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# D01-03

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Math Expert
Joined: 02 Sep 2009
Posts: 52971

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15 Sep 2014, 23:11
00:00

Difficulty:

45% (medium)

Question Stats:

61% (00:52) correct 39% (00:49) wrong based on 230 sessions

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If $$x$$ is a positive number and $$a=\sqrt{x} * x - x$$, which of the following must be true?

I. $$a$$ is even

II. $$a$$ is positive

III. $$a$$ is an integer

A. I only
B. II only
C. III only
D. I and II
E. None of the above

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Math Expert
Joined: 02 Sep 2009
Posts: 52971

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15 Sep 2014, 23:11
Official Solution:

If $$x$$ is a positive number and $$a=\sqrt{x} * x - x$$, which of the following must be true?

I. $$a$$ is even

II. $$a$$ is positive

III. $$a$$ is an integer

A. I only
B. II only
C. III only
D. I and II
E. None of the above

Note that we are asked "which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.

If $$x=\frac{1}{4}$$ then $$a=\sqrt{x} * x - x=\frac{1}{2}*\frac{1}{4}-\frac{1}{4}=-\frac{1}{8}$$. Now, $$-\frac{1}{8}$$ is not an integer at all (hence not even) and also not positive, so none of the options MUST be true.

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Joined: 22 Jul 2014
Posts: 21
GMAT 1: 450 Q38 V12
WE: Information Technology (Computer Software)

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22 Nov 2014, 11:13
Hi Bunnel,

A very basic question can fractions be classified as even / odd. Sry if it is very basic. Got a sudden doubt in the test.
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Failures are stepping stones to success !!!

Math Expert
Joined: 02 Sep 2009
Posts: 52971

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23 Nov 2014, 04:57
prashd wrote:
Hi Bunnel,

A very basic question can fractions be classified as even / odd. Sry if it is very basic. Got a sudden doubt in the test.

No, only integers can be even or odd. Even number is an integer which is divisible by 2 without a remainder and an odd number is an integer which when divided by 2 gives the remainder of 1.
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Joined: 23 Apr 2014
Posts: 63
Location: United States
GMAT 1: 680 Q50 V31
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17 Jul 2016, 09:39
I think this is a high-quality question and I agree with explanation.
Intern
Joined: 11 Aug 2016
Posts: 2
GMAT 1: 680 Q50 V32
GPA: 3.64

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12 Sep 2016, 09:40
Hi Bunuel,

I don't go with the explanation provided for the question. As per the question , x is a positive integer . But, the explanation failed to consider this condition.
For all positive integers(except 1) , the value of a is positive.

Can the explanation be corrected as stated.

Regards,
Harish Ramnath
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Joined: 11 Aug 2016
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GMAT 1: 680 Q50 V32
GPA: 3.64

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12 Sep 2016, 09:42
Intern
Joined: 15 Aug 2013
Posts: 40

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07 Dec 2017, 21:12
Hi Bunuel,
It says x is a positive number.So can we take x=1/4??

Thanks
Abhi
Math Expert
Joined: 02 Sep 2009
Posts: 52971

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07 Dec 2017, 21:38
abhinashgc wrote:
Hi Bunuel,
It says x is a positive number.So can we take x=1/4??

Thanks
Abhi

Yes, because 1/4 is a positive number. Notice that we are told that x is a positive number, not a positive integer.
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Joined: 14 Aug 2012
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21 Oct 2018, 17:51
How can you prove statement 1 is false? Anything attached with a radical is not even?
Re: D01-03   [#permalink] 21 Oct 2018, 17:51
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# D01-03

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