GMAT

Math Refresher – Diagnostic Test

GMAT 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.

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GMAT
Integer Arithmetic
Evaluate the following (without a calculator) a)

Math Refresher – Diagnostic Test

( −5 ) + ( −8 ) = ( −2 ) − 10 =

b)

c) 5 × ( −2 ) × 3 =

d)

( 10 )( −2 )( 4 ) = ( −8 )( 1)

e) 4 − ( −4 ) =

f)

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

b) -12

j)

( −5 ) − 9 − ( −10 ) =

d) 10

i) 8 − 14 =

f) 1

h)

( −6 )( −1)( −8 ) = ( −2 )( −12 )

h) -2

g)

( −10 ) − 8 + 2 =

j) -4 i) -6 g) -16 e) 8 c) -30 a) -13 2

( −5 ) + ( −1) − ( −7 ) =

Answers:

GMAT
Decimal Arithmetic
Evaluate the following (without a calculator) a) 5.278 + 0.0544 + 17.65 =

Math Refresher – Diagnostic Test

b) 1.2074 + 11.809 =

c) 6.0287 – 4.55 =

d) 1.542 – 0.9438 =

e) 8.5 × 16.3 =

Answers: h) 8.8 g) 1.35 f) 304.512 e) 138.55 d) 0.5982 c) 1.4787 b) 13.0164 a) 22.9824 3

f) 6.24 × 48.8 =

g) 57.78 ÷ 42.8 =

h) 27.5 ÷ 3.125 =

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

GMAT
Fractions

Math Refresher – Diagnostic Test

Evaluate the following and express your answer in simplest terms a)
5 5 − = 8 12 1 8 ÷ = 20 15 1 1 1 + + = 2 3 6 20 9 × = 27 16 1 3 + = 6 10

b)

c)

d)

e)

Answers: 5 a) 24 b)
3 32

1 5 f) 2 − 1 = 3 6

g)

27 1 ÷1 = 32 8 8 3 × = 15 4 7 5 − = 8 6

c) 1 d)
5 12 7 15 1 2 3 4 2 5 1 24 1 20

h)

e) f) g) h)

i)

3 3 j) 3 + 1 = 10 4

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

i)

j) 5

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GMAT
Powers
Evaluate the following: a) 5 2 = b) 2 −5 = c) 10 4 = d) ( −3 )
−3

Math Refresher – Diagnostic Test

=
Answers: a) 25

e) 4 3 =

Simplify the following f) x ⋅ x 2 ⋅ x 11 =

b)

1 32

c) 10,000 g)

x 18 = x6
⎢( ⎣

d) − e) f)

1 27

h) ⎡ x 2

)

3

⎤ = ⎥ ⎦

4

64

i)

(x ) (x )

x 14

4 5 2 7

=

g) x 12

j)

x4 ⋅ x2 ⋅ x7

(x )

3 3

=

h) x 24 i) j)

x6 x4

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

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GMAT
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

Quantitative – Algebra

Answers: a) 13x

Expand and simplify the following e) 3 x 2 ( 4 x 4 − 5 x ) f)
−4 x 3 y ( 3 xy − x 7 y 2 )

b) 5 x − 6y c) −3 xy 2 − 8 x 2 y 2 d) x − 2 y − 5 e) 12 x 6 − 15 x 3 f) −12 x 4 y 2 + 4 x 10 y 3
2 2 3 2 g) 7 x y z − 28 x y

g)

7 x 2 y ( yz − 4 xy )

h)

( x − 6 )( x + 5 ) ( 3 x − 5 )( x + 1)

i)

2 h) x − x − 30

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.”

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GMAT
Equation solving
Solve each equation for x a) 2 x + 5 = 17

Quantitative – Equation Solving

b) −3 x − 11 = 13

c)

4 x − 8 = 9 x + 22

d)

18 = 2 ( 3 − x )

Answers: a) x = 6

e)

8 − 7x + 2 + 6x = x

b) x = −8 c) x = −6

f)

4 ( x + 1) = 3 x + 11

d) x = −6 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.”

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