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If x and y are positive integers, is x even?

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If x and y are positive integers, is x even?

by M7MBA » Sat May 12, 2018 5:39 am

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If x and y are positive integers, is x even?

(1) x-3y=27
(2) x+2y=37

The OA is the option B

How can I give an answer here without knowing the value of "x" and "y"? Can anyone help me here? Please.
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by Vincen » Sat May 12, 2018 7:12 am

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M7MBA wrote:If x and y are positive integers, is x even?

(1) x-3y=27
(2) x+2y=37

The OA is the option B

How can I give an answer here without knowing the value of "x" and "y"? Can anyone help me here? Please.
Hello M7MBA.

You don't need to know the value of "x" and "y". Let's see how can we solve this DS question.

(1) x-3y=27

This tells us that $$x=27-3y=3\left(9-y\right).$$ Now, this last expression can be even or odd depending on the value of y. Hence. this statement is NOT SUFFICIENT.

(2) x+2y=37

This tells us that $$x=37-2y.$$ Now, here we are subtracting an ODD number and an EVEN number, the result will be always an ODD number. Therefore, here the answer is NO, x is not even.

This implies that this statement is SUFFICIENT.

Hence. the correct answer is the option B.

I hope this explanation may help you.

Regards.
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by [email protected] » Sat May 12, 2018 1:31 pm

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Hi M7MBA,

We're told that X and Y are POSITIVE INTEGERS. Were asked if X is EVEN. This is a YES/NO question can be solved with Number Properties.

1) X - 3Y = 27

IF....
Y = ODD, then X = EVEN and the answer to the question is YES.
Y = EVEN, then X = ODD and the answer to the question is NO.
Fact 1 is INSUFFICIENT.

2) X + 2Y = 37

(2Y) will ALWAYS be EVEN (since any integer multiplied by 2 ends in an EVEN). Thus...
X + EVEN = 37
X will ALWAYS be ODD and the answer to the question is ALWAYS NO.
Fact 2 is SUFFICIENT.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich
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