Solutions

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Question

If T is a list of consecutive integers in increasing order, what is the sum of integers in T?

I. The difference between the last integer in T and the first integer in T is 100.

II. The fourth integer in T is -6


 

Option A:

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Option B:

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

Option C:

BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

Option D:

EACH statement ALONE is sufficient to answer the question asked.

Option E:

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Difficulty Level

Easy

Solution

Option C is the correct answer.


Option Analysis

Statement I is insufficient: The difference between the last integer in T and the first integer in T is 100. This implies that there are 101 integers in the list. T could be any list of 101 consecutive integers. For example, {0, 1, 2, …, 100} or {1, 2, 3, …, 101}. Not sufficient.

Statement II is insufficient: The fourth integer in T is -6. This implies that the first integer is -9. We don’t know how many integers are there in the list, hence cannot get the sum. Not sufficient.

Together I and II, We know that the first integer is -9 and that there are total of 101 integers in the list: T = {-9, -8, -7, -6, …, 91}. We can get the sum. Sufficient.