Hi fiza gupta,

This DS question can be solved by TESTing VALUES.

We're told that [X] = the largest integer that is SMALLER than X. We're asked if [X] > [-X]. This is a YES/NO question.

1) X = [X] + 1

IF....
X = 1
[1] = 0 and 1 = 0+1
[-1] = -2 and the answer to the question is YES.

IF....
X = 0
[0] = -1 and 0 = -1+1
[-0] = -1 and the answer to the question is NO.
Fact 1 is INSUFFICIENT

2) X + 1 > 0

Both of the TESTs that I used in Fact 1 also 'fit' the information in Fact 2....

IF....
X = 1
[1] = 0 and 1 = 0+1
[-1] = -2 and the answer to the question is YES.

IF....
X = 0
[0] = -1 and 0 = -1+1
[-0] = -1 and the answer to the question is NO.
Fact 2 is INSUFFICIENT

Combined, we already have two TESTs that fit both Facts - and we have two different answers to the given question.
Combined, INSUFFICIENT

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

Here are two similar questions to practice with:
- https://www.beatthegmat.com/ds-t276593.html
- https://www.beatthegmat.com/number-prope ... 71768.html

Cheers,
Brent

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.

And since the GMAT really loves this construction, here's another one to add to Brent's list:
https://www.beatthegmat.com/ds-t281646.html#738122