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D01-03

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D01-03  [#permalink]

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New post 16 Sep 2014, 00:11
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

63% (01:24) correct 37% (01:30) wrong based on 152 sessions

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Re D01-03  [#permalink]

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New post 16 Sep 2014, 00:11
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.


Answer: E
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Re: D01-03  [#permalink]

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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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Re: D01-03  [#permalink]

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New post 23 Nov 2014, 05:57
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Re D01-03  [#permalink]

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New post 17 Jul 2016, 10:39
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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New post 12 Sep 2016, 10:40
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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Re: D01-03  [#permalink]

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New post 12 Sep 2016, 10:42
My bad. Didn't read the question properly. Please ignore my above message.
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Re: D01-03  [#permalink]

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New post 07 Dec 2017, 22:12
Hi Bunuel,
It says x is a positive number.So can we take x=1/4??

Thanks
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Re: D01-03  [#permalink]

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New post 07 Dec 2017, 22:38
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Re: D01-03  [#permalink]

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New post 21 Oct 2018, 18:51
How can you prove statement 1 is false? Anything attached with a radical is not even?
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Re: D01-03  [#permalink]

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New post 05 Mar 2019, 08:22
Hi everyone

I have doubt for this question.

Its given x is positive number and not positive integer.

In this case if we consider, x = 3/2, then a = 3/2*(sqrt(3/2) - 1) = 1.5*(1.22..- 1) = 1.5*0.22.. which means a is positive which is option II but correct answer is "none of the above"...am I missing something here..Please explain.

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Re: D01-03  [#permalink]

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New post 05 Mar 2019, 08:39
SWAPNILP wrote:
Hi everyone

I have doubt for this question.

Its given x is positive number and not positive integer.

In this case if we consider, x = 3/2, then a = 3/2*(sqrt(3/2) - 1) = 1.5*(1.22..- 1) = 1.5*0.22.. which means a is positive which is option II but correct answer is "none of the above"...am I missing something here..Please explain.

Thanks


Note that we are asked "which of the following MUST be true", not COULD be true. ct answer. While II COULD be true it's not always true, so it's not a "MUST be true statement".
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Re: D01-03   [#permalink] 05 Mar 2019, 08:39
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