GMAT-MathRefresher-DiagnosticTest

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

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)=

g)(−10)−8 + 2 =

h)(−(6−)(2)(−1−)(12−)8) =

i)8 −14 =

j)(−5)−9 −(−10)=

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

Answers:

-4	j)
-6	i)
-2	h)
-16	g)
1	f)
8	e)
10	d)
-30	c)
-12	b)
-13	a)

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GMAT

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 =

f)6.24 × 48.8 =

g)57.78 ÷ 42.8 =

h)27.5 ÷ 3.125 =

Answers:

8.8	h)
35.1	g)
512.304	f)
55.138	e)
5982.0	d)
4787.1	c)
0164.13	b)
9824.22	a)

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

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GMAT

Math Refresher – Diagnostic Test

Fractions

Evaluate the following and express your answer in simplest terms

a)58 − 125 =

b)201 ÷ 158 =

c)21 + 31 + 61 =

d)2027 ×169 =

e)	1 +				3	=		Answers:
				10
	6							a)		5
									24
f)	1					5				3
	2 3			−16			=	b)
									32
g)	27					1		c)	1
	32			÷18			=				5
								d)
h)		8	× 3			=			12
	15			4				e)		7
									15

i)78 − 56 =

j)3 103 +134 =

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

f)21

g)34

h)52

i)1

24

j)5 201

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GMAT

Math Refresher – Diagnostic Test

Powers

Evaluate the following:

a)52 =

b)2−5 =

c)104 =

d)(−3)−3 =

e)	43 =	Answers:
		a)	25
Simplify the following		b)		1
f)	x x2 x11 =		32
		c)	10,000

g)x18 =

x6

h)(x2 )3 4 =

i)	(x4 )5
	(x2 )7 =
		x4 x2 x7
j)			=
		(x3 )3

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

d)− 271

e)64

f)x14

g)x12

h)x24

i)x6

j)x4

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GMAT

Quantitative – Algebra

Algebra

Simplify the following

a)8x + 5x

b)4x − y + x −5y

c)xy 2 −8x2y 2 − 4xy 2

d)x + x +6y + 4 −3y +7x −5y −8x −9

Expand and simplify the following

e)3x2 (4x4 −5x )

f)−4x3y (3xy − x7y 2 )

g)7x2y (yz − 4xy )

h)(x −6)(x +5)

i)(3x −5)(x +1)

j)(7x +1)(7x −1)

Answers:

a)13x

b)5x −6y

c)−3xy 2 −8x2y 2

d)x −2y −5

e)12x6 −15x3

f)−12x4 y 2 + 4x10y 3

g)7x2y 2z −28x3y 2

h)x2 − x −30

i)3x2 −2x −5

j) 49x2 −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

Quantitative – Equation Solving

Equation solving

Solve each equation for x

a) 2x + 5 = 17

b)−3x −11 = 13

c)4x −8 = 9x +22

d)18 = 2(3 − x )

e)8 −7x +2 +6x = x

f)4(x +1)= 3x +11

g)x +2x + x = 24 −2x

h)15 = 7x +22

Answers:

a)x = 6

b)x = −8

c)x = −6

d)x = −6

e)x = 5

f)x = 7

g)x = 4

h)x = −1

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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