Statement 1: The sum of all 14 terms in List A is 98.himu wrote:Are all of the terms in List A equal?
The sum of all 14 terms in List A is 98.
The sum of any 3 terms in List A is 21.
Average of all 14 terms = 98/14 = 7.
It's possible that the terms are 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, in which case all 14 terms are equal.
It's possible that the terms are 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 8, in which case all 14 terms are NOT equal.
INSUFFICIENT.
Statement 2: The sum of any 3 terms in List A is 21.
It's possible that the terms are 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, in which case all 14 terms are equal.
Now let's see whether we can change one of the numbers:
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6?
Doesn't work, because 7+7+6 = 20, and the sum of ANY 3 NUMBERS must be 21.
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8?
Doesn't work, because 7+7+8 = 22, and the sum of ANY 3 NUMBERS must be 21.
If we change even ONE of the numbers, statement 2 is not satisfied.
The implication:
To satisfy statement 2 -- to ensure that the sum of ANY 3 NUMBERS will be 21 -- all of the numbers must be 7.
Since all of the numbers must be equal, SUFFICIENT.
The correct answer is B.
In the question stem and in the statements, I've replaced Set A with List A.
A SET is a collection of DISTINCT elements.
The GMAT typically refers to a collection of non-distinct elements as a LIST.
