BTGModeratorVI wrote: ↑

Wed Jan 06, 2021 8:02 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: A
Source: Veritas Prep

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