fiza gupta wrote:If [x] denotes the largest integer smaller than x, is [x] > [−x]?
(1) x = [x] + 1
(2) x + 1 > 0
OA:E
Before testing values, it's often helpful to translate the question into words. When the GMAT says "[x] denotes the largest integer smaller than x," what they really mean is "round down (to the left on the number line) to the nearest integer."
So when would [x] > [−x]? When would the rounded-down-integer from x be greater than the rounded-down-integer from -x? When x is positive, and -x is negative. (If x = 0, then both x and -x would round down to -1).
Target question: is x > 0?
(1) x = [x] + 1
If x is 1 greater than the rounded-down-integer from x, this simply tells us that x is any integer. For example,
if x = 3, [x] = 2
if x = -5, [x] = -6
This is insufficient to answer our target question.
(2) x + 1 > 0
Rearrange:
x > -1
Since our target question is "is x positive?", this is insufficient. If x = -0.5, we'd get a "no" answer to our question, but if x = 2, we'd get a "yes" answer.
1 & 2 combined
With the two statements together, we know that x is an integer greater than -1. This might seem at first to answer our question, but remember to consider 0:
if x = 0, [x] = -1 and [-x] = -1. So the answer to our question is "no."
if x = 4, [x] = 3 and [-x] = -5, so the answer is "yes."
Insufficient. The answer is
E.
