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# Is the positive integer x an even number?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4865
GPA: 3.82
Is the positive integer x an even number? [#permalink]

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25 Jan 2018, 03:04
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[GMAT math practice question]

Is the positive integer $$x$$ an even number?

1) The smallest prime factor of $$x$$ is $$3$$.
2) The greatest prime factor of $$x$$ is $$17$$.
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
Posts: 43792
Re: Is the positive integer x an even number? [#permalink]

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25 Jan 2018, 04:31
MathRevolution wrote:
[GMAT math practice question]

Is the positive integer $$x$$ an even number?

1) The smallest prime factor of $$x$$ is $$3$$.
2) The greatest prime factor of $$x$$ is $$17$$.

Almost identical question: https://gmatclub.com/forum/is-a-positiv ... 44435.html
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Math Expert
Joined: 02 Aug 2009
Posts: 5649
Re: Is the positive integer x an even number? [#permalink]

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25 Jan 2018, 05:35
MathRevolution wrote:
[GMAT math practice question]

Is the positive integer $$x$$ an even number?

1) The smallest prime factor of $$x$$ is $$3$$.
2) The greatest prime factor of $$x$$ is $$17$$.

ONLY even prime factor is 2, which also happens to be the smallest prime factor..

1) The smallest prime factor of $$x$$ is $$3$$.
this means x does not have 2 as a factor, so x is ODD
suff

2) The greatest prime factor of $$x$$ is $$17$$.
2 can be a factor or may not be..
insuff

A
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Math Revolution GMAT Instructor
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GPA: 3.82
Re: Is the positive integer x an even number? [#permalink]

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28 Jan 2018, 17:43
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variable (x) and 0 equations, D is most likely to be the answer. So, we should first consider each condition on its own.

Condition 1)
Since all prime factors of x are greater than or equal to 3, 2 is not a prime factor of x, and x is not an even number.
This condition is sufficient by CMT (Common Mistake Type) 1, which tells us that the unique answer ‘no’ also means that the condition is sufficient.

Condition 2)

If x = 2*17 = 34, then the answer is ‘yes’.
If x = 17, then the answer is ‘no’.
Since we do not have a unique answer, condition 2) is not sufficient.

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Re: Is the positive integer x an even number?   [#permalink] 28 Jan 2018, 17:43
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