BTGModeratorVI wrote: ↑

Mon Sep 07, 2020 7:04 am

Set S consists of n consecutive integers, where n > 1. What is the value of n?

(1) The sum of the integers in Set S is divisible by 7.
(2) The sum of the integers in Set S is 14.

Answer: E
Source: Manhattan prep

Given: Set S consists of n consecutive integers, where n > 1.

Target question: What is the value of n?

IMPORTANT: Notice that the two statements are VERY SIMILAR. That is, if the sum of the values is 14 (statement 2), then it is guaranteed that the sum is divisible by 7 (statement 1).
So, let's start with statement 2.

Statement 2: The sum of the integers in set S is 14.
Let's TEST some values.
Here are two cases that satisfy statement 2:
Case a: set S = {2, 3, 4, 5}. In this case, the answer to the target question is n = 4
Case b: set S = {-1, 0, 1, 2, 3, 4, 5}. In this case, the answer to the target question is n = 7
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statement 1: The sum of the integers in set S is divisible by 7.
Notice that we can reuse the same cases we used for statement 2:
Case a: set S = {2, 3, 4, 5}. In this case, the answer to the target question is n = 4
Case b: set S = {-1, 0, 1, 2, 3, 4, 5}. In this case, the answer to the target question is n = 7
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient.
So, the same counter-examples will satisfy the two statements COMBINED.
In other words,
Case a: set S = {2, 3, 4, 5}. In this case, the answer to the target question is n = 4
Case b: set S = {-1, 0, 1, 2, 3, 4, 5}. In this case, the answer to the target question is n = 7
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent