• 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW
This topic has expert replies
Moderator
Posts: 1198
Joined: 29 Oct 2017
Followed by:2 members

Last year Manfred received 26 paychecks...

by AAPL » Thu Jan 04, 2018 2:04 pm
Last year Manfred received 26 paychecks. Each of his first 6 paychecks was $750; each of his remaining paychecks was $30 more than each of his first 6 paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his paychecks for the year?

A. $752
B. $755
C. $765
D. $773
E. $775

The OA is D.

I don't have clear this PS question, I appreciate if any expert explain it for me. Thank you so much.

User avatar
Legendary Member
Posts: 2666
Joined: 14 Jan 2015
Location: Boston, MA
Thanked: 1153 times
Followed by:125 members
GMAT Score:770

by DavidG@VeritasPrep » Thu Jan 04, 2018 2:12 pm
AAPL wrote:Last year Manfred received 26 paychecks. Each of his first 6 paychecks was $750; each of his remaining paychecks was $30 more than each of his first 6 paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his paychecks for the year?

A. $752
B. $755
C. $765
D. $773
E. $775

The OA is D.

I don't have clear this PS question, I appreciate if any expert explain it for me. Thank you so much.
You could just do simple arithmetic. The first 6 paychecks were$750, for a total of 6*750 = 4500. The next 20 paychecks were all for 780 for a total of 20*780 = 15600. In all, the paychecks were worth 4500 + 15600 = 20,100. On average, the 26 checks would be worth 20,100/26 = about 773. The answer is D.
Veritas Prep | GMAT Instructor

Veritas Prep Reviews
Save $100 off any live Veritas Prep GMAT Course

User avatar
Legendary Member
Posts: 2666
Joined: 14 Jan 2015
Location: Boston, MA
Thanked: 1153 times
Followed by:125 members
GMAT Score:770

by DavidG@VeritasPrep » Thu Jan 04, 2018 2:18 pm
AAPL wrote:Last year Manfred received 26 paychecks. Each of his first 6 paychecks was $750; each of his remaining paychecks was $30 more than each of his first 6 paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his paychecks for the year?

A. $752
B. $755
C. $765
D. $773
E. $775

The OA is D.

I don't have clear this PS question, I appreciate if any expert explain it for me. Thank you so much.
You could also use the number line. We know that the ratio of 750 checks to 780 checks is 6:20 or 3:10. So let's call the distance from each check to the overall average 10x and 3x. (We know that the overall average will be far closer to 780 than 750 as there are far more 780 checks, so the 3x will represent the gap between the 780 and the overall average and the 10x will represent the gap between 750 and the overall average.) Our number line will look like this:

750------------10x---------AVG--3x--780

10x + 3x = 780-750
13x = 30
x = 30/13
3x = 90/13, which is very close to 7.

So the AVG = 780 - 7 = 773. The answer is D
Veritas Prep | GMAT Instructor

Veritas Prep Reviews
Save $100 off any live Veritas Prep GMAT Course

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 4039
Joined: 25 Apr 2015
Location: Los Angeles, CA
Thanked: 43 times
Followed by:20 members

by Scott@TargetTestPrep » Mon Sep 02, 2019 5:58 pm
AAPL wrote:Last year Manfred received 26 paychecks. Each of his first 6 paychecks was $750; each of his remaining paychecks was $30 more than each of his first 6 paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his paychecks for the year?

A. $752
B. $755
C. $765
D. $773
E. $775

The OA is D.

I don't have clear this PS question, I appreciate if any expert explain it for me. Thank you so much.

Manfred received 6 paychecks of $750 each and 20 paychecks of $780 each.

The first 6 paychecks summed to 6(750) = 4,500.

The next 20 paychecks summed to 20(780) = 15,600.

So, the average of all the checks is:

(4,500 + 15,600)/26 = 20,100/26 ≈ 773

Answer: D

Scott Woodbury-Stewart
Founder and CEO
scott@targettestprep.com

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage