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GMAT > Quant > Flashcards

Quant Flashcards

1
Q

2 equations 2 unknowns

A

Can be solved (sim eqn if needed) to give the variables IF they are different (ie must check it’s not just the same equation simplified)

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2
Q

x^(n-1) > x^(n); eg. x > x^2 (i.e. raising to larger exponent gives smaller number)

A

0< x <1 (x is a fraction) OR x is a negative number and n is an odd number

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3
Q

exponents

A

to which base?

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4
Q

Population problem (growth)

A

Population chart

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5
Q

Comparing inequalities with a variable

A

Draw it out on number line; don’t multiply or divide by variable UNLESS sign is known!

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6
Q

Inequalities

A

DRAW NUBMER LINE! Might need to use modulus to make sense of it

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7
Q

Two separate inequalities

A

Can I line them up or add them up? (add only if direction is same; also NEVER subtract or divide)

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8
Q

Inequalities that can’t be summed or other method

A

Test cases: with a positive and negative integer, and a positive and negative fraction!

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9
Q

Absolute value equation with variable on both sides

A

Set equal to plus/minus AND check final answers work by plugging back in (find that usually only one does)

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10
Q

Expression in absolute value signs

A

Can expression actually be negative? If with an x^2 maybe not!

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11
Q

sqrt(x^2)

A

modulus(x)

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12
Q

Modulus linear eqn

A

DRAW NUBMER LINE! Might need to use modulus to make sense of it

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13
Q

A quadratic in a DS problem

A

Can one of the solutions be eliminated based on some contraint in the problem? Or are the two solutions the same? Or give the same answer

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14
Q

A sequence that is not arithmetic or consecutive

A

Write it out, don’t try and come up with a formula!

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15
Q

what is the units digit

A

Last digit shortcut: only pay attention to units digit (for multiply and plus only)

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16
Q

terminating decimal

A

Put in form of: some integer/some power of 10; if after being fully reduced has any prime factors besides 2 or 5, will not terminate!

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17
Q

Compare fractions; which is bigger?

A

Cross-multiply (don’t bother finding LCD)

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18
Q

Fraction question with fractions in the answers

A

Use smart numbers

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19
Q

x = -y

A

Same absolute value; 0 is halfway between on number line

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20
Q

Is a divisible by b?

A

Prime Factorization! Break a and b down into their primes, a MUST be divisible by the primes of b (USE DIVISIBILITY RULES!). Faster than long division

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21
Q

ab/c

A

Either a or b or both is divisble by c

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22
Q

asking whether a number with a high power is divisible by another (meaning it would take a long time to find the number)

A

Factorise and break into primes

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23
Q

a is a divisor of b; b is divisible by a

A

Prime factorization; b = an (where n is a positive integer); b > a; odd or even?

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24
Q

a is a factor of b

A

Prime factorization; b = an (where n is a positive integer); b > a

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25
Q

b is a a multiple of a

A

Prime factorization; b = an (where n is a positive integer); b > a

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26
Q

Prime number question

A

Is number odd or even? Cannot be even and >2

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27
Q

Remainder; eg. a has a remainder of c when divided by b

A

a - c = bn: aka subtract remainder then will be divisible by b

28
Q

Remainder; eg. a has a remainder of c when divided by b

A

Manipulate expression to put in terms of what you know is divisible by b: since if N is a divisor of x and y, then N is a divisor of x +/- y

29
Q

2n + 1

A

Odd number

30
Q

Divisible by 2

A

Even number

31
Q

Odd number being divided by another number or that is the product of other numbers that are stated as odd or even

A

Turn into multiplication form: odd number can only result from odd x odd; otherwise doesn’t result in integer

32
Q

Problem asking if expression is odd or even in DS

A

Test cases with x = odd and x = even! Then can probably rephrase as x being odd or even will make expression either odd or even

33
Q

Expression > 0 or < 0

A

Positives and negatives question! Make a table and test cases with each combination of + and - for the variables (don’t forget to test for = 0 too!)

34
Q

The factors of a variable instead of a number

A

PARTIAL prime box, only take overlapping factors as others might be redundant

35
Q

7, 5, 3, 2 in a question

A

Prime Factorization!

36
Q

b/a results in a positive integer

A

a is a factor of b

37
Q

A quadratic in a DS problem

A

Can one of the solutions be eliminated based on some contraint in the problem? Or are the two solutions the same? Or give the same answer

38
Q

A sequence that is not arithmetic or consecutive

A

Write it out, don’t try and come up with a formula!

39
Q

what is the units digit

A

Last digit shortcut: only pay attention to units digit (for x and + only)

40
Q

terminating decimal

A

Put in form of: some integer/some power of 10; if after being fully reduced has any prime factors besides 2 or 5 _ will not terminate!

41
Q

Compare fractions - which is bigger?

A

Cross-multiply (don’t bother finding LCD)

42
Q

Fraction question with fractions in the answers

A

Use smart numbers

43
Q

Ratio Q that has real value (ground the ratio to real values)

A

Find the unknown multiplier to find the actual values

44
Q

Two types of things, whose relationship to one another changes and is only given in RELATIVE VALUES

A

RATIOS! Relative values are just ratios in disguise

45
Q

several correct possible answer in a PS problem

A

Is there an integer constraint?

46
Q

Integer or other constraints bc objects or people, esp on DS

A

FIRST thought should be: TEST CASES! Then check if algebra works Esp wth variable in exponent

47
Q

Need to do long division or long multiplication

A

Break down into prime factors and match (two equal numbers MUST have same number of prime factors)

48
Q

points on a coordinate system

A

Draw out the picture - use logic if algebra doesn’t work

49
Q

Find the area of a triangle/polygon that is not straightfoward to find using standard formula, but is circumscribed in another shape

A

Is it easier to find area by subtracting overall shape by smaller shapes surrounding desired area?

50
Q

Triangle with sides 3-4-5 or other known triples

A

Triangle must be a right triangle

51
Q

A small triangle and a big triangle

A

Are they similar? Check for matching angles

52
Q

Special triangle (3-4-5; 45-45-90 etc)

A

LABEL all additional information that can be found from known relationships

53
Q

Square and diagonal

A

Special triangle 45-45-90: can find diagonal with side and vice versa

54
Q

If there is a triangle inscribed in a circle with a right angle

A

Hypotenus must be the diameter of the circle

55
Q

(n-1)n(n+1) OR JUST (n+1)(n+2)(n+3)

A

Consecutive integers! Exactly one term in the set of k integers will be divisible by k

56
Q

x is the sum of 5 consecutive numbers

A

x + x + 1 + x +2 + x + 3 +…; even number = sum is not a multiple of number of terms; odd number = sum is multiple of number of terms

57
Q

A words problem with percents as variables

A

Use smart numbers; easier to grasp with concrete numbers

58
Q

Find the average time for a given distance

A

Put two times in terms of distance and speed; for fxed distance: ratio of speed = inverse of ratio of time

59
Q

List of numbers with two variables, and the median

A

Test cases to see where the variables can be placed to give median

60
Q

mixture problem (eg. 20percent of A and 50percent of B give 80percent of the total (A+B)

A

find ratio of two elements

61
Q

Sum of consecutive integers

A

if n = even: sum is NOT a multiple of n

if n = odd: sum IS a multiple of n

62
Q

product of consecutive integers

A

is divisble by k!

Will constain EXACLTY ONE multiple of k

63
Q

equilateral triangle

A

30-60-90 triangle

height = sqrt(3)/2 * side

64
Q

If N is a divisor of x

and N is a divisor of y

A

N is a divisor of x + y

See how to manipulate equation to be in terms of what you know is divisble by the number:

makes it into an expression, then maybe separated term is also divisible by that number so whole expression is divisible by that number

65
Q

sum of two primes is odd

A

one of primes must be 2

66
Q

sum of two primes, neither of which is 2

A

must be even

GMAT (3 decks)

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