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D01-03

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D01-03  [#permalink]

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New post 15 Sep 2014, 23:11
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A
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E

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  35% (medium)

Question Stats:

62% (00:52) correct 38% (00:47) wrong based on 226 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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Re D01-03  [#permalink]

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New post 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.


Answer: E
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Re: D01-03  [#permalink]

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New post 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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Re: D01-03  [#permalink]

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New post 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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re D01-03  [#permalink]

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New post 17 Jul 2016, 09:39
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, 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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Re: D01-03  [#permalink]

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New post 12 Sep 2016, 09:42
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, 21:12
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, 21:38
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Re: D01-03  [#permalink]

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New post 21 Oct 2018, 17:51
How can you prove statement 1 is false? Anything attached with a radical is not even?
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Re: D01-03 &nbs [#permalink] 21 Oct 2018, 17:51
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