# GRE Math Refresher Diagnostic Test

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```					GRE                                                           Math Refresher – Diagnostic Test

GRE Math Refresher Diagnostic Test

Please take the time to complete the following diagnostic test.
If you have difficulty with any of the topics, you will be directed to one of several short
refresher lessons available.

1
GRE                                                          Math Refresher – Diagnostic Test

Integer Arithmetic

Evaluate the following (without a calculator)

a)   ( −5 ) + ( −8 ) =

b)   ( −2 ) − 10 =

c) 5 × ( −2 ) × 3 =

( 10 )( −2 )( 4 )
d)                     =
( −8 )( 1)

e) 4 − ( −4 ) =

f)   ( −5 ) + ( −1) − ( −7 ) =                                                         j) -4
i) -6
g)   ( −10 ) − 8 + 2 =                                                                h) -2
g) -16
h)   ( −6 )( −1)( −8 )
=
( −2 )( −12 )
f) 1
e) 8

i) 8 − 14 =                                                                           d) 10
c) -30

j)   ( −5 ) − 9 − ( −10 ) =                                                          b) -12
a) -13

If you had difficulty with any of these questions, you may want to print and complete
the Math Refresher lesson “Integer Arithmetic.”

2
GRE                                                          Math Refresher – Diagnostic Test

Decimal Arithmetic

Evaluate the following (without a calculator)

a) 5.278 + 0.0544 + 17.65 =

b) 1.2074 + 11.809 =

c) 6.0287 – 4.55 =

d) 1.542 – 0.9438 =

e) 8.5 × 16.3 =
h) 8.8
g) 1.35
f) 6.24 × 48.8 =
f) 304.512
e) 138.55
g) 57.78 ÷ 42.8 =                                                                     d) 0.5982
c) 1.4787
b) 13.0164
h) 27.5 ÷ 3.125 =
a) 22.9824

If you had difficulty with any of these questions, you may want to print and complete
the Math Refresher lesson “Decimal Arithmetic.”

3
GRE                                                          Math Refresher – Diagnostic Test

Fractions

5 5
a)    −   =
8 12

1   8
b)      ÷   =
20 15

1 1 1
c)    + + =
2 3 6

20 9
d)     ×   =
27 16

e)
1 3
6 10                                                                         5
a)
24
1   5
f) 2 − 1 =                                                                          3
3   6                                                                      b)
32

27   1                                                                    c) 1
g)      ÷1 =
32   8
5
d)
12
8 3
h)     × =
15 4                                                                            7
e)
15
7 5                                                                              1
i)    − =                                                                      f)
8 6                                                                              2

3
3  3                                                                      g)
j) 3 + 1 =                                                                            4
10  4
2
h)
5
If you had difficulty with any of these questions, you may want to print and            1
complete the Math Refresher lesson “Fractions.”                                   i)
24
1
j) 5
20

4
GRE                                                         Math Refresher – Diagnostic Test

Powers

Evaluate the following:

a) 5 2 =

b) 2 −5 =

c) 10 4 =

d) ( −3 )
−3
=

a) 25

Simplify the following                                                                1
b)
32
f) x ⋅ x 2 ⋅ x 11 =
c) 10,000

x 18                                                                           1
g)        =                                                                 d) −
x6                                                                            27

e)   64
⎢(     )
4
h) ⎡ x 2             ⎤ =
3

⎣               ⎥
⎦
f)   x 14

i)
(x ) 4 5

=
(x ) 2 7                                                               g) x 12

x4 ⋅ x2 ⋅ x7                                                          h) x 24
j)                           =
(x )   3 3

i)   x6

j)   x4
If you had difficulty with any of these questions, you may want to print and
complete the Math Refresher lesson “Powers.”

5
GRE                                                                         Quantitative – Algebra

Algebra

Simplify the following

a) 8 x + 5 x

b) 4 x − y + x − 5 y

c) xy 2 − 8 x 2 y 2 − 4 xy 2

d)   x + x + 6y + 4 − 3y + 7 x − 5 y − 8 x − 9                             Answers:

a) 13x

Expand and simplify the following
b) 5 x − 6y

e) 3 x 2 ( 4 x 4 − 5 x )
c) −3 xy 2 − 8 x 2 y 2

f)   −4 x 3 y ( 3 xy − x 7 y 2 )                                             d) x − 2 y − 5

g)   7 x 2 y ( yz − 4 xy )                                                   e) 12 x 6 − 15 x 3

f) −12 x 4 y 2 + 4 x 10 y 3
h)   ( x − 6 )( x + 5 )
g) 7 x y z − 28 x y
2 2        3 2

i)    ( 3 x − 5 )( x + 1)
h) x − x − 30
2

j)    ( 7 x + 1)( 7 x − 1)
i) 3 x 2 − 2 x − 5

j) 49 x 2 − 1

If you had difficulty with any of these questions, you may want to print and
complete the Math Refresher lesson “Algebra.”

6
GRE                                                             Quantitative – Equation Solving

Equation solving

Solve each equation for x

a) 2 x + 5 = 17

b) −3 x − 11 = 13

c)   4 x − 8 = 9 x + 22

d)   18 = 2 ( 3 − x )

a) x = 6

e)   8 − 7x + 2 + 6x = x                                                       b) x = −8

c) x = −6

d) x = −6
f)   4 ( x + 1) = 3 x + 11
e) x = 5

f)   x =7
g) x + 2 x + x = 24 − 2 x
g) x = 4

h) x = −1

h)   15 = 7 x + 22

If you had difficulty with any of these questions, you may want to print and
complete the Math Refresher lesson “Equation Solving.”

7

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