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# GMAT Diagnostic Test Question 3

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Re: GMAT Diagnostic Test Question 3 [#permalink]

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19 Sep 2012, 21:07
Tried with 1 , 2 and 0 so anwer will be 0 as its neither positive nor negative...(neutral infact), hence E the answer.
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Re: GMAT Diagnostic Test Question 3 [#permalink]

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20 Sep 2012, 03:18
bb wrote:
GMAT Diagnostic Test Question 3
Field: Arithmetic, Roots
Difficulty: 700-750
 Rating:

If $$x$$ is an integer and $$\sqrt{x} * x - x = a$$ , 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

BELOW IS REVISED VERSION OF THIS QUESTION:

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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Re: GMAT Diagnostic Test Question 3 [#permalink]

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01 Oct 2012, 04:43
agree for Not integer , +ve but how we can prove for EVEN ??
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Re: GMAT Diagnostic Test Question 3 [#permalink]

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01 Oct 2012, 05:08
archit wrote:
agree for Not integer , +ve but how we can prove for EVEN ??

Check revised version of this question with a solution here: gmat-diagnostic-test-question-79331-20.html#p1123418

Hope it helps.
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Re: GMAT Diagnostic Test Question 3 [#permalink]

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01 Oct 2012, 07:31
archit wrote:
agree for Not integer , +ve but how we can prove for EVEN ??

If a number is not an integer, then for sure is not even. The question asks "...must be true?"
So, if the number can be a non-integer, it means that it can be not even.
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Re: GMAT Diagnostic Test Question 3 [#permalink]

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13 Oct 2012, 01:32
cant we change the eqaution like this..

a+x=X*square root x..

AND then..

a/x+1=sqaure root of x..

ans will be E..because a and x cud b any num..
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Re: GMAT Diagnostic Test Question 3 [#permalink]

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13 Oct 2012, 04:35
sanjoo wrote:
cant we change the eqaution like this..

a+x=X*square root x..

AND then..

a/x+1=sqaure root of x..

ans will be E..because a and x cud b any num..

You cannot divide an equation by $$x,$$ unless you know that $$x$$ is non-zero.
In the original question, $$x$$ was given as an integer, so it can be 0.
In the revised question (by Bunuel), $$x$$ was given as a positive integer, therefore in this case, you are allowed to divide by $$x,$$ because now you are sure that $$x$$ cannot be 0.

It is not clear why from the equation $$\sqr{x}=1+\frac{a}{x}$$ it is (more) evident that $$a$$ and $$x$$ could be any number.
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Re: GMAT Diagnostic Test Question 3 [#permalink]

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13 Oct 2012, 04:47
bb wrote:
GMAT Diagnostic Test Question 3
Field: Arithmetic, Roots
Difficulty: 700-750
 Rating:

If $$x$$ is an integer and $$\sqrt{x} * x - x = a$$ , 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

The question asks for statements that must be true. There are infinitely many positive numbers. The question is whether $$a$$ can be 0? The answer is YES!
The smallest possible value for $$x$$ is 1, for which $$a = 0.$$ So, definitely, statement II must not necessarily be true.

Choosing $$x=2$$, we obtain $$a=2(\sqr{2}-1),$$ which evidently is not an integer. Not being an integer, for sure is not an even number.
We can immediately deduce that neither III, nor I must be true.

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Re: GMAT Diagnostic Test Question 3 [#permalink]

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13 Oct 2012, 04:53
Bunuel wrote:
bb wrote:
GMAT Diagnostic Test Question 3
Field: Arithmetic, Roots
Difficulty: 700-750
 Rating:

If $$x$$ is an integer and $$\sqrt{x} * x - x = a$$ , 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

BELOW IS REVISED VERSION OF THIS QUESTION:

If $$x$$ is a positive integer 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.

$$x=\frac{1}{4}$$ is not an integer.
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Re: GMAT Diagnostic Test Question 3 [#permalink]

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13 Oct 2012, 06:49
EvaJager wrote:
Bunuel wrote:
bb wrote:
GMAT Diagnostic Test Question 3
Field: Arithmetic, Roots
Difficulty: 700-750
 Rating:

If $$x$$ is an integer and $$\sqrt{x} * x - x = a$$ , 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

BELOW IS REVISED VERSION OF THIS QUESTION:

If $$x$$ is a positive integer 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.

$$x=\frac{1}{4}$$ is not an integer.

There was a typo. It should be "if x is a positive number".
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Re: GMAT Diagnostic Test Question 3 [#permalink]

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28 Sep 2013, 23:33
bb wrote:
Explanation:

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.

How can you assume x = 1/4 when the question states that x is an integer?!
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Re: GMAT Diagnostic Test Question 3 [#permalink]

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29 Sep 2013, 12:16
igotthis wrote:
bb wrote:
Explanation:

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.

How can you assume x = 1/4 when the question states that x is an integer?!

There was a typo. It should be "if x is a positive number".

Check here: gmat-diagnostic-test-question-79331-20.html#p1123418
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Re: GMAT Diagnostic Test Question 3 [#permalink]

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04 Oct 2013, 02:45
If $$x$$ is an number and $$\sqrt{x} * x - x = a$$ , 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[/quote]

This question we make assumptions by taking the value of x as follows:-

x * sqrt(x) - x = a.

if we choose x=0,
so lets compute the calculation of it.

a) If x=0, we have a=0.
ie 0 is neither negative nor positive number.

b) If x=4,
4 * 2 - 4 = 8-4 = 4.

c) If x=2, we obtain a=2(\sqr{2}-1), which evidently is not an integer. Not being an integer, for sure is not an even number.
We can immediately deduce that neither III, nor I must be true.

So, we can result the answer is E.
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Re: GMAT Diagnostic Test Question 3 [#permalink]

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22 Oct 2013, 22:26
Kudos to BB!!!
Re: GMAT Diagnostic Test Question 3   [#permalink] 22 Oct 2013, 22:26

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# GMAT Diagnostic Test Question 3

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