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GMAT > Quant > Flashcards

Quant Flashcards

1
Q

1/6

A

0.167

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2
Q

1/7

A

0.143

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3
Q

1/9

A

0.111

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4
Q

How do you determine the number of solutions (quadratic)

A

Look at the value of b^2-4ac:
Positive: 2
0:1
Negative:0

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5
Q

In quadratic equation, what is the sum of 2 solutions

A

-b/a

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6
Q

In quadratic equation, what is the product of the two solutions

A

c/a

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7
Q

Divisibility rule of 2

A

If the units digit is even

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8
Q

Divisibility rule of 3

A

The sum of all the digits is divisible by 3

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9
Q

Divisibility rule of 4

A

If the last 2 digits of a number are divisible by 4

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10
Q

Divisibility rule of 5

A

The last digit is 0 or 5

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11
Q

Divisibility rule of 6

A

If the number in question is an even number whose digits sum to a multiple of 3

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12
Q

Divisibility rule of 8

A

If the number is even, divide the three last digits by 8

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13
Q

Divisibility rule of 9

A

The sum of all the digits is divisible by 9

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14
Q

Divisibility rule of 11

A

If the sum of odd-numbered place digits minus the sum of the even placed-digits is divisible by 11

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15
Q

Divisibility rule of 12

A

If a number is divisible by 3 and 4

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16
Q

How do you determine the number of trailing zeros

A

The number of 5x2 pairs

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17
Q

Find the value of n when 21!/3^n

A

Divide 21/3 = x
Divide 21/3^2 = y
Until we cannot divide 3^n by something, you then do the sum of x,y …

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18
Q

How do you use the shortcut to determine the number of n in x! when it is even

A

You just need to break the non-prime number into prime factors and just use

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19
Q

When determining the units digits for numbers, what is the maximum number of combinations

A

4

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20
Q

Approximate square roots:
2,3,5,6,7,8

A

14.
1.7
2.2
2.4
2.6
2.8

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21
Q

Approximate cube roots
2,3,4,5,6,7,9

A

1.3
1.4
1.6
1.7
1.8
1.9
2.1

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22
Q

Approximate fourth roots
2,3,4,5,6,7,8,9

A

1.2
1.3
1.4
1.5
1.6
1.6
1.7
1.7

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23
Q

Special trick when adding like bases with equal exponents

A

4 * 4^n = 4^(n+1)

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24
Q

The product of any n consecutive integers is always divisible by

A

n!

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25
Q

The product of consecutive even integers is divisible by

A

2^n *n!

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26
Q

How do you know the value of p*q

A

Multiply the LCD and GCF

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27
Q

In a problem of constant growh, make sure to look at whether it is increasing by a constant amount or constant growth factor.

A

If it is a constant amount: x + #y
If it is a constant factor: xy^#

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28
Q

What is the difference between simple and compound interest

A

The simple is : principalratetime
The compound is : P(1+r/n)^(nt)

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29
Q

There is also one very important thing about the interest

A

It is always on 100.

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30
Q

Exponential growth problems

A

Initial value * growth^n

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31
Q

Digits problems

A

The value of any 2 digit number will follow the equation:
10a+b = x

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32
Q

What is the reverse number

A

10b+a = ba

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33
Q

What are the attributes of a dry mixture problem

A

Component, units and quantity

34
Q

What are the attributes of a wet mixture

A

Components, concentration and quantityO

35
Q

Object in line

A

If you are the m^th person counted from the begining of the line and the n^th from the end, the number of people in line is m+n-1.

36
Q

What is the rate-distance formula

A

Distance = rate*time
Time = Distance/rate
Rate = Distance/time

37
Q

What are the 2 important things in rate problems regarding time

A

Use the travel time, not time of day
The units must be compatible

38
Q

What is the formula if rate-distance questions ask about average

A

Average rate = total distance/total time

39
Q

What is the distance if the object travels from one point to another and then back.

A

D1=D2 => Total distance = 2D

40
Q

In converging and diverging rate questions, what is unique

A

The total distance traveled is equal to the sum of the individual distances each object travels
D1+D2 = total distance
In addition, if they have traveled the same amount of time they both have t.

41
Q

If two objects leave at different times

A

Their travel times must reflect the difference between their departure time. The object that leaves early is t+x and the 2nd is t.

42
Q

If one object travels faster than the other.

A

The faster is r+x.
Sometimes this is expressed as a percentage.

43
Q

In catch-up rate

A

They both travel the same distance but the one that started later is t+x.

44
Q

What is the shortcut in catch-up problems

A

Time = delta distance/delta rate

45
Q

What is the formula of rate-time-work

A

Work = rate*time
Rate=work/time

46
Q

If you have the question z is what percent of y

A

z = x/100 * y

47
Q

What do you do in overlapping sets

A

Always do a matrix

48
Q

What is different in 3 overlapping sets

A

Use the venn diagram

49
Q

What is important about the venn diagram

A

Remember that if you need to calculate, always start from the center and remove numbers to arrive at the larger brackets

50
Q

When counting inclusive sets, what is the formula

A

Highest-lowest + 1

51
Q

If we count excluding the first and last, what is the formula

A

Last-first-1

52
Q

What is the formula to determine the median placement for odd and even numbers

A

odd: (n+1)/2

53
Q

What is the placement for even numbers

A

Between n/2 and (n+2)/2

54
Q

What is the combination formula

A

n! /
(n-k)!*k!

55
Q

What do you do in handshake questions

A

total number * number of people you can meet /2

56
Q

What is the equivalent property of combinations

A

nCk = nCn-k

57
Q

What is the formula for permutations

A

n! /
(n-k)!

58
Q

What is the permutation formula for indistinguishable items

A

n!/(r1!)*(r2)!

59
Q

Counting 2 dimensional pathways

A

Identify every checkpoints and determine the number of ways to travel between each pair of successive points, and multiply them.

60
Q

When it is a grid (no beg and end checkpoints) what do you do

A

Use the permutation formula for indistinguishable items because you will have many of the same movements (2 down, 3 right).
In addition, if there are 2 sections because each path leads to the following, there is not a choice between the 2, multiply them.

61
Q

Circular arrangements

A

number of ways = (k-1)!

62
Q

For triangle problems of non-collinear problems, what is the formula

A

Combination formula

63
Q

For collinear problems

A

Determine the total number of ways to select 3 points - the number of ways to select 3 collinear points

64
Q

For geometry, what planes go where (I, II, III, IV)

A

Starting from top right, it goes counter-clockwise

65
Q

What is the slope of a line

A

delta y / delta x

66
Q

What is the difference between a zero slope and undefined

A

Zero is horizontal, undefined is vertical. The reason why they are undefined is because of the slope formula cannot divide by 0 (the delta x is zero).

67
Q

What do the different types of reflections look like:
Origin, y=x, y=-x, y=b, x=a

A

The first is over the origin point, the image is in the opposite quadrant.
y=x is the line that passes exactly at the origin through the quadrant I and III. The y=-x the same but is negative and passes through quadrant II and IV.
The image of y=b is (x, 2b-y)
The image of x=a is (2a-x, y)

68
Q

What is the distance between 2 points

A

((delta x)^2 + (delta y)^2)^0.5

69
Q

What is the midpoint formula

A

((x1+x2)/2, (y1+y2)/2))

70
Q

What is the equation for a circle

A

(x-a)^2 + (y-b)^2 = r^2
Where (a,b) is the center of the circle. If the origin is the center, the formula is just:
x^2 + y^2 = r^2

71
Q

What is the difference between the domain and range

A

The domain is the set of all the numbers a function can use as inputs.
The range is the set of numbers that the function can output.

72
Q

How do you solve compound fractions

A

You need to work from the inside out

73
Q

Maximum and minimum values of quadratic functions

A

If a>0: minimum occurs when
x = -b/2a
If a<0, the maximum occurs when x=-b/2a

74
Q

How do you determine whether a graph is the graph of a function

A

The vertical line test states that any vertical line can only intersect the graph at exactly one point.

75
Q

What is the formula of an arithmetic sequence

A

an = a1 + (n-1)*d
Where d is the common difference

76
Q

What is the sum of the terms of an arithmetic sequence

A

Sn = n/2 * (a1+an)

77
Q

What is a geometric sequence

A

The difference between every pair of 2 consecutive terms is the same
an = a1*r^(n-1)

78
Q

How do you find the number of factors

A

find the number of prime factors and do every exponent +1 and then multiply them all

79
Q

When finding the number of permutations of a triangle within non-collinear points, what formula do you use

A

combination:
nC3

80
Q

When finding the number of permutations of a triangle withing collinear points, what formula do you use

A

Find the total number of ways using the combination formula and deduct from it the number of ways it could be collinear (using the combination formula)

GMAT (1 decks)

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