DS

Hi jaspreetsra,

This DS question is an example of a Symbolism question. In Symbolism questions, you'll be given a "made up" math symbol to work with and a description of how the Symbol "works." You'll then be asked to perform a calculation using the symbol.

Here, we're told that [X] is the LEAST INTEGER that is GREATER THAN OR EQUAL to X. We're asked if [X] = 0? This is a YES/NO question.

Before we get into the 2 Facts, here are some examples of how this Symbol works:

[2] = 2 since 2 is the LEAST integer that is greater than or equal to 2.
[1/2] = 1
[-2.5] = -2

Fact 1: -1 < X < 1

Here, we can TEST VALUES.

IF....
X = 0, then [0] = 0 and the answer to the question is YES.
X = 1/2, then [1/2] = 1 and the answer to the question is NO.
Fact 1 is INSUFFICIENT

Fact 2: X < 0

IF...
X = -1, then [-1] = -1 and the answer to the question is NO.
X = -1/2, then [-1/2] = 0 and the answer to the question is YES.
Fact 2 is INSUFFICIENT

Combined, we know that...
-1 < X < 1
X < 0

So we have a range of.....
-1 < X < 0

This means that X is a NEGATIVE FRACTION. According to the Symbol, no matter what negative fraction we use for X, the LEAST INTEGER that is greater than or equal to X will be 0 EVERY TIME. Thus, the answer to the question is ALWAYS YES.
Combined, SUFFICIENT.

Final Answer: C

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

Hi jaspreetsra,

Now that you've seen a couple of approaches, here are two more questions to practice with:
- https://www.beatthegmat.com/ds-t276593.html
- https://www.beatthegmat.com/number-prope ... 71768.html

Cheers,
Brent

The constructions "least integer greater than or equal to x" and "greatest integer less than or equal to x" are quite common on the GMAT. The key is to translate these into common English:

"[x] is the least integer greater than or equal to x" --> if x is an integer, then [x] just equals x itself. If x is a non-integer, then we ROUND UP to the nearest integer: [2.3] = 3

"[x] is the greatest integer less than or equal to x" --> if x is an integer, then [x] again just equals x itself. If x is a non-integer, then we ROUND DOWN to the nearest integer: [2.3] = 2

In OG13, see PS 156 and DS 104. And see this post: https://www.beatthegmat.com/ds-t276593.html#719492