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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8005
GMAT 1: 760 Q51 V42 GPA: 3.82
Is the positive integer x an even number?  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 62% (00:44) correct 38% (01:23) wrong based on 69 sessions

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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 $$17$$.

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 58336
Re: Is the positive integer x an even number?  [#permalink]

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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
_________________
Math Expert V
Joined: 02 Aug 2009
Posts: 7958
Re: Is the positive integer x an even number?  [#permalink]

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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
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8005
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Is the positive integer x an even number?  [#permalink]

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=>

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.
The answer is ‘no’.
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.

Therefore, the answer is A.
_________________ Re: Is the positive integer x an even number?   [#permalink] 28 Jan 2018, 18:43
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