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

Question

If x and y are positive integers, is x an even integer? (1) x(y + 5) is an even integer. (2) 6y^2 + 41y + 25 is an even integer. Question 28.JPG

Bunuel · Answer

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

(1) x(y+5) is an even integer --> if y is an odd integer then y+5=even and x can be even or odd. Not sufficient.

(2) 6y^2 + 41y + 25 is an even integer --> 6y^2 + 41y + 25=even+41y+odd=even --> odd+41y=even --> 41y=odd --> y=odd, still insufficient as no info about x.

(1)+(2) As from (2) y=odd then from (1) x can be even as well as odd. Not sufficient.

Answer: E.

Spidy001 · Answer

My answer is E.

1. is not sufficient , as the expression is satisfied for both o and e values of x.

2. no info about x. not sufficient

together y is odd, x can still be odd or even . so not enough

subhashghosh · Answer

(1) x(y+5) is an even integer --> x can be odd, y can be odd too, not sufficient

(2) 6y^2 + 41y + 25 is an even integer --> y(6y + 41) + 25 => y (even + odd) + odd , no info about x though, so not enough

Combining (1) and (2), from (2) we only know that y (even + odd) is odd, so y is odd, but even this can't make x odd necessarily in (1)

x * even = even, so again x can be odd or even
So the answer is E.

opus88 · Answer

I got this wrong this the first time around when pressed for time but it's pretty clear where I went wrong.

1) and 2) were easy to rule out as insufficient on their own.

x could be even or odd from the situation given in 1). 2) doesn't give us any information at all about x.

The answer must be C or E.

When looking at 1) + 2) I got confused how to pry information for 2). I kept seeing a quadratic equation, although factoring it would obviously do no good in this case.

When reviewing and having more time, I saw that:

6y^2 + 41y + 25 = even
6y^2 + 41y + odd = even
6y^2 + 41y = odd

Therefore, in 6y^2 and 41y must be one odd and one even. Y must be odd, otherwise you would have two evens.

Looking back at 1), if Y is odd, this all we know:

x(even) = even

We know nothing. :-D

Answer is E.

Answer is E.

stonecold · Answer

Another Quality Question from the GMAT prep
Here we are given that x,y are two integers
We need to examine x for its even/odd nature

Lets look at statement
Statement 1
Here if y is odd 
x can be even or odd
hence not sufficient 
Statement 2
This statement tells us that 41y=> even-even-odd=> odd so => y must be odd
No clue of x 
hence not sufficient 
Combing the two statements 
as y is odd => y+5 will be even
hence x(y+5 will always be even irrespective of whether x is even or not
Hence we can't say whether x is even or not
Hence insufficient

Hence E

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards