GMAT Math : Problem-Solving Questions

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Example Questions

Example Question #13 : Range

A large group of students is given a standardized test. The following information is given about the scores:

Mean: 73.8

Standard deviation: 6.3

Median: 71

25th percentile: 61

75th percentile: 86

Highest score: 100

Lowest score: 12

What is the interquartile range of the tests?

Possible Answers:

More information about the scores is needed.

12.6 $\displaystyle 12.6$

2.8 $\displaystyle 2.8$

$\displaystyle 25$

$\displaystyle 88$

Correct answer:

$\displaystyle 25$

Explanation:

The interquartile range of a data set is the difference between the 75th and 25th percentiles:

$\textrm{IQR }= 86-61=25$ $\displaystyle \textrm{IQR }= 86-61=25$

All other given information is extraneous to the problem.

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Example Question #1 : Calculating Arithmetic Mean

Salaries for employees at ABC Company: 1 employee makes $25,000 per year, 4 employees make $40,000 per year, 2 employees make $50,000 per year and 5 employees make $75,000 per year.

What is the average (arithmetic mean) salary for the employees at ABC Company?

Possible Answers:

$\dpi{100} \small \$ 53,500$ $\displaystyle \dpi{100} \small \$ 53,500$

$\dpi{100} \small \$ 58,000$ $\displaystyle \dpi{100} \small \$ 58,000$

$\dpi{100} \small \$ 46,250$ $\displaystyle \dpi{100} \small \$ 46,250$

$\dpi{100} \small \$ 48,640$ $\displaystyle \dpi{100} \small \$ 48,640$

$\dpi{100} \small \$ 55,000$ $\displaystyle \dpi{100} \small \$ 55,000$

Correct answer:

$\dpi{100} \small \$ 55,000$ $\displaystyle \dpi{100} \small \$ 55,000$

Explanation:

The average is found by calculating the total payroll and then dividing by the total number of employees. $\frac{(1\cdot 25,000)+(4\cdot 40,000)+(2\cdot 50,000)+(5\cdot 75,000)}{1+4+2+5}$ $\displaystyle \frac{(1\cdot 25,000)+(4\cdot 40,000)+(2\cdot 50,000)+(5\cdot 75,000)}{1+4+2+5}$

$\frac{25,000+160,000+100,000+375,000}{12} = \frac{660,000}{12}= $55,000$ $\displaystyle \frac{25,000+160,000+100,000+375,000}{12} = \frac{660,000}{12}= $55,000$

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Example Question #2022 : Problem Solving Questions

A bowler had an average (arithmetic mean) score of 215 on the first 5 games she bowled. What must she bowl on the 6th game to average 220 overall?

Possible Answers:

$\dpi{100} \small 258$ $\displaystyle \dpi{100} \small 258$

$\dpi{100} \small 245$ $\displaystyle \dpi{100} \small 245$

$\dpi{100} \small 225$ $\displaystyle \dpi{100} \small 225$

$\dpi{100} \small 25$ $\displaystyle \dpi{100} \small 25$

$\dpi{100} \small 145$ $\displaystyle \dpi{100} \small 145$

Correct answer:

$\dpi{100} \small 245$ $\displaystyle \dpi{100} \small 245$

Explanation:

For the first 5 games the bowler has averaged 215. The equation to calculate the answer is

$\frac{(215\cdot 5)+x}{6}=220$ $\displaystyle \frac{(215\cdot 5)+x}{6}=220$

where $\dpi{100} \small x$ $\displaystyle \dpi{100} \small x$ is the score for the sixth game. Next, to solve for the score for the 6th game $\dpi{100} \small (x)$ $\displaystyle \dpi{100} \small (x)$ multiply both sides by 6:

$(215\cdot 5)+x =1,320$ $\displaystyle (215\cdot 5)+x =1,320$

which simplifies to:

$1,075+x =1,320$ $\displaystyle 1,075+x =1,320$

After subtracting 1,075 from each side we reach the answer:

$x =1,320 - 1, 075 = 245$ $\displaystyle x =1,320 - 1, 075 = 245$

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Example Question #1 : Calculating Arithmetic Mean

Ashley averaged a score of 87 on her first 5 tests. She scored a 93 on her 6th test. What is her average test score, assuming all 6 tests are weighted equally?

Possible Answers:

$\dpi{100} \small 92$ $\displaystyle \dpi{100} \small 92$

$\dpi{100} \small 87$ $\displaystyle \dpi{100} \small 87$

$\dpi{100} \small 88$ $\displaystyle \dpi{100} \small 88$

$\dpi{100} \small 91$ $\displaystyle \dpi{100} \small 91$

$\dpi{100} \small 90$ $\displaystyle \dpi{100} \small 90$

Correct answer:

$\dpi{100} \small 88$ $\displaystyle \dpi{100} \small 88$

Explanation:

We can't just average 87 and 93! This will give the wrong answer! The average formula is $\dpi{100} \small average = \frac{sum}{number\ of\ terms}$ $\displaystyle \dpi{100} \small average = \frac{sum}{number\ of\ terms}$.

For the first 5 tests, $\dpi{100} \small 87=\frac{sum}{5}$ $\displaystyle \dpi{100} \small 87=\frac{sum}{5}$. Then $\dpi{100} \small sum=87\times 5=435$ $\displaystyle \dpi{100} \small sum=87\times 5=435$.

Now combine that with the 6th test to find the overall average.

$\dpi{100} \small average = \frac{435+93}{6}=88$ $\displaystyle \dpi{100} \small average = \frac{435+93}{6}=88$

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Example Question #1 : Calculating Arithmetic Mean

Sabrina made $3,000 a month for three months, $4,000 the next month, and $5,200 a month for the following two months. What was her average monthly income for the 6 month period?

Possible Answers:

$\dpi{100} \small \$ 4500$ $\displaystyle \dpi{100} \small \$ 4500$

$\dpi{100} \small \$ 4950$ $\displaystyle \dpi{100} \small \$ 4950$

$\dpi{100} \small \$ 3400$ $\displaystyle \dpi{100} \small \$ 3400$

$\dpi{100} \small \$ 3900$ $\displaystyle \dpi{100} \small \$ 3900$

$\dpi{100} \small \$ 4200$ $\displaystyle \dpi{100} \small \$ 4200$

Correct answer:

$\dpi{100} \small \$ 3900$ $\displaystyle \dpi{100} \small \$ 3900$

Explanation:

$\dpi{100} \small average = \frac{3\times 3000 + 4000 + 2\times 5200}{6} = \$ 3900$ $\displaystyle \dpi{100} \small average = \frac{3\times 3000 + 4000 + 2\times 5200}{6} = \$ 3900$

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Example Question #2 : Calculating Arithmetic Mean

Luke counts the number of gummy bears he eats every day for 1 week: {39, 18, 24, 51, 40, 15, 23}. On average, how many gummy bears does Luke eat each day?

Possible Answers:

$\dpi{100} \small 27$ $\displaystyle \dpi{100} \small 27$

$\dpi{100} \small 37$ $\displaystyle \dpi{100} \small 37$

$\dpi{100} \small 30$ $\displaystyle \dpi{100} \small 30$

$\dpi{100} \small 41$ $\displaystyle \dpi{100} \small 41$

$\dpi{100} \small 25$ $\displaystyle \dpi{100} \small 25$

Correct answer:

$\dpi{100} \small 30$ $\displaystyle \dpi{100} \small 30$

Explanation:

$average = \frac{39+18+24+51+40+15+23}{7} = 30$ $\displaystyle average = \frac{39+18+24+51+40+15+23}{7} = 30$

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Example Question #6 : Arithmetic Mean

The average of 10, 25, and 70 is 10 more than the average of 15, 30, and x. What is the missing number?

Possible Answers:

$25$ $\displaystyle 25$

$35$ $\displaystyle 35$

$20$ $\displaystyle 20$

$15$ $\displaystyle 15$

$30$ $\displaystyle 30$

Correct answer:

$30$ $\displaystyle 30$

Explanation:

The average of 10, 25, and 70 is 35: $\frac{10+25+70}{3}=35$ $\displaystyle \frac{10+25+70}{3}=35$

So the average of 15, 30, and the unknown number is 25 or, 10 less than the average of 10, 25, and 70 (= 35)

so $\frac{15+30+x}{3}=25$ $\displaystyle \frac{15+30+x}{3}=25$

$15+30+x=75$ $\displaystyle 15+30+x=75$

$45+x=75$ $\displaystyle 45+x=75$

$x=30$ $\displaystyle x=30$

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Example Question #1 : Calculating Arithmetic Mean

What is the average of 2x, 3x + 2, and 7x +4?

Possible Answers:

not enough information

3x + 4

4x + 2

Correct answer:

4x + 2

Explanation:

$average = \frac{sum}{terms} = \frac{2x + 3x + 2 + 7x + 4}{3} = \frac{12x + 6}{3} = 4x +2$ $\displaystyle average = \frac{sum}{terms} = \frac{2x + 3x + 2 + 7x + 4}{3} = \frac{12x + 6}{3} = 4x +2$

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Example Question #1 : Arithmetic Mean

The average high temperature for the week is 85. The first six days of the week have high temperatures of 89, 76, 92, 90, 80, and 84, respectively. What is the high temperature on the seventh day of the week?

Possible Answers:

$\displaystyle 82$

$\displaystyle 84$

$\displaystyle 85$

$\displaystyle 86$

$\displaystyle 83$

Correct answer:

$\displaystyle 84$

Explanation:

$average = \frac{sum}{days}$ $\displaystyle average = \frac{sum}{days}$

$85=\frac{89+76+92+90+80+84+x}{7}=\frac{511+x}{7}$ $\displaystyle 85=\frac{89+76+92+90+80+84+x}{7}=\frac{511+x}{7}$

$\displaystyle 595=511+x$

x=84 $\displaystyle x=84$

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Example Question #3 : Calculating Arithmetic Mean

Jimmy's grade in his finance class is based on six equally-weighted tests. If Jimmy scored 98, 64, 82, 90, 70, and 88 on the six tests, what was his grade in the class?

Possible Answers:

$\displaystyle 86$

$\displaystyle 82$

$\displaystyle 88$

$\displaystyle 80$

$\displaystyle 84$

Correct answer:

$\displaystyle 82$

Explanation:

$avg=\frac{98+64+82+90+70+88}{6}=\frac{492}{6}=82$ $\displaystyle avg=\frac{98+64+82+90+70+88}{6}=\frac{492}{6}=82$

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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 #13 : Range

Example Question #1 : Calculating Arithmetic Mean

Example Question #2022 : Problem Solving Questions

Example Question #1 : Calculating Arithmetic Mean

Example Question #1 : Calculating Arithmetic Mean

Example Question #2 : Calculating Arithmetic Mean

Example Question #6 : Arithmetic Mean

Example Question #1 : Calculating Arithmetic Mean

Example Question #1 : Arithmetic Mean

Example Question #3 : Calculating Arithmetic Mean

All GMAT Math Resources

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