# GMAT OFFICIAL GUIDE DS – If ⌈x⌉ denotes the least integer…

## Solution:

We are given that ⌈x⌉ denotes the least integer greater than or equal to x. We must determine whether ⌈x⌉ = 0.

Statement One Alone:

-1 < x < 1

From the information in statement one we know that x is a positive or negative proper fraction, or zero. Let’s test a few examples for x.

If x = 1/2, then ⌈x⌉ = ⌈1/2⌉= 1.

⌈1/2⌉ = 1 because 1 is the least integer greater than or equal to ½.

If x = -1/2, then ⌈x⌉ = ⌈-1/2⌉= 0.

⌈-1/2⌉ = 0 because 0 is the least integer greater than or equal to -½.

Statement one is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

x < 0

Simply knowing that x is less than zero is not enough information to determine whether ⌈x⌉ = 0.  We can eliminate answer choice B.

Statements One and Two Together:

Using the information in statements one and two we know that x must be a negative proper fraction. That is, -1 < x < 0. Thus, regardless of which negative proper fraction we select for x, 0 will always be the least integer greater than or equal to x. Thus ⌈x⌉ = 0.