GMAT Math : Problem-Solving Questions

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Example Questions

Example Question #2061 : Problem Solving Questions

The arithmetic mean of and is 66. The arithmetic mean of and is 60. The arithmetic mean of and is 72. Give the arithmetic mean of , , and .

Possible Answers:

Insufficient information is given to determine the mean.

Correct answer:

Explanation:

The arithmetic mean of and is 64, so

$\frac{x+ y}{2}= 66$

Similarly,

$\frac{x+ z}{2}= 60$

$\frac{y+ z}{2}= 72$

Add the expressions:

$\frac{x+ y}{2} + \frac{x+ z}{2}+ \frac{y+ z}{2}= 66+ 60 +72$

$\frac{2x+2 y+ 2z}{2} = 198$

x+y+z= 198

The arithmetic mean of , , and is

$\frac{x+y+z}{3}= \frac{198}{3} = 66$

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Example Question #55 : Descriptive Statistics

The arithmetic mean of and is 76. The arithmetic mean of and is 63. The arithmetic mean of and is 84.

Order , , and from least to greatest.

Possible Answers:

y, z, x

z, x, y

x, y, z

x, z, y

z, y, x

Correct answer:

x, z, y

Explanation:

The arithmetic mean of and is 76, so

$\frac{x+ y}{2}= 76$

Similarly,

$\frac{x+ z}{2}= 63$

Subtract:

$\frac{x+ y}{2}- \frac{x+ z}{2}= 76-63$

$\frac{ y-z}{2}}= 13$

$\frac{ y-z}{2}}\cdot 2= 13 \cdot 2$

y-z = 26

y = z + 26 ,

so y > z

By similar reasoning:

$\frac{x+ y}{2}= 76$

$\frac{y+ z}{2}= 84$

$\frac{y+ z}{2}- \frac{x+ y}{2}= 84 - 76$

$\frac{ z-x}{2}}= 8$

$\frac{ z-x}{2}}\cdot 2 = 8 \cdot 2$

z-x = 16

z= x+16

so z > x

Therefore, x< z< y .

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Example Question #51 : Descriptive Statistics

The arithmetic mean of , x+ 4 , 3x+7 , and 2x-8 is 40.

What is (rounded to the nearest whole number, if applicable) ?

Possible Answers:

Correct answer:

Explanation:

The arithmetic mean of , x+ 4 , 3x+7 , and 2x-8 is 40, so their sum divided by 4 is equal to 40.

$\frac{2x + (x+4)+(3x+7)+(2x-8)}{4} = 40$

$\frac{2x + x +3x +2x +4+7-8}{4} = 40$

$\frac{8x +3}{4} = 40$

$\frac{8x +3}{4} \cdot 4 = 40\cdot 4$

8x+3 = 160

8x = 157

$x = 19 \frac{5}{8}$

This rounds to 20.

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Example Question #41 : Arithmetic Mean

Which of the following is the arithmetic mean of 10 + x , x - 12 , 14 - x , and ?

Possible Answers:

x+3

0.25x+3

0.25x-3

x-3

Correct answer:

Explanation:

The arithmetic mean of 10 + x , x - 12 , 14 - x , and is the sum of the expressions divided by 4, or:

$\frac{(10 + x )+ (x-12)+ (14-x)+ (-x)}{4}$

$= \frac{x + x-x -x -12+ 14+ 10 }{4}$

$= \frac{12 }{4}$

= 3

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Example Question #2065 : Problem Solving Questions

The arithmetic mean of , , and is 200.

The arithmetic mean of and is 190.

The arithmetic mean of and is 210.

Evaluate the arithmetic mean of and .

Possible Answers:

170

200

190

230

210

Correct answer:

200

Explanation:

The arithmetic mean of , , and is 200, so

$\frac{x+y+z}{3} = 200$

$\frac{x+y+z}{3} \cdot 3 = 200 \cdot 3$

x+y+z = 600

The arithmetic mean of and is 190, so

$\frac{x+y }{2} = 190$

$\frac{x+y }{2}\cdot 2 = 190 \cdot 2$

x+ y = 380

x+y+z - (x+y) = 600 - 380

z = 220

The arithmetic mean of and is 210, so

$\frac{y+z }{2} = 210$

$\frac{y+z }{2}\cdot 2 = 210 \cdot 2$

y+z = 420

x+y+z - (y+z) = 600 - 420

x = 180

The arithmetic mean of and is

$\frac{x+z }{2} = \frac{180+220 }{2}= \frac{400}{2} = 200$

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Example Question #41 : Calculating Arithmetic Mean

Determine the mean for the following set of numbers.

{6,2,5,5,8,4}

Possible Answers:

Correct answer:

Explanation:

To find the mean, simply sum up the numbers and divide by the amount of numbers.

$\textup{mean}=\frac{6+2+5+5+8+4}{6}=5$

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Example Question #42 : Calculating Arithmetic Mean

Find the mean of the following set of numbers:

$\textup{4,6,7,7,8,10,28}$

Possible Answers:

Correct answer:

Explanation:

To find the mean, sum the numbers and divide by the quantity of numbers. Thus,

$\textup{mean}=\frac{4+6+7+7+8+10+28}{7}=\frac{70}{7}=10$

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Example Question #62 : Descriptive Statistics

Find the mean of the following data set. (Round to the nearest whole number)

89,34,117,42,367,2,989,463,865

Possible Answers:

117

371

330

444

Correct answer:

330

Explanation:

Find the mean of the following data set. (Round to the nearest whole number)

89,34,117,42,367,2,989,463,865

Finding the mean is basically like finding the average. Sum up the terms and divide by the number of terms.

89+34+117+42+367+2+989+463+865=2968

$\frac{2968}{9}=329.7\bar{7}\approx330$

Making our answer 330

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Example Question #43 : Calculating Arithmetic Mean

Find the mean of the following set of numbers:

$\textup{1,1,2,7,8,10,11}$

Possible Answers:

$\frac{40}{7}$

$\frac{7}{40}$

Correct answer:

$\frac{40}{7}$

Explanation:

To find the mean, you must sum the numbers and divide by their quantity. Thus:

$\frac{1+1+2+7+8+10+11}{7}=\frac{40}{7}$

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Example Question #2061 : Gmat Quantitative Reasoning

A = B > C > D > E

Give the arithmetic mean of the set $\left \{ A, B, C, D, E \right \}$ .

Possible Answers:

$\frac{A +B+ C+D+E }{5}$

$\frac{A+E}{2}$

$\frac{C+D}{2}$

Correct answer:

$\frac{A +B+ C+D+E }{5}$

Explanation:

The arithmetic mean of a set is the sum of its elements divided by the number of elements, which here is . This makes

$\frac{A +B+ C+D+E }{5}$

the correct choice.

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GMAT Math : Problem-Solving Questions

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #2061 : Problem Solving Questions

Example Question #55 : Descriptive Statistics

Example Question #51 : Descriptive Statistics

Example Question #41 : Arithmetic Mean

Example Question #2065 : Problem Solving Questions

Example Question #41 : Calculating Arithmetic Mean

Example Question #42 : Calculating Arithmetic Mean

Example Question #62 : Descriptive Statistics

Example Question #43 : Calculating Arithmetic Mean

Example Question #2061 : Gmat Quantitative Reasoning

All GMAT Math Resources

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