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D01-03

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Bunuel
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D01-03 [#permalink] New post   16 Sep 2014, 00:11
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E

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Question Stats:

65% (01:24) correct 35% (01:34) wrong based on 250 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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E
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Bunuel
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Re D01-03 [#permalink] New post   16 Sep 2014, 00:11
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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.


Answer: E
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Re: D01-03 [#permalink] New post   22 Nov 2014, 12:13
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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Bunuel
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Re: D01-03 [#permalink] New post   23 Nov 2014, 05:57
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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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Re: D01-03 [#permalink] New post   17 Jul 2016, 10:39
I think this is a high-quality question and I agree with explanation.
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pavanbatra
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Re: D01-03 [#permalink] New post   19 Mar 2021, 13:03
I think this is a high-quality question and I agree with explanation.

Posted from my mobile device
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Re: D01-03 [#permalink] New post   25 Dec 2022, 22:00
I think this is a high-quality question and I agree with explanation. Should Have got it correct
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D01-03 [#permalink] New post   12 May 2023, 09:09
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re D01-03 [#permalink] New post   09 Aug 2023, 10:39
I think this is a high-quality question and I agree with explanation.
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Re D01-03 [#permalink] New post   10 Mar 2024, 02:32
I think this is a high-quality question and I agree with explanation.
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Re D01-03 [#permalink]
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