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GMAT > Quant > Flashcards

Quant Flashcards

1
Q

(a-b+1)/((ab-b)-(1+a)(1-a))

A

(a-b+1)/((b(a-1)+(1+a)(1-a))
(a-b+1)/((-b(1-a)+(1+a)(1-a))
(a-b+1)/((1-a)(-b+1+a)
1/(1-a)

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2
Q

Given a/b and c/d
a/b+c/d=?
a/b-c/d=?

A

ad+cb/(db)

ad-cb/(bd)

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3
Q

Zero product property

A

If 2 things multiply to 0, at least one of them must be 0

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4
Q

Standard Deviation

A

measures “how far” a set of values are from the average of that set

High value= mean + x(sd)
Low value = mean - x(sd)
x–> the number of standard deviations from the mean

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5
Q 
sqrt(2)
sqrt(3)
sqrt(5)
sqrt(6)
sqrt(7)
sqrt(8)
A 
=1.4
=1.7
=2.2
=2.4
=2.6
=2.8
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6
Q

|a-b| >=|a|-|b| if…

A

b does not equal 0 and |a-b|=|a|-|b|
a and b share the same signs and |a|>=|b|
only true of (+)(+) or (-)(-)

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7
Q

Compound interest

A

A=P(1+r/n)^(nt)

A=Future value of investment
P=Initial value
R=Interest rate per year
n=Number of compounding periods per year
t=time(#years)
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8
Q

Area of a regular hexagon

A

3sqrt(3)/2*s^2, where S is the the length of any of the sides

3sqrt(3)/2 = 2.6

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9
Q

When solving “at least” problems, first calculate the probabilities of the mutually exclusive scenarios, then add those probabilities to determine the final

In city Y, the probability that it will snow more than 5 inches during any given snowstorm in the month of January is 1/3. If there are 3 snowstorms, what is the probability that it snows more than 5 inches in at least 2 of the snowstorms

A

Scenario 1:
YYN
Arranged in 3!/2!= 3 ways
3(1/31/3*2/3)= 6/27

Scenario 2:
YYY
(1/31/31/3) = 1/27

6/27+1/27 = 7/27

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10
Q

Determining the number of primes in a factorial when base of a divisor is power of a prime
30!/4^n

A

Determine number of 2’s in 30!. Then create and simplify an inequality

30!/4^n-->30/2^2n
30/2 = 15
30/4=7
30/8= 3
30/16= 1
15+7+3+1=26

2n<=26
n<=13

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11
Q

Zero slope vs undefined slope

which is horizontal and which is vertical

A

Zero slope is horizontal

undefined slope is vertical

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12
Q

Exponential decay example:
If money in an account decreased by 50% each week, the amount of money by which the account decreased during the 3rd week is what fraction of the amount of money at the end of the first week

A

Initial Amt Amt Removed Amt Remaining

1st: x 1/2x 1/2x
2nd: 1/2x 1/2x1/2=1/4x 1/4x
3rd: 1/4x 1/4x1/2 = 1/8x 1/8x

(1/8x)/(1/2x) = 1/4x

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13
Q

For a function in the form of f(x)=kx^n+c where n is a positive even integer and K is nonzero:

A

if k>0, the range of f(x) is all real numbers >=C

if K<0, the range is all real numbers <=c

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14
Q

Trailing 0’s

A

Created by 5x2 pairs. Each pair in a number creates 1 trailing 0

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15
Q

Square roots and squares of fractions
(a/b)^2
sqrt(x/y)

A 
(a/b)^2= a^2/b^2
sqrt(x/y)= sqrt(x)/sqrt(y)
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16
Q

x is jointly proportional to y and z

A

x = ykz

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17
Q

Leading 0’s

A

If x is an integer with K digits, then 1/x will have k-1 leading 0’s. If x is a perfect power of 10, there will be k-2 leading 0’s

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18
Q

2/7

A

.286

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19
Q

Slope intercept equation

A

y = mx+b

y= y coordinate for a point on the line
x = corresponding x coordinate for the point on the line
m - slope of the line
b = y intercept

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20
Q

If a number x has y prime factors, then x^n will have the same y factors

A 
18 = 3^2*2
18^3 = 3^3 *2^2
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21
Q

If W is divisible by 6 and 9. W must be a multiple of which of the following:

4
12
18
24
36
A

18

We are given that W is divisible by 6 and 9. In other words, W is a multiple of both 6 and 9. To determine what must be a multiple of 6 and 9, we can determine the LCM(6,9)

If Z is divisible by both x and y, Z must also be divisible by the LCM of x and y

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22
Q

Linear Growth Example:
An investment grows by the same amount each year. The value of the portfolio after year 8 was 5/4 the value after year 5. If the portfolio began with $100, what is the amount the portfolio grew by each year?

A

year 1: 100+x
year 2: 100+2x
…
year 8=100+8x

year 8=5/4(year 5)
100+8x= 5/4(100+5x)
x=14

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23
Q

“Percent of” means to multiple a given percent by a given value

5 percent of z = ?
400 percent of y =?
m percent of p =?

A

(5/100)z
(400/100)y
(m/100)*p

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24
Q

x^7 has the same sign as x

A

Numbers raised to odd powers reveal positvity/negativity

It’s impossible to determine the sign of numbers raised to even powers

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25
Q

Using trailing zeros to determine the number of digits in an integer

A
  1. PF number
  2. Count number of 5x2 pairs
  3. collect # unpaired 5 and 2 along with other non-0 pf’s and multiply together
  4. Add 5x2 pairs with total digits of number in step 3
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26
Q

Determining the number of primes in a factorial when base of a divisor is power of a prime
30!/4^n

A

Determine number of 2’s in 30!. Then create and simplify an inequality

30!/4^n-->30/2^2n
30/2 = 15
30/4=7
30/8= 3
30/16= 1
15+7+3+1=26

2n<=26
n<=13

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27
Q

Consecutive multiples of integers

A

Represented as x + (x+”multiple) + (x+”2*multiple)

Consecutive multiples of 5: x + (x+5) + (x+10) + (x+15)

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28
Q

Length of a diagonal of a rectangle

A

Sqrt(L^2+W^2)

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29
Q

When A and B are not mutually exclusive:

A

P(A or B)= P(A)+P(B) - P(A and B)

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30
Q

Exponential decay table

A

Initial Amt Amt Removed Amt Remaining
First reduction
Second reduction
3rd reduction

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31
Q

Number of seconds is one day

A

86,400

606024

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32
Q

Exponential Growth

A

amount of growth=(initial value)*(growth factor)^growth periods

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33
Q

15^2

A

225

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34
Q

Circle 3 part ratios

A

central angle/360 = arc length / circumference = area of sector/ area of circle

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35
Q

If 2 events are independent:

A

P(A and B)= P(A) * P(B)

Probability of a magician pulling a rabbit out of his hat on any attempt is 1/3. What is probability he will pull it out on the first but not the other 3.

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36
Q

Comparing Standard deviations without fully calculating standard deviation

A
  1. Determine the mean for each set
  2. For each individual mean, determine the absolute difference between the mean of the set and each data point in that set
  3. sum the differences obtained from each individual set

The set with the greater sum has the greater standard deviation

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37
Q

Pythagorean Theory

A

In any right triangle, C^2=A^2+B^2, where C is the length of the triangle’s hypotenuse.

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38
Q

17^2

A

289

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39
Q

Multiplication rules of even and odd

A

The product of an even number and any integer is always even

The product of an odd number and odd number will always be odd

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40
Q

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

A

sqrt(x+5)^2= sqrt(36)

abs(x+5)=6

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41
Q

6/7

A

.857

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42
Q

(x+y)^2 other forms

A

(x+y)(x+y)

x^2+y^2 + 2xy

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43
Q

9^3

A

729

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44
Q

If we add or subtract the same amount to or from each term in a data set, the standard deviation does not change

A

That is, we can have data sets with the same standard deviation and different averages

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45
Q

Distance between 2 points formula

A

Sqr((x2-x1)^2+(y2-y1^2))

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46
Q

LCM of a set provides all unique prime factors. Thus, it provides all the unique prime factors of the product f all numbers in the set

A

pf of x = 2,3
pf of y = 3,5
pf of z = 2,5

xyz cannot have any prime factors other than 2,3,5

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47
Q

6^3=
7^3=
8^3=
9^3=

A

6^3= 216
7^3=343
8^3= 512
9^3=729

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48
Q

If we know y divides into x, LCM(x,y) is x and GCF(x,y) is y

A 
LCM(100,25) = 100
GCF(100,25) = 25
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49
Q

Area of equilateral triangle

A

A=S^2(sqrt(3)/4

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50
Q

Properties of 0

A 
Any number divided by 0 is undefined
Square root of 0 is 0
0 raised to any positive integer is 0
Any number raised to 0 is 1
0 is even
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51
Q

0!=?

A

1

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52
Q 
Units digits of powers:
2=
3=
4=
5=
6=
7=
8=
9-
A 
2= 2,4,8,6
3= 3,9,7,1
4= 4,6
5= 5
6= 6
7= 7,9,3,1
8= 8,4,2,6
9= 9,1
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53
Q

sqrt(a)/sqrt(b) = sqrt(a/b)

A

sqrt(54)/sqrt(6) = sqrt(9)

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54
Q

X is a dividend of y

A

Means x/y

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55
Q

|a-b| >=|a|-|b| if…

A

b does not equal 0 and |a-b|=|a|-|b|
a and b share the same signs and |a|>=|b|
only true of (+)(+) or (-)(-)

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56
Q

“What percent of” problems

100 is what percent of 50

A

Can translate “what percent” into x/100, and then set up an equation to solve for x

or we can use (a/b) * 100
100/50*100

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57
Q

When an event has more than one possible outcome, each possible outcome must be considered when calculating the probability that the event will occur. Thus, to determine the actual probability:

The prob that it rains in town X on any given day is 40 percent. What is the prob that it will rain in town X on exactly 3 days in a certain 4 day period

A

(number of outcomes producing the event) * (probability of one outcome)

RRRN can be arranged in 4!/3!=4 ways.

4(2/5 * 2/5 * 2/5 * 3/5)

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58
Q

1/7

A

.143

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59
Q

18^2

A

324

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60
Q

If the product of 2 integers is 1…

A

Both are either 1 or -1

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61
Q

Adding/subtracting a constant to numerator and denominator of a fraction
(a+c)/(b+c)

A

Adding constant to both will always make the fraction larger –>3/5–> 3+2/5+2 –> 5/7 > 3/5

Subtracting will always make the fraction smaller

Multiplying will always keep the fraction the same size
3/5 –> 32/52 = 6/10

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62
Q

Formula for division

A

x/y = Q + r/y

y=xq+r

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63
Q

If 2 events are complementary:

A

P(A)+P(Not A) =1

eg. Probability that it will rain in town x is 25 percent. what is probability it does not rain in town x tomorrow

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64
Q

Area of a trapezoid

A

((Base 1 + Base 2)*Height)/2

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65
Q

When (x,y) is reflected over the line y=x

A

its image is (y,x)

2,3) becomes (3,2

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66
Q

When (x,y) is reflected over the line y=b

A

its image becomes (x, 2b-y)

(5,-2) becomes (5,4) when reflected over the line y=1

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67
Q

Determine the number of primes in a factorial

Y!/x

A

Divide 1 by powers of x (x^1, x^2, x^3…) until quotient = 0
Add quotients

21!/3^n –> 21/3= 7, 21/9=2

7+2=9

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68
Q

The sum of the interior angles of any hexagon is 720. Any one interior angle of a regular hexagon measures 120

A

A regular hexagon can be divided into 6 equilateral triangles

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69
Q

(A or B)=

Numbers of members in either set

A car dealership has 50 red cars and 35 convertibles. If there are 65 cars that are either red or convertible, how many are both red and convertible

A

(A or B)= #A + #B -#(A and B)

= 50 + 35 - 65

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70
Q

Geometric sequence is one in which the ratio between every pair of two consecutive terms is the same.

A

an=a1*r^(n-1)

Where an is the nth term, a1 is the first, and r is the common ratio

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71
Q

Sum of integers from 101 to 202, inclusive

A

(101+202)/2 = 151.5 – average

Number of terms = 202-101+1 = 102

151.5*102=15453

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72
Q 
Base 1/6 fractions
1/6=
2/6=
3/6=
4/6=
5/6=
A 
1/6=.167
2/6= .333
3/6=.5
4/6=.667
5/6= .833
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73
Q

Catch up and pass problems

A

The faster objects distance is equal to the slower objects distance plus any difference in starting points and any distance by which the faster object must pass the slower

a fast way to calculate catch up and pass is:
time= Change in distance/Change in rate

Dont attemplt this on catch up problems

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74
Q

Simple Interest

A

simple interest= principal x rate x time

When an investment grows via simple interest, the interest earned in any period on the principal investment is not factored into future amounts of interest earned

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75
Q

When A and B are mutually exclusive, P(A) or P(B):

A

P(A or B)=P(A)+P(B)

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76
Q

What is the remainder of (12 * 13 * 17)/5?

A

12/5 - R=2
13/5 - R=3
17/5 - R=2
232=12. Remove excess. Remainder= 2

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77
Q

Y divides into x evenly

A

Means x/y

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78
Q

Division rules for even/odd

A 
even/odd = even
odd/odd= odd
79
Q

the sum of the first n terms of an arithmetic sequence:

A

Sn=n/2(a1+an)

80
Q

work(object 1)+work(object 2)= Work(Total)

A

Work(Total) usually =1, because 1 job is being completed

81
Q

Catch up and pass problems

A

The faster objects distance is equal to the slower objects distance plus any difference in starting points and any distance by which the faster object must pass the slower

a fast way to calculate catch up and pass is:
time= Change in distance/Change in rate

Dont attempt this on catch up problems

82
Q

Surface area of a cube:

A

6s^2

83
Q

5/7

A

.714

84
Q

Finding the number of factors in a number

A

x = pf^e1 x pf^e2…

factors = (e1+1)(e2+2)(e3+3)

240= 2^453
factors=(4+1)(1+1)(1+1)
factors= (5)(2)(2)
factors = 20

85
Q

Price per item equation

A

Price per item = Total cost of identical purchases/(number of identical purchases)

86
Q

Change in worker problems

Proportion method

A

x workers/(combined rate of x workers) = y workers/(combined rate of y workers)

87
Q

Volume of a cylinder

A

v=pi* r^2*h

88
Q

If LCM (x,y) = p and GCF(x,y)=q, then xy=pq

A

m=24—> 2^33
n=30 –>23*5

LCM(m,n) =2^335=120
GCG(m,n) = 2*3 = 6

mn= 24*30 = 720
LCM(x,y)*GCF(x,y) = 720
89
Q

Diagonal of a cube:

A

s*sqrt(3)

90
Q

“percent less problems”

1 percent less than z=

60 percent less than z=

98 percent less than z

A

In percent less than problems, x% less than y is equivalent to (100-x)% of y

(99/100)z (99 percent of z)

(40/100)z ) 40 percent of z

(2/100)z (2 percent of z

91
Q

X is inversely proportional to cube of y and directly proportional to square root of z

A

x=k*sqrt(z)/y^3

92
Q

Area of parallogram

A

base x height

93
Q

Median

A

When a set is numerically ordered, the median is the value in the middle of the arranged set

for even numbered sets, the median is the average of the 2 middle

(n+1)/2 gives the spot of the median for an odd numbered set

94
Q

Subtracting whole number and fraction

A-b/c

A

(ac-b)/c
or (A-1)(c/c)-b/c
6-2/3 = 5(3/3)-2/3 = 5 1/3

95
Q

Y is a divisor of x

A

Means x/y

96
Q

Difference of 2 squares

A 
X^2-Y^2 = (x+y)(x-y)
4x^2-100= (2x+10)(2x-10)
1/36x^2-25 = (1/6x-5)(1/6x+5)
2^12-1 = (2^6-1)(2^6+1)
97
Q

If the value of 1 variable (x) increases while that of a second variable (y) decreases and they are inversely proportional, they are related by what equation?

A

y=k/x

98
Q

To find the number of terms between 2 numbers in a set of consecutive integers, excluding both endpoints:

A

subtract the first number from the last number and then subtract 1

Last number - first number - 1

99
Q

If 2 absolute values are equal, they are either equal or opposites

A

|r+s|=|m+n| if r+s=m+n or r+s=-(m+n)

100
Q

15q/17 –> Q must be multiple of 17 in order to be an integer

14rst/18=?

A

rst must be multiple of 9 to be an integer

101
Q

Number of minutes in 1 day

A

1440

60*24

102
Q

16^2

A

256

103
Q

Surface area of cube and rectangle

A 
Cube = 6 s^2
rectangle = 2(LW) + 2(LH) + 2(WH)
104
Q

Functions domain vs range

A

for domain- look at graph from left to right

for range - look at graph from top to bottom

105
Q

The slopes of 2 perpendicular lines multiply to -1 and are negative reciprocals of each other. Negative reciprocals multiply to -1

A

10 * -1/10 = -1

106
Q

Bow tie method to compare fraction size

A

Given a/b & c/d,

a/b > c/d if ad>bc

107
Q

Weighted average

A

sum of weighted items/total number of weighted items

OR

(data point 1)(frequency of data point 1) + (data point 2)(frequency of data point 2)/total frequency of data points

108
Q

Dry mixture problems

A

Create a table with component 1, component 2, and final mixture as the rows.

Units and total are the columns

109
Q

Dividing Decimals

A
  1. Move decimal of divisor(#after division sign) until it becomes whole number
  2. Move decimal of dividend (#before division sign) to the right same number of places as divisor
  3. Divide by long division. Keep decimal in same location as new dividend
110
Q

|a+b| <= |a|+|b| if…

A

|a+b|=|a|+|b| and a&b share the same sign

111
Q

The equation for a vertical line

the equation for a horizontal line

A

vertical line - x =a, where a is the x-intercept of that line

horizontal line - y=b, where b is the y intercept of that line

112
Q

Bookend method to find average

A

For an odd numbered set spaced evenly, add the first and last number and divide by 2.

For even numbered set spaced evenly, average of the terms is the average of the 2 middle terms

113
Q

A y=-x reflection causes the original x and y coordinates to switch positions and causes the signs of the coordinates to flip

(2,10)–?

A

(-10,-2)

114
Q

Prime numbers under 100

25 total

A

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

115
Q

If a number x has y prime factors, then x^n will have the same y factors

A 
18 = 3^2*2
18^3 = 3^3 *2^2
116
Q

Addition/Subtraction rules for even and odd numbers

A

If both numbers are even or odd, the result will be even

117
Q

14^2

A

196

118
Q

Balance point method to find average

A

In an evenly spaced set with an odd number of terms, the average of the terms in the set is the exact middle term of the set when the terms are in numerical order

In an evenly spaced set with an even number of terms, the average of the terms in the set is the average of the two middle terms of the set

119
Q

Splitting the cost

A

If 10 people split a bill, the cost per person is d/10. If 2 people leave or cant pay, the new cost is now d/8. There is a d/8-d/10=d/40 difference.

120
Q

When the ratio between 2 variables is constant, they are related by what equation?

A

y=kx

where K is a positive constant. When x increases y increases and when x decreases y decreases.

121
Q

Interior angle of a polygon

A

sum of interior angles= (n-2)*180

122
Q

You can add and subtract only like radicals

A

5sqrt(4)+4sqrt(4) = 9sqrt(4)

123
Q

Range

A

Highest in a set - lowest in a set

124
Q

When (x,y) is reflected over the point (a, b)

A

its image becomes (2a-x, 2b-y)

5, -2) becomes (-1, 4

125
Q

Fractional parts of the whole example:

A pilot is required to fly a certain number of hours in one day. In the morning, she flew 1/4 of the required hours plus 2 more. In the afternoon, she flew 2/5 of the remaining hours. In the evening, she flew 4 more. How many hours did she fly?

A

h=Total number of hours

AM: 1/4h +2

126
Q

X is a multiple of y

A

Means x/y

127
Q

8^3

A

512

128
Q

The rate at which an object is performing a task =?

A

work/time

129
Q

Profit equation

A

profit=total revenue - (fixed costs + variable costs)

130
Q

Divisibility Rule

A

Div by 4- if last 2 digits are divisible by 4
Div by 6- even number whose digits sum to a multiple of 3
Div by 8- Even, last 3 digits divisible by 8
Div by 11- Sum of odd placed digits minus sum of even place digits is div by 11
Div by 12- Div by both 3 and 4

131
Q

sqrt(a)*sqrt(b) = sqrt(ab)

A

sqrt(5) * sqrt(7) = sqrt(35)

132
Q

A y=-x reflection causes the original x and y coordinates to switch positions and causes the signs of the coordinates to flip

(2,10)–?

A

(-10,-2)

133
Q

Finding the LCM

A
  1. Prime factorize each number
  2. Take highest exponent for any repeated PF
  3. Take remaining PF’s
  4. Multiply remaining
134
Q

Perfect square ends

A 
0
1
4
5
6
9
135
Q

Mixed fraction A B/C

A

(AC+B)/B

136
Q

|a-b| >=|a|-|b| if…

A

b does not equal 0 and |a-b|=|a|-|b|
a and b share the same signs and |a|>=|b|
only true of (+)(+) or (-)(-)

137
Q

When (x,y) is reflected over the line x=a

A

its image becomes (2a-x,y)

(5,-2) becomes (-1,-2) when reflected over the line x =2

138
Q

Word problems with divisibility

A 
W= Original Price
N= New/Sale Price
Example:
Sale price of 16% of original Price
N= (16/100)W
N=(4/25)W
W=(25N/4)
N must be a multiple of 4
139
Q

Probability of dependent events:

A

P(A and B)= P(A) * P*B|A), where P(B|A) is the probability that B will occur after A has already occurred

140
Q

x is divisible by y

A

Means x/y

141
Q

Y is a factor of x

A

Means x/y

142
Q

Any integer that has prime factors of at least one 2 and at least one 5 must end with at least one zero

A

What is units digit of positive integer x?
1. 7, 15, 24, and n are all factors of x.

Since integer x has factors 15 and 24, it has at least one prime factor of 5 and at least one prime factor of 2. Thus, integer x will always have a units digit of 0

143
Q

Counting consecutive multiples in a set

A

(Highest # Divisible by the given number - Lowest # divisible by the given number)/given number + 1

How many multiples of 2 are between 51 and 99 inclusive?
(98-52)/2+1 = 24

144
Q

19^2

A

361

145
Q 
Base 8 fractions
1/8
2/8
3/8
4/8
5/8
6/8
7/8
A 
1/8=.125
2/8=.25
3/8=.375
4/8=.5
5/8=.625
6/8=.75
7/8=.875
146
Q

When liquid is filling a container:

A

time=volume of container/rate

147
Q

When setting up equation for rate problem with actual speed vs hypothetical speed:

A

time of actual= time of hypothetical + additional time

148
Q

Median strategy for even numbered set

A

If a set of numbers has n terms and if N is even, the median is the average of the values at n/2 and n+2/2, when the numbers are in numerical order

149
Q

Average Rate Questions

A

Average Rate = Total Distance/Total Time

or = (D1+D2)/(T1+T2)

Remember that T=D/R

150
Q

if x/y is an integer, then x/(any factor of y) is an integer

A

100/20

100/(1,2,4,5,10,20) all work

151
Q

At the Vet, there are 5 cats and 3 dogs. If 5 of these animals are to be randomly selected, what is the probability that 3 cats and 2 dogs will be selected

A

Method 1:

P(CCCDD)- arranged in 5!/3!2! = 10 ways
10(5/84/73/63/52/4) = 30/56

152
Q

X-intercept

A

x= - b/m

153
Q

Slope

A

Rise over run

y2-y1)/(x2-x1

154
Q

Another way to express -1

A

(x-y)/(y-x)=-1

155
Q

Arithmetic sequence

A

Sequence in which the difference between every pair of two consecutive terms is the same

1,4,7,10,13 …

an=a1+(n-1)d

an is the nth term in the sequence, a1 is the first term, d is the common difference

156
Q

When setting up equation for rate problem with actual speed vs hypothetical speed:

A

time of actual= time of hypothetical + additional time

157
Q

(x-y)^2 other forms

A

(x-y)(x-y)

x^2+y^2- 2xy

158
Q

Inequality word problems

Up to=
More than=
At least=
Exceeds=
No more=
At most=
As few as=
A 
<= less than or equal to
> greater than
>= greater than or equal to
>greater than
< less than
<= less than or equal to
>= greater than or equal to
159
Q

4/7

A

.571

160
Q

Midpoint formula

A

midpoint (x,y) = (x1+x2)/2, (y1+y2)/2

161
Q

Properties of 1

A 
1 is a factor of all numbers, all #'s are multiples of 1
1 raised to any power is 1
1 is odd
1 is only number with 1 factor
1 is not prime
162
Q

To find the longest line that can be drawn within a rectangular solid, use the extended pythagorean theorem:

Solid is a cube?

A

d^2=L^2+W^2+H^2

d=s*sqrt(3)

163
Q

Linear growth formula

A 
F=KN+P
F=Final value after growth
P=Initial value
K=Growth periods
N=Number of growth periods

An initial value grows by the same amount each growth period

164
Q

7^3

A

343

165
Q

3 Circle venn diagrams

A

Total # Unique Members= #A Only + #B only + #C Only + #Double Overlaps + #Triple Overlap + #Neither

166
Q

6^3

A

216

167
Q

Another way to express -1

A

(x-y)/(y-x)=-1

168
Q

Wet mixture problems

A

Create a table with solution 1, solution 2. and final mixture as the rows.

Concentration, quantity, and total are the columns

169
Q

Multiples

A

X is a multiple of y only if x/y is an integer.

Only get clean divisions when x/y (multiple/factor) is an integer

170
Q

Multiplying/Dividing complex fractions (multiplying num. and den. by the LCD)

A

(1/3)/(1/5)= 15(1/3)/15(1/5)= (15/3)/(15/5)
= 5/3

(1+3/(b+2))/(1+7/(b-2))
= multiply both top and bottom by (b+2)(b-2)

171
Q

Determining the # primes in a factorial when divisor is not prime
40!/6^n

A

Break into pf’s. Use larger pf of x and apply divisibility shortcut

40!/6^n=50/2^n*2^n 
40/3 = 13
40/9=4
40/27=1
13+4+1= 18
172
Q

One object travels faster than another object. Which is “r” and which is “r + difference in speeds”

A

When one object is travelling faster than another object, consider letting the slower object’s speed be some variable “r” and the faster object’s speed be “r+ difference in speeds”

173
Q

Surface area of a cylinder

A

c=2pir^2+2pir*h

174
Q

Percent greater than problems

25 percent greater than z

450 percent greater than z

A

Final value = initial value (1+percent greater than/100)

(125/100)z (125 percent of z)

(550/100)z (550 percent of z)

175
Q

Finding GCF

A
  1. Prime factorize each number
  2. Identify repeating pf’s and take the smallest exponent. If no repeating PF’s, GCF = 1
  3. Multiply numbers from step 3
176
Q

To find the number of terms in a set of consecutive integers that includes only one of its endpoints but not both:

A

Subtract the 1st number from the last number

last number-first number

177
Q

Fractional parts of the whole

A

Must sum to the whole

Fractional part 1 + fractional part 2 + fractional part n +any remaining = original number

178
Q

Surface area of a rectangular solid

A

=2(LW) + 2(LH) + 2(WH)

179
Q

Change in worker problems

Defining the rate of 1 worker method

A

find rate of all workers (work/time), then divide that rate by the number of workers to find the rate of 1 worker.

180
Q

Dividing decimal example (10.36/2.8)

A

Move decimals over to make it 103.6/28

181
Q

3/7

A

.429

182
Q

Leading 0’s

A

If x is an integer with K digits, then 1/x will have k-1 leading 0’s. If x is a perfect power of 10, there will be k-2 leading 0’s

183
Q

2 Objects leave at different times. Which is represented as “T’ and which is “T+difference in time”

A

When two objects leave at different times and converge at a constant rate, the travel time of the object that leaves later can be represented by some variable t; the travel time of the object that leaves earlier can be represented by “t + the difference between their departure times”

184
Q

Probability that some number of items must be selected:

A

ways some number of items can be selected/# ways that all items can be selected

185
Q

When (x,y) is reflected over the line y=-x

A

its image becomes (-y, -x)

-1,4) becomes (-4, 1

186
Q

Equations with fractions efficient approach

A 
Eliminate fractions by multiplying each term by the LCM of denominators 
3/x + 3/5= 3
(3*5*x)/x + (3*5*x)/5 = 3*5*x
15+3x = 15x
15=12x
15/12 = x
187
Q

Bow tie method to compare fraction size

A

Given a/b & c/d,

a/b > c/d if ad>bc

188
Q

x is directly proportional to the square of y

A

x = k * y^2

189
Q

When a question asks for the probability that “at least 1” outcome will occur, consider using complementary events to simplify the problem

Cannot be used on non-complementary events

On any given day, the probability that a certain student is abset from class is 1/5. In a span of 4 days, what is probablity that the student will be abset at least 1 day

A

P(At least 1 outcome) = 1 - P(none of the outcomes occur)

1-(4/54/54/5*4/5) = 369/625

190
Q

There are 10 marbles in a jar, consisting of only red and blue. If the prob of choosing 2 red marbles, one after the other is 2/15, how many red marbles are in the jar

A

R/10 * (R-1)/9= 2/15

191
Q

Age problems

A
  1. Define variable for present day
  2. Represent each age in the future or past
  3. Organize into matrix
  4. Use matrix and problem stem to solve
192
Q

Vertical line test

A

If a graph is the graph of a function, then any vertical line can only intersect the graph at exactly one point or no points

A vertical line itself is not a function

193
Q

Probability that some number of items must not be selected

A

ways some number of items must not be selected/#ways that all items can be selected

194
Q

One object is relatively faster than another

A

When the first object is “x” times as fast as the second object, let the rate of the second object be “r” and the rate of the first object be xr. When the first object is “x” percent as fast as the second object, let the rate of the second object “r” and the rate of the first object “(x/100)*r”

GMAT (4 decks)

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