Question 2

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bacali: Master | Next Rank: 500 Posts; Posts: 245; Joined: Thu Aug 16, 2007 12:41 pm

by bacali » Sat Nov 29, 2008 7:04 am

The average (arithmetic mean) score on a test taken by 10 students was x. If the average score for 5 of the students was 8, what was the average score, in terms of x, for the remaining 5 students who took the test?

A. 2x - 8
B. x - 4
C. 8 - 2x
D. 16 - x
E. 8 - x/2

A

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Source: Beat The GMAT — Problem Solving | Sat Nov 29, 2008 7:04 am

dmateer25: Community Manager; Posts: 1049; Joined: Sun Apr 06, 2008 5:15 pmFollowed by: 27 members; Location: Pittsburgh, PA; Thanked: 113 times; GMAT Score:710

by dmateer25 » Sat Nov 29, 2008 7:10 am

x= average

10x = the total score for all students

total score for 5 students with an average of 8 is 5 * 8 = 40

10x-40 is the total score for the 5 remaining students

(10x-40)/5 = average of the remaining 5 students

2x-8 = average

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iamcste: Legendary Member; Posts: 940; Joined: Tue Aug 26, 2008 3:22 amFollowed by: 1 member; Thanked: 55 times

Re: Question 2

by iamcste » Sat Nov 29, 2008 7:13 am

bacali wrote:The average (arithmetic mean) score on a test taken by 10 students was x. If the average score for 5 of the students was 8, what was the average score, in terms of x, for the remaining 5 students who took the test?

A. 2x - 8
B. x - 4
C. 8 - 2x
D. 16 - x
E. 8 - x/2

A

x= [ 5*8 + (total marks of 5 students)]/ 10

5* 8 would be total marks of 5 students whose marks are known

10x-40= total marks of 5 students

hence average= 10x-40/5

=2x-8

IMO A

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Sat Nov 29, 2008 11:28 am

This is weighted average concept.

Let k be the average of the 5 students that we need to find

Average mark x is =

5*8 + 5 * k / 10 = x

40+5k = 10x
8+k=2x
k=2x-8

A)

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jnellaz: Master | Next Rank: 500 Posts; Posts: 114; Joined: Mon Oct 20, 2008 7:03 pmFollowed by: 5 members; Thanked: 4 times

by jnellaz » Tue Dec 02, 2008 7:51 am

I backsolved this one. So..

For the average score of the REMAINING 5 students I chose 9. The average of the total 10 students would be:

Average of first 5 students: 8 which is 5 * 8 = 40
Average of remaining 5 students 9 which is 5 * 9 = 45

So the average for all 10 students is 85/10 or 8.5. Thus our x is 8.5.

Starting with the answer choices we substitue 8.5 with x to see which answer choice will give us 9 as the answer. (Average of remaining students):

A. is the only solution that gives us 9.

2(8.5) - 8 = 17 - 8 = 9.

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jmm2: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Tue Dec 02, 2008 1:30 pm; Location: Boston, MA

by jmm2 » Tue Dec 02, 2008 2:55 pm

I backsolved as well..

If half of the students scores averaged 8, pretend the other half averaged 12 so that x = 10, an easy number to work with. Solve each of the equations with x = 10 and see which answer gives you 12 as a solution.

A. 2(10) - 8 = 12 < YES
B. (10) - 4 = 6
C. 8 - 2(10) = -12
D. 16 - (10) = 6
E. 8 - (10)/2 = 3

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8137; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Fri Dec 08, 2017 6:43 am

bacali wrote:The average (arithmetic mean) score on a test taken by 10 students was x. If the average score for 5 of the students was 8, what was the average score, in terms of x, for the remaining 5 students who took the test?

A. 2x - 8
B. x - 4
C. 8 - 2x
D. 16 - x
E. 8 - x/2

We are given that the average score on a test taken by 10 students was x and need to find the average score in terms of x if the average score for 5 of those students was 8.

Thus, the overall sum was 10x and the sum for the 5 students was (5)(8)= 40.

We need to determine the average of the 5 remaining students.

The sum for the 5 remaining students was 10x - 40, and thus the average is:

(10x - 40)/5 = 10x/5 - 40/5 = 2x - 8

Answer: A

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