If x and y are integers, is xy even?

Hi bunuel... what if y=-1 and x=0 in case 1 ?

For (1) if y=-1 and x=0, then xy=0=even.

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 and as zero is evenly divisible by 2 then it must be even (in fact zero is divisible by every integer except zero itself).

Hope it's clear.

It is not explicitly mentioned that x cannot equal y!

In this case :

X/Y yields 1 and XY would therefore yield 1 -> an odd number

I would have expected an extra constraints saying that X doesn't equal Y to make it a 100% clear - or am I missing out something?

For (2) x/y cannot be 1, because (2) says that x/y is even and 1 is odd.

Does this make sense?

Hi Bunuel - makes perfectly sense.. I somehow missed that it says even integer.
Thank you for your answer

Am I missing something? Part 2 says x/y is even. Odd / Odd is even. Even / Even is even. Even / Odd is also even (24/3=8). How can we be sure what x & y are?

Hi hersheykitts,

You have to be careful with your 'generalizations' and Number Properties.


First off, ODD/ODD is NOT an even.... it's either ODD or it's a non-integer (which means it's neither even nor odd)

Here are some examples:

3/3 = 1
9/3 = 3
7/5 = 1.4

In that same way, EVEN/EVEN is usually even or a non-integer....but COULD be odd (if the two evens are the SAME NUMBER)....

2/2 = 1
4/2 = 2
6/4 = 1.5

EVEN/ODD is either even or a non-integer....

2/1 = 2
12/3 = 4
4/3 = 1.33333

To answer your question, the prompt tells us that X and Y are integers and Fact 2 tells us that X/Y is an EVEN INTEGER. This means that AT LEAST one of the two variables is even....

4/1 = 4
6/3 = 2
4/2 = 2
Etc.

The question asks if XY is even. Since one or both of the variables will be even in this situation, the answer to the question is ALWAYS YES. Fact 2 is SUFFICIENT.

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

Question : Is xy an even Integer?

Statement 1: x=y+1
i.e. if y is odd then x is even
OR
if y is Even then x is odd but in each case xy will be even as one of them is even and other is odd. hence
SUFFICIENT

Statement 2: x/y is even
i.e. x must be an even Integers as both are Integers that is already given and also y is a factor of x
SUFFICIENT

Answer: Option D

Target question: Is xy even?

Aside: For xy to be even, we need x to be even, or y to be even (or both even).

Statement 1: x = y+1
This tells us that x is 1 greater than y.
This means that x and y are consecutive integers.
If x and y are consecutive integers, then one must be odd and the other must be even.
As such, the product xy must be even.
So, statement 1 is SUFFICIENT

Statement 2: x/y is an even integer.
If x/y is an even integer, then we can write x/y = 2k (where k is an integer)
Now take the equation and multiply both sides by y to get: x = 2ky
If k and y are both integers, we can see that 2ky (also known as x) must be even.
If x is even, then the product xy must be even.
So, statement 2 is SUFFICIENT

Answer =

for some reason i can't see options, any help

Hi Pranav_Gajjar,

This is an example of a Data Sufficiency (DS) question. With DS questions, the 5 answer choices are always the same 5 answers. Those answers are:

A – (1) ALONE is sufficient, but (2) alone is not sufficient.
B – (2) ALONE is sufficient, but (1) alone is not sufficient.
C – TOGETHER are sufficient, but NEITHER ALONE is sufficient.
D – EACH ALONE is sufficient.
E – NEITHER ALONE NOR TOGETHER is the statements sufficient.

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

Contact Rich at: Rich.C@empowergmat.com
www.empowergmat.com