Are x and y integers? (1) The product xy is an integer. (2) x + y

Question

Are x and y integers?

(1) The product xy is an integer. 
(2) x + y is an integer.

chetan2u · Accepted Answer

Hi,
in these type of Q one should know that there are various complex numbers which can fit in..
say  x=2+\sqrt{3}  and  y=2-\sqrt{3} 
so xy=(2+\sqrt{3})*(2-\sqrt{3})=1..
and x+y= 2+\sqrt{3}+2-\sqrt{3}=4..

here the reason is we can take these two as roots of an equation, then 
the eq becomes..
z^2+(x+y)z+xy... this will always give you the roots x and y as int ,frac or complex number, even if the product and sum of roots are integer..
hence answer is E

BrainLab · Answer

(1) 2*2 YES, 2*1/2 NO
(2) 2+2 YES, 0.5 + 0.5 NO
(1)+(2) hmm... for statement 1 to be an integer we need either 2 integers or reciprocals, but I don't think that there are reciprocals that total an integer, that's why only integer pair satisfies both expressions. Please correct me if I'm wrong...

Pragnya87 · Answer

I tried the following

For statement 1, x = 2 and y = 1/2, x*y = 2*1/2 = 1 (an integer) No
 x= 2 and y = 1, x*y = 2*1 = 2(also an integer) Yes

For statement 2, x = 2.5,y=1.5, x+y = 2.5+1.5 (an integer) No
 x= 2, y = 1, x+y = 2+1 = 3( an integer) Yes

Combining 1+2, we might arrive at an answer E, how ever consider the possibility that x = 0 and y = 0 , both are integers 
and this would satisfy both the conditions and so the answer is C according to me.

chetan2u · Answer

Hi,
you can always find values of x and y as an integers satisfying the given conditions..
BUT we have to be sure that there are no values fittin as non integer, ecause the Q is a 'must ' Q..
hope it helped

QuantMadeEasy · Answer

Lets x = -square root 2
y = square root 2

(1) xy = -2. Insufficient

(2) x+y = 0. Insufficient

(1)+(2), Also gives no information regarding whether x and y are integers or not

E is correct

elevateV · Answer

For the product xy to be an integer, x and y both necessarily may not be integers
eg: x=0.2 and y=10 gives xy=2

But for x+y to be an integer, both must necessarily be integers
eg: 1+0 = 1, 2+(-2)=0

Therefore, Statement (2) is sufficient.
Answer (B)

Nidzo · Answer

1) If both are integers, we will get an integer. However, let x=0.5 and y=6 xy=3
 INSUFFICIENT

2) Once again, if both are integers it will yield an integer. However, let x = 0.5 and y = 0.5 and then x+y = 1
 INSUFFICIENT

1+2) Does not give us anything new.

Answer E

Gknight5603 · Answer

imo C

1+2= on combining provides....y(y+int) = int

so Y will be integer

Posted from my mobile device

SangamJena · Answer

Stmt 1
2/3 * 3/2 = 1 (Integer)

hence insufficient.

Stmt 2

1/3+2/3 = 1 (Integer)

hence insufficient.

Combining both if we take x & y both as root2
We get yes & no.

Hence E is the answer

amoghhlgr · Answer

I'm going with C.

When you combine 1 and 2, there is no way you can have fractions for x and y. So it will be C.

Bunuel · Answer

This problem turned out to be more challenging than I though it would be. C is not correct. Oddly enough Princeton Review also says that the OA is C and is wrong about it. The correct answer is E.

If  x=\sqrt{2}  and  y=-\sqrt{2}  then the answer is NO but if  x = y = 1 , the answer is YES. Not sufficient.

Answer: E.

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

Are x and y integers? (1) The product xy is an integer. (2) x + y

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

Are x and y integers? (1) The product xy is an integer. (2) x + y

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