Last year, Christine received 12 monthly paychecks. Each of

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BTGmoderatorLU: Moderator; Posts: 2650; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Sun Apr 15, 2018 2:13 pm

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Last year, Christine received 12 monthly paychecks. Each of the first four months' paychecks was for $4,500, and each of the remaining months' paychecks was for $4,800. What was her average paycheck for the year?

A. $4,600
B. $4,650
C. $4,700
D. $4,750
E. $4,800

The OA is C.

I solved this PS question as follow,

$$Average\ =\frac{\ 4\cdot4500+8\cdot4800}{12}=4700$$

Please, can anyone explain another way to solve it? Thanks in advance!

Source: Beat The GMAT — Problem Solving | Sun Apr 15, 2018 2:13 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Apr 15, 2018 3:20 pm

BTGmoderatorLU wrote:Last year, Christine received 12 monthly paychecks. Each of the first four months' paychecks was for $4,500, and each of the remaining months' paychecks was for $4,800. What was her average paycheck for the year?

A. $4,600
B. $4,650
C. $4,700
D. $4,750
E. $4,800

Another approach is to use weighted averages.

Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

In this question, the proportion of $4500 paychecks = 4/12 = 1/3
And the proportion of $4800 paychecks = 8/12 = 2/3

Plugging these values into the formula, we get: average paycheck = (1/3)($4500) + (2/3)($4800)
= $1500 + $3200
= $4700

Answer: C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Tue Apr 17, 2018 3:36 pm

BTGmoderatorLU wrote:Last year, Christine received 12 monthly paychecks. Each of the first four months' paychecks was for $4,500, and each of the remaining months' paychecks was for $4,800. What was her average paycheck for the year?

A. $4,600
B. $4,650
C. $4,700
D. $4,750
E. $4,800

We can create a weighted average equation:

(4 x 4500 + 8 x 4800)/12 = (18,000 + 38,400)/12 = 4,700

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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