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Is the positive integer x an even number?

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by Max@Math Revolution » Thu Jan 25, 2018 2:56 am
[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.
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Source: — Data Sufficiency |
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by DrMaths » Thu Jan 25, 2018 6:36 am
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.

1) SUFFICIENT because all even numbers have the prime factor 2
2) INSUFFICIENT: could be 3 x 17 = ODD or 2 x 17 = EVEN
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by Max@Math Revolution » Sun Jan 28, 2018 5:37 pm
=>

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.
Answer: A
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