## If k is an integer…

## Solution:

We are given that k is between 56 and 66. We must determine the value of k.

**Statement One Alone: **

If k were divided by 2, the remainder would be 1.

This means k must be an odd number. However, since 56 < k < 66, k can be any odd integer between 56 and 66, which means that k could be 57, 59, 61, 63, or 65. Statement one is not sufficient to determine a value of k. We can eliminate answer choices A and D.

**Statement Two Alone: **

If k + 1 were divided by 3 the remainder would be 0.

This means k + 1 is a multiple of 3. However, since 56 < k < 66, there is more than one value between 56 and 66 that, when increased by 1, will be a multiple of 3. For example, since 60, 63 and 66 are all multiples of 3, we see that k could be 59, 62 or 65. Since we have three possible values for k, statement two is not sufficient to answer the question. We can eliminate answer choice B.

**Statements One and Two Together: **

From statement one we know that k can be 57, 59, 61, 63, or 65, and from statement two we know that k could be 59, 62 or 65. From the combined statements, then, k could be either 59 or 65; thus, we can’t determine a unique value for k. Statements one and two together are not sufficient to answer the question.

**Answer:** E