Last Updated on May 9, 2023
GMAT OFFICIAL GUIDE DS
Solution:
We need to determine whether [x] = 0 where [x] denotes the greatest integer less than or equal to x. If the rule is hard to follow, let’s use a few examples.
[12.53] = 12, since 12 is the greatest integer less than or equal to 12.53. [-1/2] = -1, since -1 is the greatest integer less than or equal to -1/2. [1/2] = 0, since 0 is the greatest integer less than or equal to 1/2.Using this last example, we know that if x is a positive fraction between zero and one, or is zero itself, the answer will be yes.
Statement One Alone:
5x + 1 = 3 + 2x
Let’s first simplify the equation.
5x + 1 = 3 + 2x
3x = 2
x = 2/3
Since 0 is the greatest integer less than or equal to 2/3, we see that [2/3] = 0.
Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.
Statement Two Alone:
0 < x < 1
Because 0 < x < 1, x is a number between 0 and 1 (but, of course, not including 0 nor 1). Thus, the greatest integer less than or equal to such a number will always be zero. Statement two alone is also sufficient to answer the question.
Answer: D
