OG The sum of the weekly salaries

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AbeNeedsAnswers: Master | Next Rank: 500 Posts; Posts: 394; Joined: Sun Jul 02, 2017 10:59 am; Thanked: 1 times; Followed by:5 members

OG The sum of the weekly salaries

by AbeNeedsAnswers » Thu Aug 17, 2017 7:14 pm

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The sum of the weekly salaries of 5 employees is $3,250. If each of the 5 salaries is to increase by 10 percent, then the average (arithmetic mean) weekly salary per employee will increase by

A. $52.50
B. $55.00
C. $57.50
D. $62.50
E. $65.00

E

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Source: Beat The GMAT — Problem Solving | Thu Aug 17, 2017 7:14 pm

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by [email protected] » Fri Aug 18, 2017 10:15 am

Hi AbeNeedsAnswers,

We're told that the SUM of the weekly salaries of 5 employees is $3,250 and that each of the 5 salaries is to increase by 10 percent. We're asked for the AVERAGE increase in weekly salary per employee.

This question ultimately comes down to working through some arithmetic, but there are a couple of different ways to do that math (and some require fewer 'steps' than others).

Since the TOTAL of the salaries is $3,250, a 10% increase in those salaries would be $325. That increase, when averaged across the 5 employees, would be...

$325/5 = $65

Final Answer: E

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by Matt@VeritasPrep » Fri Aug 18, 2017 1:32 pm

Say our salaries are a, b, c, d, e.

We know that (a + b + c + d + e) = 3250. If everybody's salary goes up by 10%, then we just multiply each side by 1.1:

1.1 * (a + b + c + d + e) = 1.1 * 3250

Since the average = 3250/5, we can see that average went up by 10% too, and we're set.

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by Scott@TargetTestPrep » Wed Nov 15, 2017 3:51 pm

AbeNeedsAnswers wrote:The sum of the weekly salaries of 5 employees is $3,250. If each of the 5 salaries is to increase by 10 percent, then the average (arithmetic mean) weekly salary per employee will increase by

A. $52.50
B. $55.00
C. $57.50
D. $62.50
E. $65.00

The original average salary is 3,250/5 = 650.

If each of the 5 salaries will increase by 10%, the new sum of the salaries will also increase by 10%. Thus, the new sum is:

0.1 x 3,250 + 3,250 = 325 + 3,250 = 3,575

Thus, the new average salary is 3575/5 = 715 and each salary increases by 715 - 650 = $65.

Alternate Solution:

If each of the salaries is increased by 10%, then the average salary will increase by 10% as well. The original average salary is 3,250/5 = 650. Thus, a 10% salary increase is 650 x 0.10 = 65 per person.

Answer: E

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