Fastest method to solve this??

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vishal.pathak: Master | Next Rank: 500 Posts; Posts: 176; Joined: Thu Sep 22, 2011 5:32 am; Thanked: 5 times

by vishal.pathak » Sat Mar 24, 2012 1:13 pm

A salesman's income consists of two components: commission and base salary. His base salary is $350 per week, and his goal is
to earn enough money from commissions to average $500 in total income per week. Over the past 5 weeks, his weekly income
totals have been $406, $413, $420, $436 and $395. By approximately what percent does he need to raise his average (arithmetic
mean) weekly commission earnings, over the next two weeks, to raise his average weekly income to $500 over the 7-week period?
A. 74%
B. 88%
C. 176%
D. 276%
E. 470%
OA E

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Source: Beat The GMAT — Problem Solving | Sat Mar 24, 2012 1:13 pm

seal4913: Master | Next Rank: 500 Posts; Posts: 106; Joined: Wed Mar 23, 2011 4:56 pm; Thanked: 8 times

by seal4913 » Sat Mar 24, 2012 3:05 pm

You would first have to find the commission he had over the 5 weeks so take those number and subtract the base pay of 350. You get 56, 63, 70, 86, and 45. The total of that is 320.

So (320 + 2x)/7 = 150. Total commision so far plus the unknown he needs to make for the next 2 weeks divided by 7 (average 7 weeks) needs to equal 150 (350 + 150 = 500 goal).

So 320 + 2x = 1050; 2x = 730; x = 365; So 365 - 64 (average of weekly commission 320/5) = 301/64 =
apprx 300/64 = 150/32 = 75/16; 16 x 4 = 64 so it's over 4 which is over 400% so you get E

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Mar 24, 2012 4:27 pm

vishal.pathak wrote:A salesman's income consists of two components: commission and base salary. His base salary is $350 per week, and his goal is
to earn enough money from commissions to average $500 in total income per week. Over the past 5 weeks, his weekly income
totals have been $406, $413, $420, $436 and $395. By approximately what percent does he need to raise his average (arithmetic
mean) weekly commission earnings, over the next two weeks, to raise his average weekly income to $500 over the 7-week period?
A. 74%
B. 88%
C. 176%
D. 276%
E. 470%
OA E

First 5 weeks:
Determine the commissions by subtracting 350 from each of the weekly totals:
56, 63, 70, 86, 45.
Sum of the commissions = 56+63+70+86+45 = 320.
Average weekly commission = 320/5 = 64.

Last 2 weeks:
For the average weekly income over the 7 weeks to be 500, the salesman must earn a commission of 150 each of the 7 weeks.
Total required over all 7 weeks = 7*150 = 1050.
Thus, the total required over the last 2 weeks = 1050-320 = 730.
Average required over the last 2 weeks = 730/2 = 365.

Percent increase:
Required increase in the average weekly commission from the first 5 weeks to the last 2 weeks = 365-64 = 301.
Since 301 is a little less than 500% of 64, the correct answer is E.

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