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

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.

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