musabber wrote:
If [x] denotes the greatest integer less than or equal to x, is [x] = 0 ?
(1) 5x + 1 = 3 + 2x
(2) 0 < x < 1
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.
The answer is D.
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