What is the average of the terms in set J? (1) The sum of a

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Thu Oct 08, 2015 10:08 am

What is the average of the terms in set J?

(1) The sum of any three terms in set J is 21.
(2) Set J consists of 12 total terms.

Answer: option A

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Source: Beat The GMAT — Data Sufficiency | Thu Oct 08, 2015 10:08 am

GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Thu Oct 08, 2015 10:09 am

GMATinsight wrote:What is the average of the terms in set J?

(1) The sum of any three terms in set J is 21.
(2) Set J consists of 12 total terms.

Answer: option A

Question : What is the average of the terms in set J?

Statement 1: The sum of any three terms in set J is 21.
this is possible only when all the terms in the set are 7 or when there are only three terms with sum of them as 21
in both cases the average of terms will be 7. hence
SUFFICIENT

Statement 2: Set J consists of 12 total terms
There is no information about sum of the terms. Hence,
NOT SUFFICIENT

Answer: option A

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu Oct 08, 2015 11:11 am

GMATinsight wrote:What is the average of the terms in set J?

(1) The sum of any three terms in set J is 21.
(2) Set J consists of 12 total terms.

Target question: What is the average of the terms in set J?

Statement 1: The sum of any three terms in set J is 21.
This is a very powerful statement, because it tells us that all of the numbers in the set are equal.
Let's let a,b and c be three of the numbers in set J.
We know that a + b + c = 21
Notice that if I replace ANY of these three values (a,b or c) with d, the sum must still be 21.
This tells us that a, b and c must all equal d.
Using similar logic, I can show that ALL of the numbers in the set must equal d, which means all of the numbers in the set must be equal.
If all of the numbers are equal, then EVERY number must equal 7, which means the average of set J MUST equal 7
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: Set J consists of 12 total terms
There are several possible scenarios that satisfy this statement. Here are two.
Case a: J = {2,2,2,2,2,2,2,2,2,2,2,2}, in which case the average of set J = 2
Case b: J = {1,1,1,1,1,1,1,1,1,1,1,1}, in which case the average of set J = 1
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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