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GMAT Math > Math Shortcuts > Flashcards

Math Shortcuts Flashcards

1
Q

two digit number divided by 99

A

becomes a decimal with that two digit number repeating. For instance –> 49/100 = 0.494949….

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2
Q

FDP: Scientific Notation

A
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3
Q

FDP: Compensating Decimals

A
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4
Q

FDP: Solution Less Traveled

A
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5
Q

Quadratic Formula

A
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6
Q

The discriminant (b^2 - 4ac) which is under the radical in the quadratic formula can tell you how many solutions.

A

b^2 - 4ac > 0 –> 2 solutions
b^2 - 4ac = 0 –> 1 solutions
b^2 - 4ac = 0 –> 0 solutions

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7
Q

Conjugate of square root expression involving addition or subtraction

A
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8
Q

multiply by a negative number in an inequality

A

flip the sign

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9
Q

On test cases, when I see |x|, I will try

A

absolute value: + and -

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10
Q

On test cases, when I see x^2, I will try

A

exponents: 0, 1, and fractions

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11
Q

On smart numbers, I will avoid…

A

0 and 1 and usually #s that appear in the problem

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12
Q

On smart numbers when choosing 2 variables, I will…

A

pick two differen tnumbers

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13
Q

decimal raised to exponent = how many decimal places?

A

of decimals * exponent

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14
Q

decimals for a root = how many decimal places

A

of decimals / root
=# of decimals * (1/root)

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15
Q

What is the pattern if the denominator is a number equal to a power of 10 - 1 (eg 9, 99, 999, etc)

A

then the numerator is repeating

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16
Q

How to check if a number will terminate?

A

The denominator only has 2 and 5 as prime factors once fraction is in smallest form

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17
Q

Digit Place Value questions

example two digit number -A -> how to represent this

A

A = 10x + y

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18
Q

Find units digit or a remainder after division of 10

A

you can pay attention to only the digits

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19
Q

x^2 - y^2

A

(x+y)(x-y)

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20
Q

x^2 + 2xy + y^2

A

(x+y)(x+y) = (x+ y)^2

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21
Q

x^2 - 2xy - y^2

A

(x-y)(x-y) = (x+ y)^2

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22
Q

inequality statement –> what is the implication?

xy>0

A

x and y are both positive or negative

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23
Q

inequality statement –> what is the implication?

xy < 0

A

one positive, one negative

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24
Q

inequality statement –> what is the implication?

x^2 - x < 0
x^2 < x

A

0 < x < 1

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25
Q

When combining inequalities can yo subtract?

A

NO

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26
Q

direct proportions > what to use?

A

ratios

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27
Q

indirect proportions > what to use?

A

products

28
Q

Reciprocals of Inequalities

A

Only flip the inequality if both are the same sign. If you do not know the sign, then you cannot take reciprocals

29
Q

squaring inequalities

if both sides are known to be negative then

A

then flip the inequality sign. if this is not known you can’t do this

30
Q

squaring inequalities

if both sides are known to be positive then

A

do not flip the sign

31
Q

squaring inequalities

if one is positive and one is negative then

A

likely choose another technique besides squaring

32
Q

squaring inequalities

if sign is unknown then

A

you cannot square

33
Q

Compound interest formula

A
34
Q

Rate -> how to express

A

ALWAYS distance over time
use one unit of time

35
Q

If object moves the same distance twice at different rates, what’s the average weighted towards?

A

weighted towards slower!!

36
Q

For evenly spaced sets what is the relation between the mean and median?

A

they are equal

37
Q

For evenly spaced sets the median equals to

A

(first+ last)/2

38
Q

Products of x consecutive integers is always divisible by what?

A

x!

39
Q

Sums of consecutive integers

A

Odd: the sum is always a multiple of the number of items (sum = average * # of items)

Even: the sum of all the items is NEVER multiple of then number of items. b

40
Q

Counting integers formula

A

last - first +1

41
Q

Is the average of n consecutive integers an integer?

A

Yes if n is odd
No, if n is even

42
Q

Composites

A

three or more factors (not 1 or prime)

43
Q

factor foundation rule

A

if a is a factor of b, and b is a factor of c, then a is a factor of c

44
Q

x and y are both a multiple of r.

Is x + y a multiple of r?

A

Yes!

And so would ax + by

45
Q

What prime number is not odd?

A

2

46
Q

If the sum of two prime numbers is odd, what must be one of the primes?

A

2

47
Q

If the sum of two prime numbers is even, what must not be one of the primes?

A

2

48
Q

Prime

A

only 2 factors > therefore 1 is not prime

49
Q

even * even

A

even

50
Q

even * odd

A

even

51
Q

odd * odd

A

odd

52
Q

even +/- even

A

even

53
Q

odd +/- odd

A

even

54
Q

odd +/- even

A

odd

55
Q

4!

A

24

56
Q

5!

A

120

57
Q

6!

A

720

58
Q

arranging group of n without restrictions

A

n!

59
Q

if you add(or subtract) a multiple of N to a non multiple of N, is the result a multiple of N

A

NO

60
Q

if you add (or subtract) two non multiples of N, is the answer a multiple of N

A

maybe

61
Q

if a number has a prime factorization of
a^xb^yc^z,

what is the total number of factors?

A

(x+1)(y+1)(z+1)

62
Q

perfect square

A

squares of other integers (25,4,9)

63
Q

what does it mean if a number has an odd number of total factors

A

it is a perfect it must be a perfect square, cube, etc

Otherwise it would be a pair!!

64
Q

What does it mean if a number’s prime factorization contains any odds?

A

It is not a perfect square!

65
Q

remainder formula

A

dividend = quotient * divisor + remainder

66
Q
A

GMAT Math (2 decks)

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