A set of 10 numbers has an average (arithmetic mean) of 12. When a subset of numbers, which has an average of 15, is

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members; Thanked: 1 times

by M7MBA » Wed Sep 09, 2020 1:28 am

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A set of 10 numbers has an average (arithmetic mean) of 12. When a subset of numbers, which has an average of 15, is removed from the original set, the sum of the remaining numbers is 60. How many numbers remain from the original set?

A. 3
B. 4
C. 5
D. 6
E. 8

Answer: D

Source: Princeton Review

Source: Beat The GMAT — Problem Solving | Wed Sep 09, 2020 1:28 am

gmatter2012: Master | Next Rank: 500 Posts; Posts: 138; Joined: Sat May 05, 2012 7:03 pm; Thanked: 1 times

Re: A set of 10 numbers has an average (arithmetic mean) of 12. When a subset of numbers, which has an average of 15, is

by gmatter2012 » Fri Sep 11, 2020 4:17 am

M7MBA wrote: ↑
Wed Sep 09, 2020 1:28 am
A set of 10 numbers has an average (arithmetic mean) of 12. When a subset of numbers, which has an average of 15, is removed from the original set, the sum of the remaining numbers is 60. How many numbers remain from the original set?

A. 3
B. 4
C. 5
D. 6
E. 8

Answer: D

Source: Princeton Review

So total is 12*10= 120
After removing certain elements = remaining total is 60
Hence total of 60 was removed . Now since avg is 15 total number of elements removed must be 4 because 15*4 =60
IF 4 elements are removed we should have 8 elements remaining .
Ans- E

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: A set of 10 numbers has an average (arithmetic mean) of 12. When a subset of numbers, which has an average of 15, is

by Scott@TargetTestPrep » Tue Sep 15, 2020 4:45 am

M7MBA wrote: ↑
Wed Sep 09, 2020 1:28 am
A set of 10 numbers has an average (arithmetic mean) of 12. When a subset of numbers, which has an average of 15, is removed from the original set, the sum of the remaining numbers is 60. How many numbers remain from the original set?

A. 3
B. 4
C. 5
D. 6
E. 8

Answer: D

Solution:

We can let the number of numbers removed = n and create the equation:

10 x 12 - 15n = 60

120 - 15n = 60

60 = 15n

4 = n

Since 4 numbers are removed, there are 6 numbers remaining.

Answer: D

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