If ⌈x⌉ denotes the least integer…
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.