GMAT Math : Calculating arithmetic mean

Study concepts, example questions & explanations for GMAT Math

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Example Questions

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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 \$ 46,250

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

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

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

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

Correct answer:

\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}

 


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

Example Question #2 : Calculating Arithmetic Mean

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 225

\dpi{100} \small 25

\dpi{100} \small 145

\dpi{100} \small 245

\dpi{100} \small 258

Correct answer:

\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

where \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) multiply both sides by 6:

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

which simplifies to:

1,075+x =1,320

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

x =1,320 - 1, 075 = 245

Example Question #3 : 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 88

\dpi{100} \small 87

\dpi{100} \small 92

\dpi{100} \small 91

\dpi{100} \small 90

Correct answer:

\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}.

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

Example Question #4 : 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 \$ 3900

\dpi{100} \small \$ 4500

\dpi{100} \small \$ 4950

\dpi{100} \small \$ 3400

\dpi{100} \small \$ 4200

Correct answer:

\dpi{100} \small \$ 3900

Explanation:

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

Example Question #5 : 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

\dpi{100} \small 41

\dpi{100} \small 30

\dpi{100} \small 37

\dpi{100} \small 25

Correct answer:

\dpi{100} \small 30

Explanation:

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

Example Question #6 : Calculating 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:

30

25

20

15

35

Correct answer:

30

Explanation:

The average of 10, 25, and 70 is 35: \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

15+30+x=75

45+x=75

x=30

Example Question #7 : Calculating Arithmetic Mean

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

Possible Answers:

4x + 2

4

7x

3x + 4

not enough information

Correct answer:

4x + 2

Explanation:

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

Example Question #7 : Calculating 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:

Correct answer:

Explanation:

Example Question #8 : 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:

Correct answer:

Explanation:

Example Question #9 : Calculating Arithmetic Mean

Sandra's grade in economics depends on seven tests - five hourly tests, a midterm, and a final exam. The midterm counts twice as much as an hourly test; the final, three times as much.

Sandra's grades on the five hourly tests are 84, 86, 76, 89, and 93; her grade on the midterm was 72. What score out of 100 must she achieve on the final exam so that her average score at the end of the term is at least 80?

Possible Answers:

She cannot achieve this average this term

Correct answer:

Explanation:

This is a weighted mean, with the hourly tests assigned a weight of 1, the midterm assigned a weight of 2, and the final assigned a weight of 3. The total of the weights will be

 .

If we let  be Sandra's final exam score, Sandra's final weighted average will be

For Sandra to get a final average of 80, then we set the above equal to 80 and calculate :

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