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by jaspreetsra » Mon Jan 05, 2015 10:29 pm
If ⌈x⌉ denotes the least integer greater than or equal to x, is ⌈x⌉ = 0?
(1) -1<x<1
(2) x<0
Need help for this question.
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Source: — Data Sufficiency |
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by MartyMurray » Mon Jan 05, 2015 11:16 pm
jaspreetsra wrote:If ⌈x⌉ denotes the least integer greater than or equal to x, is ⌈x⌉ = 0?
(1) -1<x<1
(2) x<0
Need help for this question.
Statement 1 tells us that x could be fractionally below 0, which would make ⌈x⌉ = 0. x could also be 0, which would create ⌈x⌉ = 0. x could also be fractionally above 0, which would result in ⌈x⌉ = 1. So this creates two results.

Insufficient

Statement 2 tells us that x can be any number below 0 and so ⌈x⌉ can be any integer <= 0.

Insufficient

Combined we know that the minimum is 0, from Statement 1, and the maximum is 0, from Statement 2.

Sufficient

Choose C.

Wasn't so tough. Maybe you need to have more confidence in yourself and be a little more determined to figure 'em out.
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by [email protected] » Mon Jan 05, 2015 11:49 pm
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

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by Brent@GMATPrepNow » Tue Jan 06, 2015 12:48 am
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
Brent Hanneson - Creator of GMATPrepNow.com
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by ceilidh.erickson » Wed Jan 07, 2015 8:32 am
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
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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