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# Last year the average (arithmetic mean) salary of the 10

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Manager
Joined: 13 Dec 2005
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Last year the average (arithmetic mean) salary of the 10 [#permalink]  02 Dec 2006, 07:07
00:00

Difficulty:

25% (medium)

Question Stats:

70% (01:39) correct 30% (00:33) wrong based on 90 sessions
Last year the average (arithmetic mean) salary of the 10 employees of Company X was $42,800. What is the average salary of the same 10 employees this year? 1) For 8 of the 10 employees, this year's salary is 15 percent greater than last year's salary. 2) For 2 of the 10 employees, this year's salary is the same as last year's salary. Official Guide 12 Question  Question: 46 Page: 26 Difficulty: 700 Find All Official Guide Questions Video Explanations: [Reveal] Spoiler: OA  Kaplan Promo Code Knewton GMAT Discount Codes Manhattan GMAT Discount Codes Senior Manager Joined: 20 Feb 2006 Posts: 373 Followers: 1 Kudos [?]: 2 [0], given: 0 [#permalink] 02 Dec 2006, 07:21 E for me From 1) Depending on which two employees didn't get 15% increase would affect the overall total. Eg if top two salaries didn't get the 15% increase then it would yield a lower total and hence average than if the bottom two salaries didn't get a 15% increase. INSUFF From 2) This tells us even less than 1). What % change in salary did others get? Which two salaries didn't get increase? INSUFF Together, Still dont know which two employees didn't get increase and the respective salaries of the others. Director Affiliations: FRM Charter holder Joined: 02 Dec 2006 Posts: 736 Schools: Stanford, Chicago Booth, Babson College Followers: 8 Kudos [?]: 35 [0], given: 4 [#permalink] 02 Dec 2006, 07:21 Straight E. If they were to mention in the second statement that, these 2 are excluding those 8, then something is possible. Manager Joined: 13 Dec 2005 Posts: 64 Followers: 1 Kudos [?]: 4 [0], given: 0 Explanation? [#permalink] 02 Dec 2006, 07:23 Can you please explain why? From statement 1 wouldn't you know that for 8 of the 10 employees, the salary is now$49,220 (42,800 * 1.15)...and from statement 2 you would know that the salary of the remaining 2 is (still) 42,800? Thus you could do:

(49220*8) + (42800*2)
--------------------------- = average salary
10

..and thus the answer would be C. How is that wrong?
Senior Manager
Joined: 20 Feb 2006
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aurobindo wrote:
Straight E.

If they were to mention in the second statement that, these 2 are excluding those 8, then something is possible.

It still wouldn't help - taking both together we know that 8 got 15% increase but 2 got no increase (or loss). However, we'd still need to know where in the range of salaries those two employees were.

Eg.
Take a set of numbers 2,3,5,6 Mean = 4

If you double the lowest 3 numbers you get 4,6,10,6 Mean = 6.5
If you double the highest 3 numbers you get 2,6,10,12 Mean = 7.5

So simply knowing that x number of employees got/didn't get an increase doesn't help
Director
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Last year the average (arithmetic mean) salary of the 10 employees of Company X was \$42,800. What is the average salary of the same 10 employees this year?

1) For 8 of the 10 employees, this year's salary is 15 percent greater than last year's salary.

2) For 2 of the 10 employees, this year's salary is the same as last year's salary.

Let the salaries of the 10 be a1, a2...a10

given: 42800 = (a1+a2+..+a10)/10 => sum(a1...+a10) = 428000
also: a1+a2..a8 = (42800)-(a9+a10)

also given: a1(year2) = 1.15a1..similarly till a8

1.15a1+1.15a2.....1.15a8 = (a1...a8)+0.15(a1...a8)

from 2:

a9, a10 is same

combining
(a1+a2...a8)+a9+a10 + 0.15(a1...a8)/10

still cannot be determined. So E
Manager
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Location: Denver, CO
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Re: OG Data Sufficiency average problem [#permalink]  19 Apr 2010, 18:15
I'm really sorry to bump such an old thread but qant to play devil's advocate with this question.
If statement 2 stated that the lowest two salaries of the ten employees stayed the same, then the both of the statements together would be sufficient correct?

The average of the salaries would be ((42800*2)+(1.15*42800*8))/10= 47936
Current Student
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Re: OG Data Sufficiency average problem [#permalink]  20 Apr 2010, 12:26
You have no information on what the lowest 2 salaries were, just that the average was 42,800. What you assumed was the extra information tells us that the two lowest salaries stayed the same is not equivalent to they were the average values.
Re: OG Data Sufficiency average problem   [#permalink] 20 Apr 2010, 12:26
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