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If x and y are integers, is xy even?

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If x and y are integers, is xy even? [#permalink] New post 19 Aug 2012, 07:03
00:00
A
B
C
D
E

Difficulty:

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Question Stats:

75% (01:42) correct 25% (00:44) wrong based on 254 sessions
If x and y are integers, is xy even?

(1) x = y + 1.
(2) x/y is an even integer.

[Reveal] Spoiler:
Official answer is that both these statements are independently sufficient (D), with the following explanations :-
(1)- since x and y are consecutive numbers, so one of these would be even and thus xy is also even.
(2) if the fraction is even, then it means x is even and hence xy is also even..

Here is my doubt...

I chose option (B), meaning (2) alone is sufficient but (1) is not.
Explanation: x and y are integers which means x could be 0 as well, in that case y will be 1, or x could be -1 and then y would be 0.
in both these cases the product xy will not be even.

Can someone please help me in clarifying this doubt!

TIA
[Reveal] Spoiler: OA

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Last edited by Bunuel on 13 Dec 2012, 05:03, edited 2 times in total.
Edited the question.
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Re: If x and Y are integers, is xy even? [#permalink] New post 19 Aug 2012, 07:27
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If x and Y are integers, is xy even?

In order the product of two integers to be even either (or both) of them must be even. So, the question basically asks whether either x or y is even.

(1) x = y + 1. If x is odd then y is even and vise-versa. Sufficient.
(2) x/y is an even integer --> \frac{x}{y}=even --> x=y*even=even. Sufficient.

Answer: D.

As for your doubt: if either x or y is zero, then xy=0=even, because zero is an even integer. Zero is nether positive nor negative, but zero is definitely an even number.

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 helps.
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Re: If x and Y are integers, is xy even? [#permalink] New post 19 Aug 2012, 08:17
thank you Bunnel, this is what happens when you don't brush up your basics before preparing for quant!

I was not considering 0 as an even number.
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Re: If x and Y are integers, is xy even? [#permalink] New post 19 Apr 2013, 10:35
Hi bunuel... what if y=-1 and x=0 in case 1 ?

Bunuel wrote:
If x and Y are integers, is xy even?

In order the product of two integers to be even either (or both) of them must be even. So, the question basically asks whether either x or y is even.

(1) x = y + 1. If x is odd then y is even and vise-versa. Sufficient.
(2) x/y is an even integer --> \frac{x}{y}=even --> x=y*even=even. Sufficient.

Answer: D.

As for your doubt: if either x or y is zero, then xy=0=even, because zero is an even integer. Zero is nether positive nor negative, but zero is definitely an even number.

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 helps.
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Re: If x and Y are integers, is xy even? [#permalink] New post 20 Apr 2013, 03:45
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vicky4113 wrote:
Hi bunuel... what if y=-1 and x=0 in case 1 ?

Bunuel wrote:
If x and Y are integers, is xy even?

In order the product of two integers to be even either (or both) of them must be even. So, the question basically asks whether either x or y is even.

(1) x = y + 1. If x is odd then y is even and vise-versa. Sufficient.
(2) x/y is an even integer --> \frac{x}{y}=even --> x=y*even=even. Sufficient.

Answer: D.

As for your doubt: if either x or y is zero, then xy=0=even, because zero is an even integer. Zero is nether positive nor negative, but zero is definitely an even number.

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 helps.


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.
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Re: If x and y are integers, is xy even? [#permalink] New post 13 Aug 2013, 12:47
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?
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Re: If x and y are integers, is xy even? [#permalink] New post 13 Aug 2013, 23:36
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pvaller1 wrote:
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?
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If x and y are integers, is xy even? [#permalink] New post 14 Aug 2013, 07:33
Bunuel wrote:
pvaller1 wrote:
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 :)
Re: If x and y are integers, is xy even?   [#permalink] 14 Aug 2013, 07:33
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