for my view is…

A main reason that…is the something

…is far better from a …standpoint as well

while there are arguments to be made for both sides, it is clear that there are

greater advantages to the…

something, something allows for….(what they ask you)

For all three reasons I therefore believe that…

Analysis of an Argument

Read and identify the conclusion, assumptions and brainstorm

List as many unstated assumptions as possible

Illustrate how to use these assumptions to make the argument more compelling

First paragraph sums the argument's conclusion

2,3,4 paragraphs attack the argument and the supporting evidence

Last paragraph sums what you have said and states how the argument could be

strengthened

The writer concludes that the present problem of poorly trained … will become less

severe in the future because…

The writer concludes that…The argument that …would be strengthened considerably

if the author provided the evidence that…

The argument that… is not entirely convincing because it ignores certain crucial assumptions.

There are 3 serious flaws in the argument…

First, the argument assumes that… upon the premise of …

Second, the argument never addresses…

Finally, the argument omits…

Thus, the argument is not completely sound. The evidence in support of the conclusion…

Ultimately, the argument might be strengthened by…

among the most pivotal shortcomings of the argument is its inability to address …

the argument in its current state contains a considerable number of defects, the most

blatant of which have been discussed above. Had the argument managed to address the

aforementioned concerns its legitimacy would have been greatly enhanced. However as it

Problems Solving Approach

PICK PICK PICK PICK PICK

Always re-read the problem for 2 seconds twice carefully!

Decipher q stems quickly

Think of alternative methods before powering thru algebra

0 is an integer

xy - xz is less than yz - zx if xz > yz therefore x > y

Prime numbers = 2, 3, 5, 7, 11, 13, 17, 19, ..61,67

2 is the only even prime number

First term means the first number of series

Always use a two by two grid

What is the P that 3 out of 4 tosses will be heads

Total outcomes = 2 * 2 * 2 * 2 = 16

Favorable outcomes are 5

P is 5/16 is the answer

Pick numbers when you have to, with common denominators

try all answers when picking numbers

The ratio of employees to non-employees is 20:11; if

we add 7 non-employees, the ratio changes to 3:2

how many people in the group. Answer below:

20x/(11x+7) = 3/2

(a + b) 2 = a2 + 2ab + b2

xa * xb = x(a+b)

(a - b)2 = a2 - 2ab + b2

a2 - b2 = (a + b)(a - b)

xc/xd = x(c-d)

(xa)b = xab

If x/4 + 24/x = 5, what are the possible values of 3x-7

use with variables

use with odd and even questions

If (x + y)/y has a remainder of 4 and x,y are integers

04 = 012 = 01 = 0

Std Dev = Sq Root of (Mean of Squares - Square of Mean)

Backsolve - always start with the middle answer

Guess if you have to - often best for hard Roman numerals

If you divide inequality by a negative number you must

then x/y has a remainder of 4

Perpendicular bisector

reverse the inequality sign

Fractions are identical to percentages

if (a - b)2 = 0, then a = b

If a triangle has a larger perimeter it doesn't mean

For DS Word problems, think - don’t crunch

Whatever the number of different variables to solve for

this many numbers of different equations needed

Rounding off is a powerful tool - USE IT OFTEN

Joe's favorite DS answers on hard Qs are C) & E); BEWARE

Data Sufficiency Approach

a) 1 is sufficient, but 2 is not

b) 2 is sufficient, but 1 is not

c) 1+2 together are sufficient, and neither one is suffcnt alone

d) either statement by itself is sufficient

e) 1+2 together are not sufficient, more info needed

DS topics

Ratios 30%, Algebra 25%, Number properties 25%, Geo 15%

The goal is what info you need to answer the Q, not what the A is

60% of the time one statement will be sufficient

3 Steps

focus on question stem

Look at each statement separately

that it has a larger area also

If a2 - 1 is odd, then a2 is even

Distance = Rate * time

Work problem - 1/T = 1/R + 1/G + 1/S

Cubing a number preserves its sign

What is the mean of a & b; 2) a = 520 - b

If 2x is a multiple of y, then y/2x is an integer

45 is what % of 9; 45 = % * 9 => 500%

3/5% = 3/500

If a is even and b is odd, then ab is even

Multiples of:

2 - Last digit is even = 72

3 - sum of all digits is a mult. of 3 = 216

4 - last 2 digits are a mult. of 4 = 3,028

5 - last digit is 0 or 5

6 - number is a multiple of 2 and 3

9 - sum of all digits is a mult. of 9

10 - last digit is 0

of the triangle to the area of the sq. Ans is 4

y = xq + r; q is quotient, r is remainder

/9

x2 + 6 = 5x -> x2 - 5x + 6 = 0 -> (x-2)(x-3) = 0

2n; 2n+2; 2n+4 etc are consecutive even integers

x is either 2 or 3

If 5x - 2y = -9 & 3y - 4x = 6, how much is x+y

5x - 2y = -9 + 3y - 4x = 6 equals x + y = 3

Linear equation - y = mx + b; m is slope

positive slope slopes from left to right

negative slope slopes from right to left

slope of 0 is a flat line; b is the Y intercept

The third side of a triangle is smaller than the

sum of the other two sides and larger

than their difference.

Sum of interior angles in a polygon with n sides

(n-2) * 180 degrees

1 angle = [(n-2) * 180 degrees] / n

Length of an arc = n/360deg * 2πr

Area of a sector = n/360deg * πr2

Surface area of a solid = 2 * ( L*H + L*W + W*H)

Diagonal in a rectangular solid - Use Pyth theorem twice

2n+1; 2n+3; 2n+5 etc are consecutive odd integers

(137 + 147 + 15 7 + 167) / 58 has a remainder of 0

When numbering pages from 1 to 1000, 3 is written

300 times

45 boy-boy handshakes and 105 girl-girl handshakes

mean that there are 150 boy-girl handshakes

First term of geo sequence is 1/2 and common ratio is

1/2, then 1st = 1/2, 2nd = 1/2 * 1/2, 3rd = 1/2 * 1/2 * 1/2

What % of retailers bought PCs

1) 85% of retailers who own their store bought PCs

2) 40% of retailers surveyed own their store

Answer is E - be very careful!!!

Last year the mean salary for 10 employees was $10,000

What is their salary this year

1) 8 of the 10 empl have 15% greater salary

2) 2 of the 10 empl has the same salary

Answer is E - be very careful!!!

Volume of a cylinder = πr2 * H

Any fraction is denominator of 4 is terminal

What is common multiple - break to prime factors

135 = 3 * 3 * 3 * 5

3 & 3 & 5 in common

225 = 3 * 3 * 5 * 5

3 is 1, 5 is 1, 3 * 3 is 9, 3 * 5 is 15, 3 * 3 * 5 is 45

sum 1 + 1 + 9 + 15 + 45 = 61 is the answer

Lowest common multiple of 28 and 42

28 = 2 * 2 * 7 the two numbers share 2 & 7

42 = 2 * 3 * 7

28 * 42 = 1,176; 1,176/2 = 588; 588/7 is 84

84 is the answer

The avg of evenly spaced numbers is the avg of the

smallest and the largest number.

Avg of 13…77 is (13 + 77)/2 = 45 is the answer

The number of integers from a to b inclusive is

b-a+1

The sum of consectuive numbers is the avg times

Volume of a sphere = 4/3 * πr 3

if Z/3 is an odd integer, then Z is an odd integer

The sum of 4 consecutive integers must always be even

Even if all 4 sides are equal, the quadracep may not

be inscribed in a circle

200 households; 80 use neither B, nor A; 60 use A only;

for each households using both brands - 3 use B only;

how many use both brands - answer is 15

Of the 3 digit integers greater than 700, how many have

2 digits that are equal to each other and the remaining

digit different from the other two

9 * 9 - 1 = 80

Distinct numbers cannot be equal

0.4 = 2/5; 0.6 = 3/5 ; 0.667 = 2/3; 0.8 = 4/5

Fraction is Part 3 divided by Whole 7

Ratio is Part 3 divided by Part 4

$100, 20% interest, compunded semiannually

@ 6 mos & 10% interest = $10 so total = $110

$110 @ 6 mos & 10 % interest = $11 interest

$121 is the final balance

The number insider the square root is called radical

9 girls and 9 boys; pick one 4 times and return

What is the P that a G is chosen at least once

1/2 * 1/2 * 1/2 * 1/2 = 1/16 = P that a G isnt picked

1 - 1/16 = 15/16 is the answer

Sq root of 2 is approx 1.4; sq root of 3 is approx. 1.7

Vertical angles are opposite each other and have the same

the number of terms

sum of 10..50; (10+50)/2 = 30, 50-10+1 = 41

30 * 41 = 1,230 is the answer

Mode is the number that appears most often

Median is the middle number

Range is the difference between the largest

and smallest value

Ratio = of/to

|x - 3| < 2 => (x-3) <2 and -(x-3) <2

e = p and e + q = 180 degrees

meet after 150/80mph = 1.875 hours

Train A has 15 mins headstart going @ 60mph, train B

goes @45mph, they are 281 miles apart, when do they

meet?

15 mins headstart @ 60mph = 15 miles -> S = 266 miles

solve as the other problem above

1.5 hens lay 1.5 eggs in 1.5 days

1 hen lays 1 egg is 1.5 days

1 hen lays 2/3 eggs in 1 day

6 hens lay 4 eggs in 1 day

Area of triangle = 1/2 Base * height

In similar triangles, angles are equal and sides

are proportional

if AD = 6, then radius = 2

12 years from now A will be 40% older than Sarah

number of degrees

Variable raised to an odd power will have only 1 solution

If n/4 gives a remainder of 3, the n is 3 greater than a

multiple of 4

Supplementary angles = 180 sum; complementary = 90 sum

How many positive factors of 42 are not factors of 56

42 = 2 * 3 * 7

56 = 2 * 2 * 3 * 7

3 is off

3 is 1, 3 * 2 is 2, 3 * 7 is 3, 3 * 2 * 7 is 4; 4 is the answer

Pythagorean Theorem - a2 + b2 = c2

Special Right Triangles

Area of paralellogram = base * height

Area of trapezoid = (a + b)/2 * height

Circumference of a circle = 2πr

Sell X for 20% gain and receive $30 => 1.2 * X = $30

Sell X for 20% loss and get $30 => 0.8 * X = $30

Together X & Y can do 4/15 & 7/18 of 11/90 of the job per

hour, which means it takes them 90/11 hours to

finish the job

If the sum of 5 consecutive integers is 265 what are they

x + x+1 + x+2 + x+3 + x+4 + x+5 = 265; x = 51 is the answer

If the range of (3, x, y) is 0, then x = y = 3

Area of a circle = πr2

Slope of a line = Rise/Run = Change is Y/Change in X

Simple interest = $12,000 * 6% + 9/12 = $540

If -1 < x < 0, then x 3 > 1/x3

If the smallest of 5 consecutive integers is -2, then

their sum is 0

If x is an integer, then x 2 - x - 1 is always odd

In isocseles and equilateral triangles, if you know one side

you have info about the ratios of all sides

Flip a coin 6 times, what is P that tails will come out @ least

twice but not more than 5 times

1) total outcomes = 2 * 2 * 2 * 2 * 2* 2 = 64

2) unfavor. Outcomes = 0 tails is 1, 1 tail is 6, 6 tails is 1

Compound interest =

5 marbles in a bag, 2 red and 3 blue. Pick 2 marbles,

what is the P that at least one is red, Answer is 7/10

56 outcomes are OK, then 56/64 = 7/8 is the answer

1 thru 20. You draw 1 number without returning, in order to

ensure the sum of all numbers is even, how many numbers

should you draw.

Worst case scenario = 1. Draw odd number and 2. Draw only

even numbers = 10. The 12th number will have to be odd

If lots of ratios and fractions, solve as a cosmic plug in or pick

A triangle inscribed in a semicircle is always a right triangle

4 character password has 1 letter and 3 different digits. The

letter must be the 2nd or 3rd character. How many possible

passwords?

1. DLDD = 10 * 26 * 9 * 8 = 18,720

2. DDLD = 10 * 9 * 26 * 8 = 18,720

therefore 37,440 is the answer

2.2 lbs in 1 kg, to the nearest 18th, how many 18ths of a kilogram

are in 1 lb.

2.2 lbs = 1 kg => 1lb = 1/2.2 kg = 5/11 kg

5/11 = x/18 => 11x = 90 => x = 8 is the answer

Number deleted = Original sum - new sum

What is the combined ratio:

a to b is 7 to 3 and b to c is 2 to 5, what is a to c

2 * a/b = 14/6; 3* b/c = 6/15 => a/c = 14/15

How many liters of solution that is 10% alcohol

need to be added to 2 liters of solution that is

50% alcohol to create a solution that is 15% alc.

x -> 10%; 2L -> 50%; x+2 -> 15%

10% * x + 1 = 15% * (2 + x)

x = 14 is the answer

Group 1 + Group 2 + Neither - Both = Total

2! = 1 * 2; 3! = 1 * 2 * 3; 0! = 1

6! = 5! * 6

Fill all spots where order matters = n! (factoriel)

Subset & order matters = permutation

n!/(n-k)!

Subset & order doesn’t matter = combination

n!/[k!(n-k)!]

27 a-3 = 9 2a+4 => 3 3(a-3) = 3 2(2a+4)

Tom reads @ 30 pages/hr; Jan reads @ 40p/hr. Tom

starts @ 4:30p, Jan starts @ 5:20p. When will they

be reading the same page.

Until 5:20p Tom reads 25 pages

Then 25 + 30t = 40x => t=2.5 hours => J will catch T

at 7:50p

Remember that 0 is a multiple of ANY number

What is the greatest possible common divisor of

2 different positive integers which are less than 144.

71 * 2 and 71 * 3 are both less than 144 => 71 is IT

x2 - 2x - 3 = 0 => (x+1)(x-3) = 0

Are q, r, and S consecutive integers if r-q = s-r

The answer is no, this tells you that they are

evenly spaced, not consecutive

With probabilities qs - visualize the different outcomes

It takes W liters of water for every liter of syrup to

make soda. If we have M liters of syrup and soda sells

in A = B2C, if B is *2 and C * 3 then A must be multiplied by 12

If a boat travels @ 30mph and arrive 3 hrs before the

for j $/liter and syrup costs k $/liter, what is the profit

Look at both statements combined

Sufficient means only ONE value, x2 = 25 is not sufficient

The two statements will never contradict each other

Yes or No questions - needs to a solid YES or a solid NO

NO is as good as YES

Be careful that the two statements aren't identical, if they are

choose D) not A)

If 1 is sufficient, the answer must be A) or D)

If 2 is sufficient, the answer must be B) or D)

If 1 is insufficient, the answer must be B), C), or E)

If 2 is insufficient, the answer must be A), C), or E)

Examples

246 => 6 units (ones), 4 tens, 2 hundreds

Odd * Odd = Odd; Odd + Odd = Even

25 + 25 + 35 + 35 + 35 = 2(25) + 3(35) = 212 5 + 313 5 = 26 + 36

12 - number is a multiple of 4 and 3

x2 - 20x + 96 = 0 => (x-8)(x-12)=0 ; The rest is trivial

Square of an integer is 32, 42, 52, etc.

The perimeter of equilateral triangle is equal to the

perimeter of a square. What is the ratio of the area

Balance = Principal(1+rate/c)time*c

where c is the # of times compounded annually

The avg of 5 numbers is 2, delete 1 number and the

avg is -3, what number was deleted

5*2 = 10; 4*-3 = -12 => 10 - (-12) = 22 is the answer

Number added = New sum - original sum

car, how much longer is the road by water

if AB = AC, the AD = BD = DC

Lot of 70 is cut into three pieces, how many pieces are in

the largest lot; 2) largest lot equals the sum of the

other two lots

Don't be fooled by the beginning of a series, look for N

not for examples

A + 12 = 1.4(S + 12)

sales = j(M+MW); cost = kM

If s/t = 64.12 and s,t are integers, which of the following

could be the remainder when s divided by t

Ans: 0.12t = s-64t, then 0.12t is the remainder

t=375 and 0.12t=45

The product of all primes less than 20 is closest to which:

product is 9,699,690 thus the answer is 10 7

% increase from 24 to 30 = 6/24

% decrease from 30 to 24 = 6/30

P1 or P2 = P1 + P2 - P1and2

Arithmetric progression = a; a+d; a+2d…

n-th member is a+(n-1)d

Geometric progression = a; ar; ar2; ar 3...

n-th member is ar(n-1)

Ratio of women to children is 5 to 2. What is the # of men

1) Ratio of children to men is 5 to 11

2) Number of women is less than 30

solution - if w/c = 5x/2x and c/m = 5x/11x, then w/m = 25x/22x

women are less than 30 and multiple of 25x => w are 25; m=22

ABCD are on the # line. If AB=18 and CD=8, BD=?

1) AC=BC; 2) A is to the left of D

solution-from 1) you know that C is the middle point of AB

therefore AC=BC=9; therefore BD=1 or 17

from 2) you learn nothing new, therefore answer is E

If $10,000 is invested @ x% simple annual ratefor N years, what

represents the total amount of INTEREST ONLY that will be

earned by this investment in N years; answer=10,000N(x/100)

For how many integers n is 2n=n2

Answer is 2 (n=2 and n=4)

If R & S are positive integers, is R/S an integer

1) every factor of S is a factor of R

2) every prime factor of S is a prime factor of R

Answer is A)

For which of the following functions is f(a+b)=f(a)+f(b) for all

positive #s a and b; answer is f(x) = -3x

Does the line with equation y=3x+2 contain the point (r,s)?

1) (3r+2-s)(4r+9-s)=0; 2) (4r-6-s)(3r+2-s)=0

From 1) s =0, r=2 or -9/4. In 2) we eliminate r=-9/4 =>C is answer

Select 2 chairs and 2 tables from a collection that are all different

from each other. If there are 5 chairs and if 150 combinations

are possible, how many tables are there

solution - 5!/(2!3!) * x!/(2!(x-2)!) = 150. You plug and => 6

TRICK QUESTION = rates for typing are $5/page for the first time a

page is typed, and $3/page every time a page is revised. If 100

pages of which 40 revised once, 10 TWICE and the rest no

revisions, what is the cost. Answer = $680

6 countries sent a total of 75 reps to a congress. No 2 countries sent

the same # of reps. Country A sent the second greatest # of

reps. Did country A sent at least 10 reps

1) 1 country sent 41 reps; 2) A sent fewer than 12 reps

Answer is E and you know why

If x & y are positive integers, is the product xy even

1) 5x-4y is even; 2) 6x-7y is even

You have to prove that x and y can't be both odd, plugging in

both equations proves so easily => answer is D

On the # line, the distance b/n X and Y is greater than that b/n

X and Z. Does Z lie b/n X and Y on the # line

1) XYZ < 0; 2) XY < 0; Answer is E and you know why

If X - Y > 10, is X - Y > X + Y

1) x = 8; 2) y = -20; Answer is D = TRICK Question

If X and Y are positive which of the following must be greater than

Answer is II only and you know why

Out of 800 employees, 70% have tenure of 10+ years, if Y of them

were to retire and no other employee changes to occur, what

value of Y would produce a % of 10+ yr employee = 60%

Answer - very tricky, you know why

Is (x-y)/(x+y)>1 ; 1) x >0; 2) y<0

Answer is e) - very tricky, you know why

Remember that ANY number line can have different units of

measurement. IT IS NOT ALWAYS in 1s

Juan bought paperback books that cost $8 each and hardcover books

that cost $25 each. If Juan bought more than 10 p. books, how

many hc books did he buy

1) total hc books cost was at least $150

2) total books cost was less than $260; Answer is C - TRICKY

Tanya prepped 4 letters and 4 envelopes. If the letters are to be

put in the envelopes @ random what is the P that only 1 letter

will be put in the correct envelope.

solution - P for L1 in E1 = 1/4; then P for L2 in E3 or E4 = 2/3

then P for L3 in E4 = 1/2. When multiplied the combined P for

1 letter = 1/12. For 4 letters, the TOTAL P is 1/3

A circular rim 28 inches in diameter rotates the same # of

inches/second as another rim 35 inches in diameter.

If the smaller rim makes X revolutions per second,

how many revolutions per minute does the larger

rim make in terms of X.

Ps=28pi, Pl=35pi. If the same rotations per s., the

larger rim rotates 28/35*X times per s. => 48X per min.

In how many arrangements can a teacher seat 3 girls and 3

boys in a row of 6 seats if the boys must have the 1st,

3rd, and 5th seats.

3*2*1 = 6 ways could be arranged; 6 ways girls could

arranged => 36 ways combined

Or B1 in 3 seats, B2 in 2 seats = 6 ways a boy can sit

3 boys can sit in 18 ways, and 3 girls can sit in 18 ways

=> 36 ways combined

A clock marks each hour by striking a # of times equal to

the hour, and the time required for a stroke is exactly

the same as the time between strokes. At 6:00 the

time between the beginning of the 1st stroke and the

end of the last stroke is 22 secs. What is that time at

12:00. Solution - 6 strikes+5 intervals = 22 secs

=> 2 secs per strike. At 12:00, there are 23 strikes+intervals => 46 seconds total duration

If OP < PQ, is the area of OPQ greater than 48. TRICKY

1) Coord. Of P are (6;8); 2) Coord. Of Q are (13; 0)

Answer is A) - very tricky

What is the value of X * Y? 1) y=x+1; 2) y=x 2+1

x is either 0 or 1, E is the answer

Sam sold 2 properties for $30,000 each. Sam sold one of

the properties for 20% gain and the other one for 20%

loss. What was his total $ gain or loss.

Positive prop => (X-30,000)/X=20% => $25,000 cost

Negative prop => (30,000-X)/X=20% =>$37.500 cost

Amy's grade was the 90th percentile of the 80 grades in

her class. Of the 100 grades from another class, 19

were higher than Amy's. Amy's grade was what

percentile of the grades of the two classes

solution - 153 to 180 is like x to 100 => x=85%

Analysis of an Issue topc = 30 mins

Analysis of an Argument topic = 30 mins

5 mins break

Quantitavie Section = Data Sufficiency + Problems = 37qs & 75 mins

5 mins break

Verbal Section = Reading Comp + Sentence Correction + CR = 41qs & 75 mins

Kaplan DS practice test, Oct 30

8 correct

16 incorrect

2 mins per question; 25% of questions are experimental

spend the most time on the first 15 questions

Bin 3 Princeton Quant, Nov 10

17 correct

9 incorrect

Verbal Section

Critical Reasoning = 12 qs

Reading Comp = 14 qs

Sentence Correction = 15 qs

Quantitative Section

Problem Solving = 22 qs

Data Sufficiency = 15 qs

Arithmetic 50%, Algebra 25%, Geometry 15%, Logic, Graphs

Practice Tests

Kaplan CR practice test, Oct 30

13 correct

7 incorrect

Kaplan SC practice test, Oct 30

17 correct

11 incorrect

Kaplan RC practice test, Oct 30

12 correct

1 incorrect

Kaplan PS practice test, Oct 30

21 correct

4 incorrect

Bin 3 Princeton Verbal, Nov 10

18 correct

8 incorrect

Bin 4 Princeton Quant, Nov 10

17 correct

9 incorrect

Cambridge Arco, Nov 5

Total = 660 to 700

GMATPrep 1, Nov 18

Quantitative = 44 (9 incorrect)

Verbal = 37 (12 incorrect)

Total = 660

Kaplan 1, Nov 19

Quantitative = 36

Verbal = 38

Total = 620

Princeton Online, Nov 23

Quantitative = 42 (11 incorrect)

Verbal = 33 (10 incorrect)

Total = 610

PowerPrep 1, Nov 24

Quantitative = 47 (86%)

Verbal = 41 (93%)

Total = 710 (95%)

Princeton 1, Nov 25

Quantitative = 40 (10 incorrect)

Verbal = 45 (10 incorrect)

Total = 690

Kaplan 2, Nov 26

Quantitative = 37 (12 incorrect)

Verbal = 30 (12 incorrect)

Total = 560

Princeton 2, Dec 2

Quantitative = 46 (7 incorrect)

Verbal = 37 (11 incorrect)

Total = 670

OG 11 RC Review = 24 questions (141 total)

2; 4; 6; 11; 16; 18i; 25; 33; 47; 51; 61; 76; 78; 86; 102; 110; 113; 114; 119; 127; 130; 132; 133; 140

OG 11 CR Review = 17 questions (124 total)

3; 6; 15; 16; 22i; 43; 51; 53; 57i; 77i; 82; 85; 89; 98; 99; 116i; 123

OG 11 SC Review = 26 questions (138 total)

3i; 4i; 14; 27i; 31; 37; 59i; 60; 62i; 69; 73i; 75; 80i; 81i; 88; 92; 97; 105; 112i; 116; 117; 121; 127; 132; 133; 136

OG11 DS Eval, Dec 19

Excellent (22 correct, 2 incorrect)

OG11 RC Eval, Dec 19

Excellent (16 correct, 1 incorrect)

OG11 CR Eval, Dec 19

Above Avg (11 correct, 6 incorrect)

OG11 SC Eval, Dec 19

Excellent (16 correct, 2 incorrect)

Kaplan Paper, Dec 3

Quantitative = 42 (6 incorrect) 88%

Verbal = 39 (9 incorrect) 89%

Total = 660 (90%)

GMATPrep 2, Dec 23

Quantitative = 48 (12 incorrect, 1 incomplete)

Verbal = 37 (14 incorrect)

Total = 690

Kaplan 3, Dec 9

Quantitative = 35 (11 incorrect)

Verbal = 34 (13 incorrect)

Total = 570 (67%)

GMATPrep 1 again, Dec 24

Quantitative = 47 (15 incorrect)

Verbal = 40 (11 incorrect)

Total = 710

Kaplan 4, Dec 10

Quantitative = 38 (8 incorrect)

Verbal = 31 (14 incorrect)

Total = 570 (67%)

PowerPrep 2, Dec 26

Quantitative = 49 (93%) 4 incorr

Verbal = 44 (97%) 3 incorrect

Total = 750 (99%)

Princeton 3, Dec 16

Quantitative = 45 (8 incorrect)

Verbal = 35 (10 incorrect)

Total = 650

Princeton 4, Dec 17

Index out of range :-)

KEY QUESTIONS

OG 11 PS Review = 39 questions (249 total)

5; 9i; 22; 53; 63; 68; 85i; 88; 95; 99; 105; 113i; 116i; 126; 127; 129; 137; 175; 176; 180i; 181i; 191; 195i; 204i; 207; 208; 209i; 216; 217; 218; 220i; 225; 228i; 234; 239; 240; 241; 248

OG 11 DS Review = 29 questions (155 total)

4; 9; 56; 65i; 69i; 80; 82i; 83i; 101; 102i; 104i; 110i; 114; 119i; 120; 124; 125; 131i; 132; 137; 138; 139; 140; 141; 145; 146; 147; 150; 154

OG11 PS Eval, Dec 18

Excellent (20 correct, 4 incorrect)

Critical Reasoning Approach

Passage is divided into: Conclusion + Premises + Assumptions

Assumptions usually aren't stated, the Conclu. And Premises are

Structure = prem+prem+prem+conclu or conclu+prem+prem+prem

8 CR question types

1) Assumption Qs - hit the conclusion

2) Strengthen the Argument Qs - hit the conclusion

The best strengthen answers provide new information

3) Weaken the Argument Qs - hit the conclusion

4) Inference Qs - hit the premise

very basic, very narrow and have little to do with conclusion

5) Parallel the Reasoning Qs

A then B, if not A then not B, if always A then always B

6) Resolve-Explain Qs

7) Evaluate the Argument Qs

8) Identify the Reasoning Qs

2) and 3) ask to find the unstated premise and support or

weaken the conclusion

3 types of Assumption Questions

1) Causal Assumption - is there another reason

2) Analogy Assumption - are these situations comparable

3) Statistical Assump - are the stats representative

Assumptions aren't stated, if an answer is stated it's not correct

If negating an assumption doesn't kill the argument, it's not assumption

Ad hominem - to the man flaws of argument

7 basic principles of Critical Reasoning

1. Understand the structure of the argument

conclusion + evidence (support for conclusion)

because, for, since precede evidence

therefore, hence, thus precede conclusion

2. Preview the Q before reading the stimulus

3. Paraphrase the author's point

4. Judge the argument's persuasiveness, be an active reader

5. Answer the Q being asked - be very specific

6. Try to prephase the answer

7. Focus on the scope of the argument

watch out for all, always, never, none - they are rarely accurate

zero in on usually, probably, sometimes - they are often accurate

CR Question Types

1. Assumption Qs - a piece of support is required for the conclusion

to remain valid. Deny or negate the statement and see if the argument

falls apart. Use the Denial Test

2. Strengthen/Weaken Qs - reveal the author's assumption to be

unreasonable. The most common on the GMAT. Weaken doesn't

mean disprove

3. Inference Qs - the conclusion doesn't depend on the inference

but on the assumption. Something that must be true if the

conclusion is true. This is an extension of the argument, not a

part of it. The Denial Test works here also.

Sentence Correction Approach

Never read choice A

Scan all answers for differences

Eliminate an answer as soon as you see 1 error in it

Don't worry about punctuation

Don't read the directions

Make sure verbs agree

a modifier should be as close as possible to the word

it modifies

the - present. Using only when action is continuing

Only animate objects are "able" to do anything

20% of the SC choices are fine the way they are

1) Pronoun errors

2) Misplaced modifiers - should immediately follow

3) Parallel Construction

4) Parallel Comparision

5) Tense

6) Subject verb agreement

7) Idioms

8) Quant. Words

SC Examples

Neither this nor that IS

Majority + audience = is

This ... in addition to = is

This … as well as that HAS

hopefully = NEVER USE

Sweden is but one of a number

of nations that ARE accepting

Unlike Tom and his program…

Mark didn't = NO; Unlike Tom

whose program… Mark didn't

= YES

Of the people who did this, the

best known IS (not one) Mary

Still harvest as they HAVE DONE

(not did)

The reason … was because = WILL

NEVER BE CORRECT

I provide you with a fuller picture

than DOES she

Very unique = BIG NO NO

Try to fix - it could be said

they, as a rule, are = NO NO

they are, as a rule, .. = yes

Mary and I told him

he told Mary and ME

whether this … or whether that

just as he can… so he can

strong grounds for opposing of the…

generate growth in industries like = no

generate growth in industries such as = YES

who might once have died in childhood

in spite of his arm crippled, he… = no

his arm being crippled, he = YES

this is a hazard for the Romans, as it is

SC Idioms

Regard AS

Consider a threat

Prefer TO

Just as… SO …

Discourage FROM

Convict AGAINST

Closer THAN

As close AS

Don't know how to do this…OR how to do that

No man but would give…

As though I WERE = when describing mood

Not only…but also..

no so much … as

defined as

regard as

modeled after

based on

as a result of

agree with

choose from

depend on

instead of

see…as

distinguish between..and..

to result in

a debate over

a dispute over

responsibility to

responsible for

different from

consequence of

so…as to be…

appear to

conclude that

due to

worry about

target as

distinguish from

so (adject) that

depicted as

as great as

better than

attributed to

credited WITH

according to

because of

contribute to

in order to

think of…as

prohibit from

so large…as to…

preference FOR

geared towards

not only ON but also ON

advances met WITH

so much THAT… AS THAT…

SC Examples - part 2

diabetes, together with X, RANKS…

The number of citizens declaring blah JUMPED = OK

The # of citizens who declared blah HAS JUMPED = NOT OK

With no predators and expanses of green = NOT OK

With no predators and WITH expanses of green = OK

In addition to her work, Mary contributed through her discovery and through her

documentation = OK

In addition to her work, Mary's contributions include her discoveries and

documentation = NOT OK

The population numbered about 20, 10 times the estimated population of 1 = OK

The population numbered about 20, 10 x that of their population of 1 = NO

To have 5 times the mass of = OK

To be 5 times Jupiter's mass = NOT OK

The symptoms that girls experience are more lively than are those that boys

experience = OK

The symptoms that girls experience are more lively than symptoms of boys

=NOT OK

That no less than a breakthrough is necessary = NO!

That a breakthrough is necessary = YES

Surpassed only by = YES

Only surpasses by = NO

Requires that pay be the same for jobs historically held by women as for jobs

requiring comparable skill that are usually held by men = OK

Requires to pay as much for jobs historically held by women as for a job(!!!)

demanding comparable skills usually held by men (!!!) = NO!

Claim to be able, from 1 page, to assess = OK

Claim the ability, from 1 page, of assessing = NO!

it has and will continue to do = NO

it has continued to do = YES

it leaves some unmoved, while overcoming..

In danger of contracting = YES

in danger to contract = NO!

that are now = YES

now that are = NO!

Reading Comp Approach

Identify the topic and scope = topic is large, scope is niche

Identify the author's purpose and structure

Identify the author's voice

Get the gist of each paragraph

Look for the main idea = HUGE

4 types of questions

Global; Inference; Logic; Explicit Detail

Don't memorize details

Structure questions = hypothesis stated & analyzed; proposal

evaluated & alternatives explored; viewpoint set forth and defended

Logic questions = answers discussing content or detail are wrong

Best Method

Attack opening paragraph

Create mental roadmap

Stop to sum up

Attack the questions

3 Passage Types

Social Passage

Science Passage

Business Passage

The answer that is vague and indisputable is usually the correct one

Respect for professionals

Pro US

Moderate emotion answers are usually accurate

Negative tones to diversity are usually inaccurate

GMAT passages rarely resolve anything - be careful

Essay Words to use

For example

Furthermore

Moreover

Surely

Truly

Most important

Certainly

Consequently

I like red gum VS While the majority

of people lean to blue gum,

I firmly believe that red gum

is better

Essays Approach

Human grader grades 30 essays per hour, 2 mins per essay

Use first, therefore, because, for example

5 mins develop; 20 mins compose; 5 mins proofread

limit the use of there is, there are, in my opinion

always outline essay prior to beginning

always provide insightful examples and support, don't just say because…

write as much as you can and @ least 4 paragraphs

digest the issue

select the points you will make

organize and lead in with the better argument

finish strongly

Analysis of an Issue

The issue of …is a controversial one. On the one hand…on the other hand… However,

in the final analysis it is clear that…

One reason for my belief is that…

A chief reson for my view is…

A main reason that…is the something

…is far better from a …standpoint as well

while there are arguments to be made for both sides, it is clear that there are

greater advantages to the…

something, something allows for….(what they ask you)

For all three reasons I therefore believe that…

Analysis of an Argument

Read and identify the conclusion, assumptions and brainstorm

List as many unstated assumptions as possible

Illustrate how to use these assumptions to make the argument more compelling

First paragraph sums the argument's conclusion

2,3,4 paragraphs attack the argument and the supporting evidence

Last paragraph sums what you have said and states how the argument could be

strengthened

The writer concludes that the present problem of poorly trained … will become less

severe in the future because…

The writer concludes that…The argument that …would be strengthened considerably

if the author provided the evidence that…

The argument that… is not entirely convincing because it ignores certain crucial assumptions.

There are 3 serious flaws in the argument…

First, the argument assumes that… upon the premise of …

Second, the argument never addresses…

Finally, the argument omits…

Thus, the argument is not completely sound. The evidence in support of the conclusion…

Ultimately, the argument might be strengthened by…

among the most pivotal shortcomings of the argument is its inability to address …

the argument in its current state contains a considerable number of defects, the most

blatant of which have been discussed above. Had the argument managed to address the

aforementioned concerns its legitimacy would have been greatly enhanced. However as it

Problems Solving Approach

PICK PICK PICK PICK PICK

Always re-read the problem for 2 seconds twice carefully!

Decipher q stems quickly

Think of alternative methods before powering thru algebra

0 is an integer

xy - xz is less than yz - zx if xz > yz therefore x > y

Prime numbers = 2, 3, 5, 7, 11, 13, 17, 19, ..61,67

2 is the only even prime number

First term means the first number of series

Always use a two by two grid

What is the P that 3 out of 4 tosses will be heads

Total outcomes = 2 * 2 * 2 * 2 = 16

Favorable outcomes are 5

P is 5/16 is the answer

Pick numbers when you have to, with common denominators

try all answers when picking numbers

The ratio of employees to non-employees is 20:11; if

we add 7 non-employees, the ratio changes to 3:2

how many people in the group. Answer below:

20x/(11x+7) = 3/2

(a + b) 2 = a2 + 2ab + b2

xa * xb = x(a+b)

(a - b)2 = a2 - 2ab + b2

a2 - b2 = (a + b)(a - b)

xc/xd = x(c-d)

(xa)b = xab

If x/4 + 24/x = 5, what are the possible values of 3x-7

use with variables

use with odd and even questions

If (x + y)/y has a remainder of 4 and x,y are integers

04 = 012 = 01 = 0

Std Dev = Sq Root of (Mean of Squares - Square of Mean)

Backsolve - always start with the middle answer

Guess if you have to - often best for hard Roman numerals

If you divide inequality by a negative number you must

then x/y has a remainder of 4

Perpendicular bisector

reverse the inequality sign

Fractions are identical to percentages

if (a - b)2 = 0, then a = b

If a triangle has a larger perimeter it doesn't mean

For DS Word problems, think - don’t crunch

Whatever the number of different variables to solve for

this many numbers of different equations needed

Rounding off is a powerful tool - USE IT OFTEN

Joe's favorite DS answers on hard Qs are C) & E); BEWARE

Data Sufficiency Approach

a) 1 is sufficient, but 2 is not

b) 2 is sufficient, but 1 is not

c) 1+2 together are sufficient, and neither one is suffcnt alone

d) either statement by itself is sufficient

e) 1+2 together are not sufficient, more info needed

DS topics

Ratios 30%, Algebra 25%, Number properties 25%, Geo 15%

The goal is what info you need to answer the Q, not what the A is

60% of the time one statement will be sufficient

3 Steps

focus on question stem

Look at each statement separately

that it has a larger area also

If a2 - 1 is odd, then a2 is even

Distance = Rate * time

Work problem - 1/T = 1/R + 1/G + 1/S

Cubing a number preserves its sign

What is the mean of a & b; 2) a = 520 - b

If 2x is a multiple of y, then y/2x is an integer

45 is what % of 9; 45 = % * 9 => 500%

3/5% = 3/500

If a is even and b is odd, then ab is even

Multiples of:

2 - Last digit is even = 72

3 - sum of all digits is a mult. of 3 = 216

4 - last 2 digits are a mult. of 4 = 3,028

5 - last digit is 0 or 5

6 - number is a multiple of 2 and 3

9 - sum of all digits is a mult. of 9

10 - last digit is 0

of the triangle to the area of the sq. Ans is 4

y = xq + r; q is quotient, r is remainder

/9

x2 + 6 = 5x -> x2 - 5x + 6 = 0 -> (x-2)(x-3) = 0

2n; 2n+2; 2n+4 etc are consecutive even integers

x is either 2 or 3

If 5x - 2y = -9 & 3y - 4x = 6, how much is x+y

5x - 2y = -9 + 3y - 4x = 6 equals x + y = 3

Linear equation - y = mx + b; m is slope

positive slope slopes from left to right

negative slope slopes from right to left

slope of 0 is a flat line; b is the Y intercept

The third side of a triangle is smaller than the

sum of the other two sides and larger

than their difference.

Sum of interior angles in a polygon with n sides

(n-2) * 180 degrees

1 angle = [(n-2) * 180 degrees] / n

Length of an arc = n/360deg * 2πr

Area of a sector = n/360deg * πr2

Surface area of a solid = 2 * ( L*H + L*W + W*H)

Diagonal in a rectangular solid - Use Pyth theorem twice

2n+1; 2n+3; 2n+5 etc are consecutive odd integers

(137 + 147 + 15 7 + 167) / 58 has a remainder of 0

When numbering pages from 1 to 1000, 3 is written

300 times

45 boy-boy handshakes and 105 girl-girl handshakes

mean that there are 150 boy-girl handshakes

First term of geo sequence is 1/2 and common ratio is

1/2, then 1st = 1/2, 2nd = 1/2 * 1/2, 3rd = 1/2 * 1/2 * 1/2

What % of retailers bought PCs

1) 85% of retailers who own their store bought PCs

2) 40% of retailers surveyed own their store

Answer is E - be very careful!!!

Last year the mean salary for 10 employees was $10,000

What is their salary this year

1) 8 of the 10 empl have 15% greater salary

2) 2 of the 10 empl has the same salary

Answer is E - be very careful!!!

Volume of a cylinder = πr2 * H

Any fraction is denominator of 4 is terminal

What is common multiple - break to prime factors

135 = 3 * 3 * 3 * 5

3 & 3 & 5 in common

225 = 3 * 3 * 5 * 5

3 is 1, 5 is 1, 3 * 3 is 9, 3 * 5 is 15, 3 * 3 * 5 is 45

sum 1 + 1 + 9 + 15 + 45 = 61 is the answer

Lowest common multiple of 28 and 42

28 = 2 * 2 * 7 the two numbers share 2 & 7

42 = 2 * 3 * 7

28 * 42 = 1,176; 1,176/2 = 588; 588/7 is 84

84 is the answer

The avg of evenly spaced numbers is the avg of the

smallest and the largest number.

Avg of 13…77 is (13 + 77)/2 = 45 is the answer

The number of integers from a to b inclusive is

b-a+1

The sum of consectuive numbers is the avg times

Volume of a sphere = 4/3 * πr 3

if Z/3 is an odd integer, then Z is an odd integer

The sum of 4 consecutive integers must always be even

Even if all 4 sides are equal, the quadracep may not

be inscribed in a circle

200 households; 80 use neither B, nor A; 60 use A only;

for each households using both brands - 3 use B only;

how many use both brands - answer is 15

Of the 3 digit integers greater than 700, how many have

2 digits that are equal to each other and the remaining

digit different from the other two

9 * 9 - 1 = 80

Distinct numbers cannot be equal

0.4 = 2/5; 0.6 = 3/5 ; 0.667 = 2/3; 0.8 = 4/5

Fraction is Part 3 divided by Whole 7

Ratio is Part 3 divided by Part 4

$100, 20% interest, compunded semiannually

@ 6 mos & 10% interest = $10 so total = $110

$110 @ 6 mos & 10 % interest = $11 interest

$121 is the final balance

The number insider the square root is called radical

9 girls and 9 boys; pick one 4 times and return

What is the P that a G is chosen at least once

1/2 * 1/2 * 1/2 * 1/2 = 1/16 = P that a G isnt picked

1 - 1/16 = 15/16 is the answer

Sq root of 2 is approx 1.4; sq root of 3 is approx. 1.7

Vertical angles are opposite each other and have the same

the number of terms

sum of 10..50; (10+50)/2 = 30, 50-10+1 = 41

30 * 41 = 1,230 is the answer

Mode is the number that appears most often

Median is the middle number

Range is the difference between the largest

and smallest value

Ratio = of/to

|x - 3| < 2 => (x-3) <2 and -(x-3) <2

e = p and e + q = 180 degrees

meet after 150/80mph = 1.875 hours

Train A has 15 mins headstart going @ 60mph, train B

goes @45mph, they are 281 miles apart, when do they

meet?

15 mins headstart @ 60mph = 15 miles -> S = 266 miles

solve as the other problem above

1.5 hens lay 1.5 eggs in 1.5 days

1 hen lays 1 egg is 1.5 days

1 hen lays 2/3 eggs in 1 day

6 hens lay 4 eggs in 1 day

Area of triangle = 1/2 Base * height

In similar triangles, angles are equal and sides

are proportional

if AD = 6, then radius = 2

12 years from now A will be 40% older than Sarah

number of degrees

Variable raised to an odd power will have only 1 solution

If n/4 gives a remainder of 3, the n is 3 greater than a

multiple of 4

Supplementary angles = 180 sum; complementary = 90 sum

How many positive factors of 42 are not factors of 56

42 = 2 * 3 * 7

56 = 2 * 2 * 3 * 7

3 is off

3 is 1, 3 * 2 is 2, 3 * 7 is 3, 3 * 2 * 7 is 4; 4 is the answer

Pythagorean Theorem - a2 + b2 = c2

Special Right Triangles

Area of paralellogram = base * height

Area of trapezoid = (a + b)/2 * height

Circumference of a circle = 2πr

Sell X for 20% gain and receive $30 => 1.2 * X = $30

Sell X for 20% loss and get $30 => 0.8 * X = $30

Together X & Y can do 4/15 & 7/18 of 11/90 of the job per

hour, which means it takes them 90/11 hours to

finish the job

If the sum of 5 consecutive integers is 265 what are they

x + x+1 + x+2 + x+3 + x+4 + x+5 = 265; x = 51 is the answer

If the range of (3, x, y) is 0, then x = y = 3

Area of a circle = πr2

Slope of a line = Rise/Run = Change is Y/Change in X

Simple interest = $12,000 * 6% + 9/12 = $540

If -1 < x < 0, then x 3 > 1/x3

If the smallest of 5 consecutive integers is -2, then

their sum is 0

If x is an integer, then x 2 - x - 1 is always odd

In isocseles and equilateral triangles, if you know one side

you have info about the ratios of all sides

Flip a coin 6 times, what is P that tails will come out @ least

twice but not more than 5 times

1) total outcomes = 2 * 2 * 2 * 2 * 2* 2 = 64

2) unfavor. Outcomes = 0 tails is 1, 1 tail is 6, 6 tails is 1

Compound interest =

5 marbles in a bag, 2 red and 3 blue. Pick 2 marbles,

what is the P that at least one is red, Answer is 7/10

56 outcomes are OK, then 56/64 = 7/8 is the answer

1 thru 20. You draw 1 number without returning, in order to

ensure the sum of all numbers is even, how many numbers

should you draw.

Worst case scenario = 1. Draw odd number and 2. Draw only

even numbers = 10. The 12th number will have to be odd

If lots of ratios and fractions, solve as a cosmic plug in or pick

A triangle inscribed in a semicircle is always a right triangle

4 character password has 1 letter and 3 different digits. The

letter must be the 2nd or 3rd character. How many possible

passwords?

1. DLDD = 10 * 26 * 9 * 8 = 18,720

2. DDLD = 10 * 9 * 26 * 8 = 18,720

therefore 37,440 is the answer

2.2 lbs in 1 kg, to the nearest 18th, how many 18ths of a kilogram

are in 1 lb.

2.2 lbs = 1 kg => 1lb = 1/2.2 kg = 5/11 kg

5/11 = x/18 => 11x = 90 => x = 8 is the answer

Number deleted = Original sum - new sum

What is the combined ratio:

a to b is 7 to 3 and b to c is 2 to 5, what is a to c

2 * a/b = 14/6; 3* b/c = 6/15 => a/c = 14/15

How many liters of solution that is 10% alcohol

need to be added to 2 liters of solution that is

50% alcohol to create a solution that is 15% alc.

x -> 10%; 2L -> 50%; x+2 -> 15%

10% * x + 1 = 15% * (2 + x)

x = 14 is the answer

Group 1 + Group 2 + Neither - Both = Total

2! = 1 * 2; 3! = 1 * 2 * 3; 0! = 1

6! = 5! * 6

Fill all spots where order matters = n! (factoriel)

Subset & order matters = permutation

n!/(n-k)!

Subset & order doesn’t matter = combination

n!/[k!(n-k)!]

27 a-3 = 9 2a+4 => 3 3(a-3) = 3 2(2a+4)

Tom reads @ 30 pages/hr; Jan reads @ 40p/hr. Tom

starts @ 4:30p, Jan starts @ 5:20p. When will they

be reading the same page.

Until 5:20p Tom reads 25 pages

Then 25 + 30t = 40x => t=2.5 hours => J will catch T

at 7:50p

Remember that 0 is a multiple of ANY number

What is the greatest possible common divisor of

2 different positive integers which are less than 144.

71 * 2 and 71 * 3 are both less than 144 => 71 is IT

x2 - 2x - 3 = 0 => (x+1)(x-3) = 0

Are q, r, and S consecutive integers if r-q = s-r

The answer is no, this tells you that they are

evenly spaced, not consecutive

With probabilities qs - visualize the different outcomes

It takes W liters of water for every liter of syrup to

make soda. If we have M liters of syrup and soda sells

in A = B2C, if B is *2 and C * 3 then A must be multiplied by 12

If a boat travels @ 30mph and arrive 3 hrs before the

for j $/liter and syrup costs k $/liter, what is the profit

Look at both statements combined

Sufficient means only ONE value, x2 = 25 is not sufficient

The two statements will never contradict each other

Yes or No questions - needs to a solid YES or a solid NO

NO is as good as YES

Be careful that the two statements aren't identical, if they are

choose D) not A)

If 1 is sufficient, the answer must be A) or D)

If 2 is sufficient, the answer must be B) or D)

If 1 is insufficient, the answer must be B), C), or E)

If 2 is insufficient, the answer must be A), C), or E)

Examples

246 => 6 units (ones), 4 tens, 2 hundreds

Odd * Odd = Odd; Odd + Odd = Even

25 + 25 + 35 + 35 + 35 = 2(25) + 3(35) = 212 5 + 313 5 = 26 + 36

12 - number is a multiple of 4 and 3

x2 - 20x + 96 = 0 => (x-8)(x-12)=0 ; The rest is trivial

Square of an integer is 32, 42, 52, etc.

The perimeter of equilateral triangle is equal to the

perimeter of a square. What is the ratio of the area

Balance = Principal(1+rate/c)time*c

where c is the # of times compounded annually

The avg of 5 numbers is 2, delete 1 number and the

avg is -3, what number was deleted

5*2 = 10; 4*-3 = -12 => 10 - (-12) = 22 is the answer

Number added = New sum - original sum

car, how much longer is the road by water

if AB = AC, the AD = BD = DC

Lot of 70 is cut into three pieces, how many pieces are in

the largest lot; 2) largest lot equals the sum of the

other two lots

Don't be fooled by the beginning of a series, look for N

not for examples

A + 12 = 1.4(S + 12)

sales = j(M+MW); cost = kM

If s/t = 64.12 and s,t are integers, which of the following

could be the remainder when s divided by t

Ans: 0.12t = s-64t, then 0.12t is the remainder

t=375 and 0.12t=45

The product of all primes less than 20 is closest to which:

product is 9,699,690 thus the answer is 10 7

% increase from 24 to 30 = 6/24

% decrease from 30 to 24 = 6/30

P1 or P2 = P1 + P2 - P1and2

Arithmetric progression = a; a+d; a+2d…

n-th member is a+(n-1)d

Geometric progression = a; ar; ar2; ar 3...

n-th member is ar(n-1)

Ratio of women to children is 5 to 2. What is the # of men

1) Ratio of children to men is 5 to 11

2) Number of women is less than 30

solution - if w/c = 5x/2x and c/m = 5x/11x, then w/m = 25x/22x

women are less than 30 and multiple of 25x => w are 25; m=22

ABCD are on the # line. If AB=18 and CD=8, BD=?

1) AC=BC; 2) A is to the left of D

solution-from 1) you know that C is the middle point of AB

therefore AC=BC=9; therefore BD=1 or 17

from 2) you learn nothing new, therefore answer is E

If $10,000 is invested @ x% simple annual ratefor N years, what

represents the total amount of INTEREST ONLY that will be

earned by this investment in N years; answer=10,000N(x/100)

For how many integers n is 2n=n2

Answer is 2 (n=2 and n=4)

If R & S are positive integers, is R/S an integer

1) every factor of S is a factor of R

2) every prime factor of S is a prime factor of R

Answer is A)

For which of the following functions is f(a+b)=f(a)+f(b) for all

positive #s a and b; answer is f(x) = -3x

Does the line with equation y=3x+2 contain the point (r,s)?

1) (3r+2-s)(4r+9-s)=0; 2) (4r-6-s)(3r+2-s)=0

From 1) s =0, r=2 or -9/4. In 2) we eliminate r=-9/4 =>C is answer

Select 2 chairs and 2 tables from a collection that are all different

from each other. If there are 5 chairs and if 150 combinations

are possible, how many tables are there

solution - 5!/(2!3!) * x!/(2!(x-2)!) = 150. You plug and => 6

TRICK QUESTION = rates for typing are $5/page for the first time a

page is typed, and $3/page every time a page is revised. If 100

pages of which 40 revised once, 10 TWICE and the rest no

revisions, what is the cost. Answer = $680

6 countries sent a total of 75 reps to a congress. No 2 countries sent

the same # of reps. Country A sent the second greatest # of

reps. Did country A sent at least 10 reps

1) 1 country sent 41 reps; 2) A sent fewer than 12 reps

Answer is E and you know why

If x & y are positive integers, is the product xy even

1) 5x-4y is even; 2) 6x-7y is even

You have to prove that x and y can't be both odd, plugging in

both equations proves so easily => answer is D

On the # line, the distance b/n X and Y is greater than that b/n

X and Z. Does Z lie b/n X and Y on the # line

1) XYZ < 0; 2) XY < 0; Answer is E and you know why

If X - Y > 10, is X - Y > X + Y

1) x = 8; 2) y = -20; Answer is D = TRICK Question

If X and Y are positive which of the following must be greater than

Answer is II only and you know why

Out of 800 employees, 70% have tenure of 10+ years, if Y of them

were to retire and no other employee changes to occur, what

value of Y would produce a % of 10+ yr employee = 60%

Answer - very tricky, you know why

Is (x-y)/(x+y)>1 ; 1) x >0; 2) y<0

Answer is e) - very tricky, you know why

Remember that ANY number line can have different units of

measurement. IT IS NOT ALWAYS in 1s

Juan bought paperback books that cost $8 each and hardcover books

that cost $25 each. If Juan bought more than 10 p. books, how

many hc books did he buy

1) total hc books cost was at least $150

2) total books cost was less than $260; Answer is C - TRICKY

Tanya prepped 4 letters and 4 envelopes. If the letters are to be

put in the envelopes @ random what is the P that only 1 letter

will be put in the correct envelope.

solution - P for L1 in E1 = 1/4; then P for L2 in E3 or E4 = 2/3

then P for L3 in E4 = 1/2. When multiplied the combined P for

1 letter = 1/12. For 4 letters, the TOTAL P is 1/3

A circular rim 28 inches in diameter rotates the same # of

inches/second as another rim 35 inches in diameter.

If the smaller rim makes X revolutions per second,

how many revolutions per minute does the larger

rim make in terms of X.

Ps=28pi, Pl=35pi. If the same rotations per s., the

larger rim rotates 28/35*X times per s. => 48X per min.

In how many arrangements can a teacher seat 3 girls and 3

boys in a row of 6 seats if the boys must have the 1st,

3rd, and 5th seats.

3*2*1 = 6 ways could be arranged; 6 ways girls could

arranged => 36 ways combined

Or B1 in 3 seats, B2 in 2 seats = 6 ways a boy can sit

3 boys can sit in 18 ways, and 3 girls can sit in 18 ways

=> 36 ways combined

A clock marks each hour by striking a # of times equal to

the hour, and the time required for a stroke is exactly

the same as the time between strokes. At 6:00 the

time between the beginning of the 1st stroke and the

end of the last stroke is 22 secs. What is that time at

12:00. Solution - 6 strikes+5 intervals = 22 secs

=> 2 secs per strike. At 12:00, there are 23 strikes+intervals => 46 seconds total duration

If OP < PQ, is the area of OPQ greater than 48. TRICKY

1) Coord. Of P are (6;8); 2) Coord. Of Q are (13; 0)

Answer is A) - very tricky

What is the value of X * Y? 1) y=x+1; 2) y=x 2+1

x is either 0 or 1, E is the answer

Sam sold 2 properties for $30,000 each. Sam sold one of

the properties for 20% gain and the other one for 20%

loss. What was his total $ gain or loss.

Positive prop => (X-30,000)/X=20% => $25,000 cost

Negative prop => (30,000-X)/X=20% =>$37.500 cost

Amy's grade was the 90th percentile of the 80 grades in

her class. Of the 100 grades from another class, 19

were higher than Amy's. Amy's grade was what

percentile of the grades of the two classes

solution - 153 to 180 is like x to 100 => x=85%