GRE Math To Memorize

Question 1

The Three Special Products

Answer 1

Special Product #1 = x² - y² = (x+y)(x-y)

Special Product #2 = x² + 2xy + y² = (x+y)(x+y) = (x-y)²

Special Product #3 = x² - 2xy + y² = (x-y)(x-y) = (x-y)²

Question 2

X percent

Answer 2

X/100

Question 3

Of

Answer 3

Multiple (usually)

Question 4

Of z

Answer 4

Z is the Whole (Percents)

Question 5

Y is X percent of Z

Answer 5

Y is the Part, and Z is the Whole

Y= (X/100)Z

Part = (Percent/100) x Whole

Question 6

Y is X percent of Z

Answer 6

Y/Z = X/100

Part/Whole = Percent/100

Question 7

A is 1/6 of B

Answer 7

A=(1/6)B

Question 8

C is 20% of D

Answer 8

C=(0.20)D

Question 9

E is 10% greater than F

Answer 9

E=(1+10/100)F = (1.1)F

Question 10

G is 30% less than H

Answer 10

G = (1-30/100)H = (0.70)H

Question 11

The dress cost $J. Then it was marked up 25% and sold. What is the profit?

Answer 11

Part = Revenue-Cost
Profit = (1.25)J-J
Profit = (0.25)J

Question 12

Ratio of X to Y

Answer 12

X/Y

Question 13

Common Square Roots

Answer 13

√0 = 0
√1 = 1
√4 = 2
√9 = 3
√16 = 4
√25 = 5
√36 = 6
√49 = 7
√64 = 8
√81 = 9

Question 14

Common Cubed Roots

Answer 14

3^√0 = 0
3^√1 = 1
3^√8 = 2
3^√27 = 3
3^√64 = 4
3^√125 = 5
3^√216 = 6
3^√343 = 7
3^√512 = 8
3^√729 = 9
3^√1000 = 10

Question 15

Pythagorean Theorem

Answer 15

a² + b² = c²

• Watch out for the triples!

Question 16

Diagonal of a square/Face of a cube

Answer 16

d = s√2

Question 17

Edge of a cube/Diagonal of a cube

Answer 17

d = s√3

Question 18

Circumference

Answer 18

C = 2πr

Question 19

Diameter

Answer 19

D = 2r

Question 20

Area of a Circle

Answer 20

A = πr²

Question 21

The length of a diagonal across opposite ends of a rectangular solid

Answer 21

D² = l² x w² x h²

Question 22

Powers of 2

Answer 22

2, 4, 8, 16, 32, 64, 128

Question 23

Powers of 3

Answer 23

3, 9, 27, 81

Question 24

Common Numbers²

Answer 24

4² = 16
5² = 25
6² = 36
7² = 49
8² = 64
9² = 81
10² = 100
11² = 121
12² = 144
13² = 169
14² = 196
15² = 225

Question 25

Common Numbers^3

Answer 25

2^3 = 8
3^3 = 27
4^3 = 64
5^3 = 125

Question 26

Gross Profit

Answer 26

Gross Profit = Sales revenue - Costs

Ex: May fruit sales = $2,500 and the average wholesale cost per pound of fruit was $0.25 and the average retail price per pound of fruit was $0.80.
1) Average gross profit per pound of fruit solid in May =
0.80 - 0.25 = 0.55
2) Gross profit on fruit sold in May = profit per pound x number of pounds of fruit sold
3) Number of pounds of fruit sold in May = total fruit revenue / revenue per pound
2500 / 0.80 = 3,125 pounds of fruit sold in May
4) Gross profit on fruit sold in May = Profit per pounds (0.55) x number of pounds of fruit sold (3,125)
5) Gross profit = $1,718.75

Question 27

50 million

Answer 27

5 x 10^7