Reference Problem # Type ReasonKaplan Gmat 2005 PS - 4 Percents Word TrickKaplan Gmat 2005 PS - 10 Algebra CarelessKaplan Gmat 2005 PS - 11 Algebra OtherKaplan Gmat 2005 PS - 13 Ratios OtherKaplan Gmat 2005 PS - 14 Algebra Other

Kaplan Gmat 2005 PS - 19 Ratios No ideaKaplan Gmat 2005 PS - 43 Geometry Forget PrincipalKaplan Gmat 2005 DS - 7 Algebra CarelessKaplan Gmat 2005 DS - 12 Geometry Lack of knowledgeKaplan Gmat 2005 DS - 18 Algebra CarelessKaplan Gmat 2005 DS - 19 N.Properties CarelessKaplan Gmat 2005 DS - 20 Geometry OtherKaplan Gmat 2005 DS - 35 Algebra Forget PrincipalKaplan Gmat 2005 DS - 37 Percents CarelessKaplan Gmat 2005 DS - 38 Algebra CarelessKaplan Gmat 2005 DS - 44 Geometry Forget PrincipalKaplan Gmat 2005 DS - 45 N.Properties Lack of knowledgeKaplan Gmat 2005 DS - 46 Algebra Forget PrincipalGmat Kaplan Online P9 Percents Lack of knowledgeGmat Kaplan Online R2 Ratios CarelessGmat Kaplan Online R3 Ratios Lack of knowledgeGmat Kaplan Online R5 Ratios No ideaGmat Kaplan Online R7 Ratios Lack of knowledge

Gmat Kaplan Online R8 Ratios Word TrickGmat Kaplan Online R9 Ratios OtherGmat Kaplan Online R16 Ratios No ideaGmat Kaplan Online R17 Ratios CarelessGmat Kaplan Online R26 Ratios OtherGmat Kaplan Online R27 Ratios Lack of knowledgeGmat Kaplan Online R30 Ratios Forget PrincipalGmat Kaplan Online F1 Factors Forget PrincipalGmat Kaplan Online F6 Factors Lack of knowledgeGmat Kaplan Online F8 Factors CarelessGmat Kaplan Online F11 Factors No ideaGmat Kaplan Online F12 Factors Lack of knowledgeGmat Kaplan Online F15 Factors OtherGmat Kaplan Online F24 Factors CarelessGmat Kaplan Online G26 Geometry Word TrickGmat Kaplan Online G36 Geometry Forget Principal

Gmat Kaplan Online G38 Geometry OtherGmat Kaplan Online G40 Geometry Lack of knowledgeGmat Kaplan Online G41 Geometry Word TrickGmat Kaplan Online G44 Geometry Lack of knowledgeGmat Review P9 Algebra Lack of knowledgeGmat Review P16 Algebra Forget PrincipalGmat Review P37 Algebra Forget PrincipalGmat Review P60 Algebra Lack of knowledgeGmat Review P61 Averages CarelessGmat Review P74 Algebra Forget Principal

Gmat Review P80 Probability Forget PrincipalGmat Review P90 Algebra Lack of knowledgeGmat Review P114 Algebra Forget PrincipalGmat Review P112 Algebra Lack of knowledgeGmat Review P129 Averages OtherGmat Review P126 Algebra CarelessGmat Review P127 Algebra CarelessGmat Review P130 Ratios Forget PrincipalGmat Review P132 Probability OtherGmat Review P133 Algebra OtherGmat Review P137 Averages CarelessGmat Review P139 Geometry CarelessGmat Review P144 Factors Word TrickGmat Review P147 Algebra Careless

Gmat Review P148 Statistics Forget PrincipalGmat Review P149 Algebra Careless

Gmat Review P151 Probability OtherGmat Review P152 Algebra Forget PrincipalGmat Review P160 Factors OtherGmat Review P167 Algebra Forget PrincipalGmat Review P169 Factors OtherGmat Review P175 Geometry Lack of knowledgeGmat Review D1 Percents Word TrickGmat Review D4 Geometry CarelessGmat Review D67 Algebra Lack of knowledgeGmat Review D72 Algebra Forget PrincipalGmat Review D78 Algebra Forget PrincipalGmat Review D79 Algebra CarelessGmat Review D83 Factors OtherGmat Review D85 Algebra CarelessGmat Review D86 N.Properties CarelessGmat Review D87 Geometry Forget Principal

Gmat Review D90 Algebra Forget PrincipalGmat Review D91 Geometry HardGmat Review D92 Algebra CarelessGmat Review D94 Algebra Lack of knowledgeGmat Review D96 Algebra Forget PrincipalGmat Review D99 Averages Word TrickGmat Review D101 Algebra OtherGmat Review D102 Algebra HardGmat Review D113 Algebra Forget PrincipalGmat Review D116 Algebra CarelessGmat Review D117 Geometry Lack of knowledgeGmat Review D115 Algebra Other

Note In Knowledge Base?Yes

Confused b-a with a-b NoGot it right, but technique would help Yesd = r*s plus picking numbers NoUse fractions instead of decimals, quicker Yes

Did not understand question noAll about special triangles and ratios YesFailed to read NoSquare and triangle theory Yes

NoFailed to pick good numbers NoI think they are wrong about (2) NoSquare root algebra! YesFailed to undestand the question NoEquations! 1 eq for each unknown Noa^2 + b^2 = c^2 noAnd careless, integers not specified. YesDivision / Multiplication and inequalities YesTricky group problem NoRead question! Found error in problem noRatios different then actual YesI think Lis sufficient. Book wrong. no

Yes

Just two equations. But tricky noNO

hard Noread mofo! Don't assume. Nogood problem Notricky NoRatios different then actual Yes

Yessee 8 divisible rule YESread mofo. no

NoYes

Hard noYes

Easy , but tricky Nono

identification of similar triangles Yesissue with symbolism used Yesimp. Of angles Yes

YesYesYesNoYesNo

I always forget this trick! Yes

Rate is comparing one thing against another! Be careful as to which is which. r can be quantity over time or time over Quantity

1-chance of NOT occurring = occurring! yesestimate No

NoNoYes

unacceptable Nounacceptable Nosolve for time! yes

yeshard No

YesNoYesYes

Need to visualize numbers laid out. NoRemember to use TABLEs to lay out info No

Yesalways look for factoring! Yes

NoYesNoYes

Easy , but tricky Nono need to solve! noI don't agree no

Nogreater than -1 is 1, not negative 2! Yesim an asshole Nogood problem yesrewrite equations to see answers noread mofo No

No

NoNoNoNoNoNo

good problem Yesgood problem No

NoNo

best yet YesHard Yes

Remember if "integers" is not stated anything goes!

read "represent two positions of same ladder!"

Percents

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.875 = 875/1000. Then reduce.

Multiple by 100%. 1/12 x 100% = 100/12 = 8.33

32% = 32/100 = 8/25

What is the % equiv of 1/8, 1/12, 1/6? 12.5%, 8.33%, 16.66%

How do you calculate % change?

What is the percent formula? ((increase/decrease)/original number)(100%) = %

X% of a number is what?

A percent of a percent is what?

80% is the remainder. So the answer would be .2*.8(x)

How does one convert a decimal to a fraction?

How do you convert a fractions to a percent?

How do you convert a percent into a fraction?

(Original - New)/Original = 600-450/600 = 150/600= 1/4(100%) = 25% change

220% of 100 = 100*2.2 = 22060% of 100 = 100*.6 = 60

How to find numbers divided by complicated decimails?

406/1.16 for example. BACKSOLVE! Take the reasonable answer choices and do reverse!!! If not, multiple by 100 to make easier calculation.

What are the principal interest formulas? Difference between simple and compound interest

Simple interest occurs when interested in not reinvested into the principal. Principal (1 + %)years = simple interestCompound = P(1+%)^years.

Like a fraction of a fraction. 25% of 25% is 1/4 of 1/4 = (1/4)(1/4)= 1/16. And these can be added to find percents of totals~!!! See Data Sufff. Challen Quiz problem 3

20% on x and 20% on remainder of x. What is the remainder?

N. Properties

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What is a prime number?

Is 1 a prime number? No, because is has only 1 factor: Itself.

What are the first 10 prime numbers? 2,3,5,7,11,13,17,19,23,29

|a+b| = |a-b| when b=0

Yes, because = to A^6 = C. Hence, C is an integer

What is Z=Z^3 It can be -1 or 1.

Is Z^3 < 2 1? We can tell because nothing says that z had to be an integer!

a = b-1 and c = b+1

What are the odd/even rules for addition?

odd + odd = even, even + even = even, even + odd = odd. So when they are mixed = odd.

what are the odd/even rules for Multiplication?

Even x Even = Even, Odd x Odd = Odd, Odd x Even = Even. So anything times Even is even. So anything with even is EVEN.

A prime number is a number that only have two factors: Itself and 1.

What quantity can we subtract or add from a positive number that leaves us with the same absolute value?

Is C an integer when A^3 = Square of C?

If a,b,c are consecutive integers. How are a and c related to b?

If the sum of 3 consecutive integers = A. What is the sum of the next 3?

A/3 = middle consecutive integer, so add to that. (a/3 +2) + (a/3 +3) etc….

What is the implication of having a the average of a set of consecutive numbers be odd?

It means that the middle term is thus odd and that there is an odd number of consecutive numbers. Means the sum of those number will be odd to. (worth playing with this to learn more)

N. Properties

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3^0 is what? 1. Anything to power of 0 is 1.

Is 0 positive or negative? Neither!

If X is POSITIVE, is x Prime? X^3 has 4 factors. X^2 - x -6 = 0

2^3 meets criteria. 6 also has 4 factors, but cube root of 6 is not even an integer! For the second one, you can get two answers, but as the stem mentions - X IS POSITIVE - so there can only be one answer which means that x is prime!

How many multiples of 4 are there between 12 and 96 inclusive?

Well, 96/4 = 24. 12 has 3 but since it said inclusive you can't count 12. So 24-2 = 22. There are 22 multiples of 4 between 12 and 96 inclusive.

You have two sets Y and X. Y has 10 and X has 18. 6 integers are in both sets. What is the union? What is the intersection? What number is in either Y or X, but no both?

The union is the amounts in X and Y minus the intersection (which the number in both). So, 10+18-6=22. That is the total number of member in both groups accounting for those members that they share! To find the number that is in either but not both you must subtract the intersection again. 22-6 = 16. Also, think about a Venn Diagram to make it easier.

Algebra

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What does the square root sign mean?

It is greater than 1. 2/3 => 3/2

It is less than -1. -2/3 => -3/2

It is smaller. (1/2)^2 = 1/4

It is larger. (-1/2)^2 = 1/4

What is the equation of line? y = mx + b. When is a formula "undefined" When its denominator = 0What does value of X in terms of y mean? Means x = y

Gp1 +Gp2 + neither -both = total

3^0 = ? 1b=0,

How are 1/3^7 and 1/3^8 Related? 1/3^8 = 1/3^7 (3^1)(13^3) and 7^3 are equivalent to what? 13*7 = 91^3 4^k+1 is = ? (4^k)(4^1)What is the squ. root Of x if x = 9a^2 and a<0?

a = root 2 + root 5, a^2 = ?

simplify (1/x)^n+1 (1/x)^n * (1/x)^1

What are the rules of inequalities?

What are the two types of exponent calculations that are easily confused?

2^3 x 2^7 = 2^10 (they are added)(2^3)^7 = 2^21 (they are multipled)

The square of 16 can be -4 or 4But the common Square sign can only mean the POSITIVE square. This is important in terms of data sufficiency.

What is the quickest way to find out which of two fractions have the larger decimal equivalent?

Cross multiply. Whichever has the bigger number on top wins.

Is the reciprocal of a fraction between 0 and 1 smaller or larger than the original

Is the reciprocal of a fraction between 0 and -1 smaller or larger than the original

Is the square of a fraction larger or smaller than the original fraction?

Is the square of a negative fractions larger or smaller than the original?

How are units found from a product of two numbers?

Multiple they units. 93x95? 3x5=15 so 5 is units.

How to you find the sum of consecutive integers?

Take the average say 10+50 / 2 = 30Take number of terms 50-10+1 = 41Sum = 30*41 = 1230

How do you solve group problems involving both/Neither?

subtracting b from both sides of b = 2b is what?

Doesn't sound intuitively but plug in number and see.: -3a.

(root 2 + root 5)(root 2 + root 5), not individual squares of roots!

Sequence starting with 6 and has sum of 63. How many in sequences?

6+7=1313+8 =21 and so on until 63

0 < p < 1. When comparing 1/p^2 and 1/(p+1)^2 what is quicker? Decimals or Fractions?

Fractions! Instead of something like .4, use something like (1/9). It squares nicely and will make comparisons quicker.

If M and N are both + what is the value of M root n if MN/Root N = 10?

The key here is to remember that you can multiple by 1 or root n / root n then use that to simplify.

If you multiple or divide by a negative number, you must switch the direction of the sign.

Algebra

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cube root -89 is between what two integers? minus 4 n 5xy=-6 and x-y=5. can I get definite x?

What is the ratio of 3/4 / 4*3/4?

N / T = S and remainder V. What does N = to?

0 < x < 1 Is x^4 - x^5 < x^2 - x^3?

x = 4/3Y

X^2>x? if x>-1?

Is r > 0? 1. rt = 12 2. r+t=7

Use substitution, then look at the exponents.

If X is not = to 0, is 1/x > 1? (1) y/x > y (2) x^3 > x^2

Analyze the stem and try to simplify. Remember the rules of inequalities. What can make this true? Only if x is positive can this be true, so x>0. Also, if x is positive then 1>x, so we are really asking is 0<x<1? (1) is dependent on y being positive or negative since it would switch the inequality signs giving two answers - so insufficient. (2) Since we know x <> 0, then we know that x^2 is positive. Simplify we get x>1 so that answer is NO.

no! x will have two answers! So despite two equations no definite - ds problem trick

Don't let this trick you. Just cross out the 3/4 on the top and bottom and you get 1/4!

N = TS + V NOT T(S+V) The remainder is tricky!!

X^4 and Y^4 = 100 what is the greatest possible value for X?

Remember! Nothing is mentioned about integers so keep that in mind. 3^4 is 81 and 4^4 is 256 so X is in between 3 and 4. Does not have to be an integer!

Remember to factor out. X^4(x-1) < x^2(x-1), so x^4<X^2 so true!

X received 1/3 more votes than Y is what mathematically?

Becareful! X>-1 means -1/2,0,1/2,2 BUT NOT -2.

Need to solve because you get a quadratic equation.

x^y < y^x. (1) x=y^2 (2) y>2. How can you compare?

Ratios

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What is a ratio? A ratio is the proportional relationship between two quantities.

What is a rate?

Formula for speed? S = D/T or rate = quantity/time

Can rates be added?

What is the work formula?

A rate is a special kind of ratio that relates one kind of quantity to a completely different kind of quantity.

yes. 200 meters/hr + 100 meters/hr = 300 meters/hr. 1800 sq meter / 300 meters/hr = 6 hr when working together

Can time in rates be added? (work problems)

It takes me 2 hours it take her 3 hours. How long does it take together? (1/2) + (1/3) = 5/6 = 1/T => T = 72 minutes or 6/5 hours

T = ab/a+b (a,b time it takes to complete job). Or the inverse of total time = sum inverse of time of individuals.

Explain the reasoning behind the work formula

if a task takes 3 days to complete, then 1 day of working would be 1/3 of the task. These one day ratios can be added. Then take the reciprocal of that addition to get total days agains. (1/3)+(1/2) => then reciprocal! = axb/(a+b)

In rate problems, when trying to solve for a variable which one get altered?

The equation you are NOT trying to solve for gets changed. Hence t+10 or r - 10 (would be for the equation that is not being asked to solve for.

What should one do when picking number in time distance based problems?

Pick the lowest common multiple of the numbers available if it makes sense.

When looking for "average speed" what formula should one be thinking about?

"Total Distance / Total Time" Remember you can't add the rates!

What is something that always catches me in distance, speed type problems?

I fail to read whether "round trip" or one way!!!!!!! Always!!!!!!!!! Pay attention!!!!!!!!!

Ratios

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x/5 + x/6 = 2 hrs/ , x = distance.

3/4 = x//16, the solve to find x.

How do you determine a combined ratio?

what is the trick with rate problems?

How to solve problem when we have speed and we want to find time and distance is the same

Since distance is the same. S(t) = S(t). Think about this: How much distance is covered in (t) time? Will the one on the left or right "cover" more distance? So 30 (t + 5/6) will cover 30 per hr plus whatever it's advantage is over the other side. Use some degree of logic.

What do you do if have rates irregardles of time?

3 day for 1 and 5 days for 1. Means 5n=3n => 5/3n=n if 42 is total, then 5/3n + n = 42. Solve for n. Then subtract n from 42 to find where they will meet.

When doing a d/s = d/s problem how does one normalize?

if the distances are crazy. Normalize to 0. So if something starts off at 11. then subtract both distances by 11 to get one to 0. Then 0 = d.

what is the alternative way to find "when will they meet problems"?

Add the speeds together, then d/(s1 + s2) = T. Multiple T by either rate to find the distances they will travel when they meet!!!

What do you do if you have rates and time for the entire trip, but are trying to total distance?

If you have a proportion, say 3/4 and wanted to find how of a missing component is necessary when you have for example, x/16, what do you do?

A:b = 7:3 and b:c = 2:5 what is the ratio of A:C? Multiple the common variables in the two ratios so that they are equal. Then you can put a:c properly.

If working with ratios is difference in speeds the same as different in ratios of speeds?

Yes. 50% faster than x is not the same as x + 4 feet. It's a trick. the former an be used the latter not.

Be careful to which Quantity is being compared to which. miles/ hr is not the same as hours per mile. See problem R7 in black book

Factors

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What is a multiple?

What is a prime factorization?

What are factors?

What is the least common multiple?

When those two integers share any factors in common.

How can you find the LCM?

An integer is divisible by 3 if? If all of its digits ADD up to a multiple of 3

A multiple is a product of a specified number and an integer. 3(1) = 3 3(2)=6. 3 and 6 are multiples of 3.

How are multiples and factors tied together?

A number that is evenly divisible by another number is also a multiple of that second number.

It is a number expressed in terms of the product of its prime factors (the factors that are prime numbers).

What is the method 1 of prime factorization?

what is the prime factorization of 210? Start low, then go up!210/2 = 105 (since 105 is not divisible by two, we go to 3)105/3 = (2)(3)(35)35/5 = (7)(5)210 = (2)(3)(5)(7)Factors, or divisors of an integer are the POSITIVE intefegers by whuch it is evenly divisible (leaving no remainder).

How can you find the Greatest Common Factor?

Break down both integers into the PRIME factors and multiple all prime factorizations they have in common. 36 = (2)(2)(3)(3), 48 = (2)(2)(2)(2)(3). Therefore they have (2)(2)(3) in common = 12 greatest common factor.

What is method 2 of prime factorization?

Find any set of factors, then drill down

The LCM is the smallest number is a multiple of each of the numbers.

When is the least common multiple smaller than simple the product of two integers?

1. Determine the prime factorization of each integer2. Write out each prime number the maximum number of times that it appears in any one multiple. 3. Multiple those number together to get the least common multiple. Take 12 and 15. it would be 2x2x3x5. You wouldn't include the 3 in 12 because it only has prime.

Factors

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An integer is divisible by 4 if? If the last two digits are a multiple of 4

An integer is divisible by 6 if? If it is divisible by 2 and 3

An integer is divisible by 9? If its digits ADD up to be a multiple of 9

an integer is divisible by 8?

What are the first 10 prime numbers? 2,3,5,7,11,13,17,19,23,29

How to tell if a number is divisible?

Any combination of prime factors that at least includes 2x3

is 71 a divisor or factor of 71? Yes! So 142 and 71 share one divisor: 71

must also be divisble by 4 - BUT ALL DIVISIBLE BY 8 ARE ALSO DIVISIBLE BY 4, BUT NOT ALL DIVISIBLE BY 4 ARE DIVISIBLE BY 8. TOOL TO LIMIT OPTIONS ONLY.

How do you find the number of factors of an integer?

Find the prime factors, then combine to see if you can rewrite with exponents. Add 1 to each exponent. Then multiply those exponents. This will give you number of factors!

How do you find which factors of an integer are divisible by a certain integer?

say you have 2,2,5,3 as prime factors (and 1) and want to find number of factors divisible by 3. Well you have 2, 5, 2x2, 2x5, 2x2x5, 1 = 6 factors that will not be divisible 3. Then subtract this number from the total number of available factors.

How best to find factors from prime factors? 2x2x2x2x3x5?

Stop from bottom - be systematic!2, 3, 52x2, 2x3, 2x52x2x2, 2x2x3, 2x2x5 etc…

Use one of the test. 51 for example = 5+1 = 6, which is divisible by 3.

If a number has the following 2x2x2x2x3. Which of its divisors(factors) are also multiple of 6?

Factors

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None

If a factor of a number is divisible by x and the number itself is divisible by x what is the implication for the other factor(s) of the number?

The implication is that the other factors is also divisible by x. r/x = integer and r+q/x = integer, then q/x must also be an integer because r/x + q/x must both be integers to make r+q/4 an integer.

Is 14 a factor of M if 14 is a factor of 15M?

Yes. Since the factors of 15 are 5x3, then the factors of 14, 7x2 must be part of M. However, if one had 16M instead, it would not necesarrily be the case because the 2 factor could be present in 16 but no in M thereby not making 14 a factor of M

How do you find the number of factors of a number that are also multiples of one of the factors?

Say 580 and 60? Prime factors of 540 are 2x2x3x3x3x5. Prime factors of 60 are 2x2x3x5. Divide 580/60 and get 9. 9 has three factors 1,3,9. So there are three multiples of 60 that are also factors of 580: 60(1), 60(3), and 60(9)

If a number is said to be a factor of another number what does that imply?

That implies that the factor is either a prime factor or a combination of the multiplication of a number's prime factors.

What does it take in terms of prime factors for a number to be a perfect square?

There must be 2 of each prime factors: 2x2x3x3x4x4 for example.

4/x +5/x + 6/x is an int and x too. Is 5/x an int?

it doesn't have to be because 15/x can be 1,3,5,15. 5/x would have to be an int for all those factors. Next would be 30/x or 2(15/x)

How many prime numbers are there between 6! + 2 and 6! + 6 inclusive?

Prob.

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What is the combination formula?

What does ! Mean? ! Is factorial. Factorial of 5 = 5x4x3x2x1Multiply the potential combinations from each group.

What are permutations?

What is a probability?

What is independent probability?

How is dependent probability calculated?

N!/k!(n-k)!, where n=number of items in group as whole; k! = number of items in each subgroup formed.

What do you do if asked to find potential combinations from multiple groups?

How do you find the number of possible subgroups when choosing one item from a set?

The number of possible subgroups will equal the number of items in the set. 5 apps, 20 main courses, 4 desserts. How many different meals? (5)(20)(4) = 400 diff meals.

The arrangements within a group. Permutations differ from combinations in that they are ordered. Typically you subtract out 1 from each descending component. ABC has (3)(2)(1) = 6 possible combinations. In essense, a factorial.

A probability is the numerical representation of the likelihood of an event or combination of events. This is expressed as a ratio of the number of desired outcomes to the total number of possible outcomes.

Independent probability occurs when events do not depend on prior events. The probability that several of these occur is the product of the probability of each event occuring individually.

It's like independent but you multiple the changing probabilities. (5/10)(4/9)

How to calculate probability of an event not occuring?

If at least one win is necessary, and 30% chance of winning any one game and there are 3 games. So 70% of not winning any one game. So .7 x .7 x .7 = .346. So 1-.346 = answer!

What is the difference between a permutation and a combination?

abc, abd, ace are combination since no group has all the same elements. Abc, cba are permutations since that have the same elements just arranged differently. They are different permutations of the same combination. Permutation are the arrangement of sequences. Combinations are the number of DISTRINCT groups that can be pulled out of a larger group.

How should one think about permutations when trying to solve?

if 8 people but only 4 positions. Say how many in first position? 8. If that position is filled, then in next position only 7 people would be available to fill it. So 8x7x6x5 would be answer.

how does one think about multiple group permutations?

Can the multiple groups be combined differently? If so, you need to do each permutation for each combination, then add them together.

How does one deal with indistinguishable elements in permutations?

like having a,a,b,c. Divide 4!/2! With the bottom being the number of indistinctual elements. If a,a,b,b,b,c,d, then 6!/2!x3!

How does one calculate the probability that either one thing will occur?

If the probably of one is 1/2 and the other 2/3, then ADD the probabilities together to find one or another.

Prob.

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How does one calculate the probability that both things will occur?

Multiple their individual probability, regardless if independent or not.

How does one calculate the probability of multiple scenarios?

Find the probability of each scenario, then add them together. However, within each scenario there could issues where you need to multiple AND probability type stuff. IMPORTANT. For 1-opposite probability, better to find probability of one scenario, then add them all together (especially if each scenario has different number of slots! SEE grape flavor question in permutation quiz!).

When should one use the subtraction method of probability?

If you are in an a multiple scenario situation where there are fewer way for an event not to occur.

Geometry

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The larger the angle, the larger the opposing side.

Make triangles in it, then count the number of triagles.

What are pythagorean triples?

What are the sides of the isosceles right triangle?

What are the side of the 30, 60, 90 triangle? 30 = x, 60 = x(square of 3), 90 = 2xWhat is a parallelogram?

What is the circumference of a circle? C = d(pie)What is the area of a circle? A = r^2(pie)How do you calculate the arc length? arc length = n/360 (circumference). n = central angle

Area = n/360(area of circle)

circles and datasufficieny?

Use the right triangle method. Pythagorean theorem.

It means that it is also a right triangle.

what is the rule of triangles related to its sides?

what is the mid point formula? average of the sum of x 1 and x 2.

What is the relationship between the angle of the triangle and the opposing side?

How can you find the internal angles of a polygon?

They are a set of integer ratios that always satisfy the pythagorean theorem. 3,4,5 or 5,12,13 or 6,8,10 (MEMORIZE)

45 degree sides = X, the 90 degree side = x (square root 2)

Has two pairs of parallel sides. Opposite sides are equal in length.

How do you calculate the area of a sector of a circle?

How can knowing the chord help you find the other sides?

A chord is the hypotenuse of an isosceles triangle. If the central angle is 45 degrees, then it is an isosceles right triangle.

If you are given any measurement (area, circumference, chord, arc) you can determine all other measurements.

How can you find the length of a line segment on a coordinate plane?

What is unique about an inscribed triangle which has one leg that is the diameter?

What is true about a right angle inscribed in a circle? And not true?

The two chords are the leg of the right triangle with a hypotenuse that is a diameter. It doesn't mean it is a special triangle unless both chords are the same length!

Take an inscribed quadrilateral. If one side is equal to the radius, is it a square?

NO! If one side equals r, then the hypotenuse is 2r or diameter. If the other chord is also equal to r (which would be required since are testing whether it is a square), then the two chords would be equal to the hypotenuse which is impossible because two side of a triangle must be larger than the third -- not equal to or smaller. Hence, it is impossible for this to be a square.

Take an inscribed quadrilateral. The degree measure of a minor arc is 45 degrees, is it a square?

No. To be a square arc of each side must be 90 degrees.

a side must be greater than the difference or smaller than the sum of the two other sides

What is the relationship between the exterior angle of a triangle and the remote interior angles of the abutting triangle?

the exterior angle is = to the sum of the remote interior angles. See gmat review ds 117.

Geometry

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See problem g38. Excellent example.

What is the area formula for a trapezoid? Average of parallel sides / heightWhat is the area formula for a parallelogram? Base * height

How do you find the volume of a sphere? 4/3PiR^3□BAE=□BCD ?

It could be any positive integer. See PS 175.

Triangles formed within rectangles. The transversal that cuts across a rectangle can be used to create smaller triangles that are similar because they share same angles but different sized legs. IF TWO ANGLES of triangle are the same, then if means the third is as well and it means that they are SIMILAR!!!

What is the difference between a trapezoid and a parallelogram?

The trapezoid only have 1 set of parallel sides unlike the parallelogram which has two.

How do you find the diagonal of a rectangular solid?

You have to use the pythagorean formula twice or look out for special triangles.

This means that the triangular portion of two sides of a trapezoid are the same.

If you have two sides of a triangle 8 and 12 what do you know?

That the 3rd sides can vary between 20 and 4. That the greatest area will occur when 12 and 8 are perpendicular to one another. There can be no area greater than that. See G44

Inscribed square that whose area has a ratio of 25 to 39. What could be the width in inches for the strip between the inscribed square and the larger area?

Geometry

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Averages

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How can use combine averages?

Averages and data suffiency?

What is the median?

What is mode? The term that appears most frequently in a set.

What is the balanced value concept and how can it be used to find the missing average?

The net sum of the difference between each value and it's average must be 0. 3-5, 7-5, 4-5, x - 5: -2 + 2 + -1 + (x-5) = 0: therefore x = 6

Use the weighted average formula. What is the average score? 100 average of 4 games, 200 average of 8 games= (100*4) + (200*8)/12 = 400+1600/12 = 2000/12 = 166.66

know the formula! Sum of terms/number of terms = average!

Is the middle number if the groups of terms is odd. If even, then the average between the two middle numbers.

What is the implication of having a the average of a set of consecutive numbers be odd?

It means that the middle term is thus odd and that there is an odd number of consecutive numbers. Means the sum of those number will be odd to. (worth playing with this to learn more)

Dec Sales are 4 times that average for the rest of the 11 months. Dec sales are what fraction of the entire years sales?

x for each of the first months, 4x for december. Total of 15x. So 4x/15x is answer.

Rememer how to do long division? 20100/26. This seems hard. Answer choices all start with 7

Since all the answer choices start with 7 you know you can use that. Then narrow it down until you can differentiate the choices. See P137.

ToMemorization

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What are pythagorean triples?

What are the first 10 prime numbers? 2,3,5,7,11,13,17,19,23,29What is the % equiv of 1/8, 1/12, 1/6? 12.5%, 8.33%, 16.66%

They are a set of integer ratios that always satisfy the pythagorean theorem. 3,4,5 or 5,12,13 or 6,8,10 (MEMORIZE)

References Types Reason DataKaplan Gmat 2005 Algebra Careless YesGmat 800 Averages Forget Principal NoGmat Review Factors Lack of knowledge Need ToGmat Quantitative Geometry No ideaGmat Coursebook N.Properties OtherGmat Kaplan Online Percents Word Trick

Probability GuessedRatios HardStatistics