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Question on Algebra in Data Sufficiency

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Question on Algebra in Data Sufficiency

by bsa5360 » Tue Mar 05, 2013 9:13 am
Hello All,

I hope this is not a duplicate query.

Question no. 96 of data sufficiency in the 13th edition of OG is

96. If [x] denotes the least integer greater than or equal to x, is [x]=0?
(1) -1 < x < 1
(2) x < 0

According to the OG, the answer is C (both statements are required)

In my opinion, the second statement depicts that [x] can never be equal to 0 which answers the question i.e. is [x]=0? The answer is No and the answer in this case will be B.

Please clarify.

Siddharth.
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by Anurag@Gurome » Tue Mar 05, 2013 9:22 am
bsa5360 wrote:If [x] denotes the least integer greater than or equal to x, is [x]=0?
(1) -1 < x < 1
(2) x < 0
Statement 1: Consider the following two cases,
x = 0.5 ---> [x] = 1
x = -0.5 ---> [x] = 0

Not sufficient

Statement 2: Consider the following two cases,
x = -0.5 ---> [x] = 0
x = -1 ---> [x] = -1

Not sufficient

1 & 2 Together: Now, we know that x is greater than -1 but less than 0.
Hence, the least integer greater than or equal to x will always be equal to 0.

Sufficient

The correct answer is C.
bsa5360 wrote:In my opinion, the second statement depicts that [x] can never be equal to 0 which answers the question i.e. is [x]=0? The answer is No and the answer in this case will be B.
Why not?
For example, for x = -0.5 (or any x between -1 and 0) the integers greater than or equal to x are 0, 1, 2, 3, etc. Among them 0 is the smallest. Hence, [x] = 0
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by GMATGuruNY » Tue Mar 05, 2013 12:47 pm
bsa5360 wrote: If [x] denotes the least integer greater than or equal to x, is [x]=0?
(1) -1 < x < 1
(2) x < 0
To visualize the required range more easily, draw a NUMBER LINE.

.........-1...............0..........

If x is WITHIN the red portion, then the least integer value greater than or equal to x is 0.
If x is OUTSIDE the red portion, then the least integer value greater than or equal to x is NOT 0.

Question rephrased: Is x within the red portion?

Statement 1: -1 < x < 1
x could be within the red portion or outside it.
INSUFFICIENT.

Statement 2: x < 0.
x could be within the red portion or outside it.
INSUFFICIENT.

Statements combined:
-1 < x < 0.
Thus, x is within the red portion.
SUFFICIENT.

The correct answer is C.
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by bsa5360 » Sat Mar 09, 2013 9:07 am
Thank you for taking the time to clarify.

My mistake was thinking [x] is an integer LESSER THAN or equal to x.

Regards,
Siddharth Acharya
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