vishu1414 wrote:

Are all of the terms in Set A equal?

(1) The sum of all 14 terms in Set A is 98.

(2) The sum of any 3 terms in Set A is 21.

OFFICIAL SOLUTION

C. Statement 1 gives us the number of terms and the sum of those terms. Since 98/14 = 7, the set certainly could contain 14 instances of 7, but it could also contain 4 7’s, 5 8’s, and 5 6’s. Insufficient. Statement 2 tells us that any 3 terms add to 21. This again is not sufficient on its own - but it might be closer than you think. If Set A only had three terms, then the terms could be any set that adds to 21 (for example, 18, 2, and 1). But if Set A has more than three terms, the only way for any three of them to add to 21 would be if they were all 7. Otherwise, consider the set: 7, 7, 3, 11. The sum of 7, 3, and 11 is 21, but the sum of 7, 7, and 3 is not, nor is 7 + 7 + 11. So the two statements together are sufficient - statement 1 guarantees that the set has more than 3 terms, and statement 2 then guarantees that they all must be the same.

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