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20 Mar 2018, 01:20
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
86% (01:29) correct
14%
(02:22)
wrong
based on 128
sessions
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The arithmetic average of 20 numbers is A. The arithmetic average of 10 of the number is 16. In terms of A, what is the arithmetic average of the remaining 10 numbers?
(A) A - 8
(B) 16 - A
(C) 16 - 2A
(D) 2A - 16
(E) 20A - 6
(A) A - 8
(B) 16 - A
(C) 16 - 2A
(D) 2A - 16
(E) 20A - 6
Updated on: 19 Jan 2020, 13:50
Originally posted by BrentGMATPrepNow on 20 Mar 2018, 11:34.
Last edited by BrentGMATPrepNow on 19 Jan 2020, 13:50, edited 1 time in total.
Last edited by BrentGMATPrepNow on 19 Jan 2020, 13:50, edited 1 time in total.
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Bunuel
Here's a different approach.
Let's create a nice set of values that satisfy the given conditions.
Let's say the set of 20 numbers is {16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16}
The arithmetic average of 20 numbers is A
So, A = 16
The arithmetic average of 10 of the numbers is 16
So, the average of {16, 16, 16, 16, 16, 16, 16, 16, 16, 16} is clearly 16
What is the arithmetic average of the remaining 10 numbers?
In other words, what is the arithmetic average of {16, 16, 16, 16, 16, 16, 16, 16, 16, 16}
Well, the average is 16
So, we want an answer choice that yields an OUTPUT of 16 when A = 16
Check the answer choices...
(A) 16 - 8 = 8. No good. We want an output if 16
(B) 16 - 16 = 0. No good. We want an output if 16
(C) 16 - 2(16) = -16. No good. We want an output if 16
(D) 2(16) - 16 = 16. PERFECT!
(E) 20(16) - 6 = 314. No good. We want an output if 16
Answer: D
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General Discussion
20 Mar 2018, 01:35
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Bunuel
Questions involving average and standard deviation can often be solved without explicit calculation, by using the underlying properties.
We'll look for such a solution, a Logical approach.
Since the average of all 20 numbers is A and we divided the numbers into two equal sets, we know they must 'balance out' to reach A.
That is, if the first 10 numbers have an average above A, the second must have an average below A, by the same amount.
So our remaining 10 numbers have an average of A + (A - 16) if A>16 or A - (16 - A) if 16>A
Either way, this comes to 2A - 16.
(D) is our answer.
