This question makes you realize that you have to have an "even integer". If the question were merely, "is this even?" you would not need the statements to answer it. If you have 2 * x * 5 * y, then you have 10xy. Generally, you need to know if you have odd * odd or odd * even, or even * even in order to know if the product is even, but when you have 10 * any number, the result will always be even because 2 of the 3 scenarios results in an even number. {1) odd*odd=odd 2) even*odd = even 3) even*even=even} If you have even just 1 even number, the product will always be even. So, since we know that there is a 2 involved, the product will always be even.

But the key is "integer", so we don't know if x = 1.15 or any other decimal which may or may not give an even integer.

Statement 1) Insuffucient. 2 + 2.5 + 5 + 2.5 = even integer of 12. But if you take 2 * 2.5 * 5 * 2.5, that gives you 62.5, not an integer at all, so it could not possibly be an even integer, but the sum is even, therefore, #1 insufficient.

2) Insufficient because if x = 3.5 and y = 0.5, then the different is 3, an odd integer, but if you take the product of 2 * 3.5 * .5 * 5, you don't get an integer at all.

Together) Insufficient. If, from statement 1, you add 2 + 5 =7, then, in order to make Statement 1 true, that the sum is an even integer, the sum of x + y must be odd, so you have odd + odd = even.

Any numbers that will sum an odd integer will never have a difference of an odd integer. 4+2=6, but 4-2=2. Take this principle to the bank. So, these statements cannot both be true at the same time.

I don't think this is a good question, because GMAT will not write questions that have contradictory statements. While I believe the answer to be E, I think the question is flawed.


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J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

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Why is not possible to have x and y which satisfy this?


what if x is any odd number and y is 0?
or x=2 and y= 1

Is product 2*x*5*y an even integer?

1) 2 + x + 5 + y is an even integer
2) x - y is an odd integer

Can someone post OA for this Q?

I think the above reasoning is not correct and the answer is C.

Question: 2*x*5*y=even. As there is 2 as a multiple, then this expression will be even if 5xy=integer. Basically we are asked is 5xy=integer true?

Note that x and y may not be integers for 2*x*5*y to be even (example x=\frac{7}{9} and y=\frac{9}{7}) BUT if they are integers then 2*x*5*y is even.


(1) 2+x+5+y=even --> 7+x+y=even --> x+y=odd. Not sufficient. (x=1 and y=2 answer YES BUT x=1.3 and y=1.7 answer NO)

(2) x-y=odd. Not sufficient. (x=1 and y=2 answer YES BUT x=1.3 and y=0.3 answer NO)

(1)+(2) Sum (1) and (2) (x+y)+(x-y)=odd_1+odd_2 --> 2x=even --> x=integer --> y=integer --> Both x and y are integers. Hence sufficient.

Answer: C.
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Is the product 2*x*5*y an even integer?

1. 2 + x + 5 + y is an even integer
2. x - y is an odd integer

OA is

Please explain.

jallenmorris's solution is not right:



Only integers can be even or odd. There is no difference in asking "is x even integer" and "is x even".



x=3=odd and y=2=even --> x+y=5=odd and x-y=1=odd OR x=6=even and y=1=odd --> x+y=7=odd and x-y=5=odd.



You are absolutely right. Pleas refer to my post for solution for this problem.
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OA for this question is C.

You should know that: zero is an even integer.

An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder.
An even number is an integer of the form n=2k, where k is an integer.

So for k=0 --> n=2*0=0.

For more on number properties check: math-number-theory-88376.html
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