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Director  Joined: 29 Nov 2012
Posts: 697
If x and y are integers, is the value of x(y + 1) even?  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 54% (01:19) correct 46% (01:10) wrong based on 706 sessions

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If x and y are integers, is the value of x(y + 1) even?

(1) x and y are prime numbers.
(2) y > 7

Why is the answer C I'm getting E aren't there multiple cases when the statements are combined?

Originally posted by fozzzy on 16 Mar 2013, 03:52.
Last edited by Bunuel on 16 Mar 2013, 03:56, edited 1 time in total.
Edited the question.
Math Expert V
Joined: 02 Sep 2009
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Re: If x and y are integers, is the value of x(y + 1) even?  [#permalink]

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fozzzy wrote:
If x and y are integers, is the value of x(y + 1) even?

(1) x and y are prime numbers.
(2) y > 7

Why is the answer C I'm getting E aren't there multiple cases when the statements are combined?

Please hide OA under the spoiler.

If x and y are integers, is the value of x(y + 1) even?

x(y + 1) will be even if x is even or/and y is odd.

(1) x and y are prime numbers. If x is ANY odd prime and y is an even prime, so 2, then x(y + 1) = odd*(even+1) = odd*odd=odd but in all other cases x(y + 1) = even. Not sufficient.

(2) y > 7. Clearly insufficient.

(1)+(2) Since y = prime > 7, then y = odd, thus x(y + 1) = x(odd + 1) = x*even = even. Sufficient.

Hope it's clear.
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Director  Joined: 29 Nov 2012
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Re: If x and y are integers, is the value of x(y + 1) even?  [#permalink]

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Thanks missed the prime part silly error. I don't know how to insert the second spoiler... I'll do that next time around.
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Re: If x and y are integers, is the value of x(y + 1) even?  [#permalink]

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fozzzy wrote:
Thanks missed the prime part silly error. I don't know how to insert the second spoiler... I'll do that next time around.

Hey
One quick point here all primes except 2, when 1 is added will give an even number.
Statement provides a clue for the above, So when it is greater than 7 the constraint of 2 is avoided.....and hence the answer is C

Consider Kudos if my post helps.

Archit
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Re: If x and y are integers, is the value of x(y + 1) even?  [#permalink]

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fozzzy wrote:
If x and y are integers, is the value of x(y + 1) even?

(1) x and y are prime numbers.
(2) y > 7

Having scanned the two statements, I can see that this question is ultimately testing whether or not we recognize that ALL prime numbers are odd EXCEPT for 2 (which is even).

Target question: Is x(y+1) an even number?

Statement 1: x and y are prime numbers.
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = 2 and y = 3, in which case x(y+1) is EVEN
Case b: x = 3 and y = 2, in which case x(y+1) is ODD
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y > 7
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = 2 and y = 8, in which case x(y+1) is EVEN
Case b: x = 3 and y = 8, in which case x(y+1) is ODD
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
If y is a prime number and y > 7, we know that y MUST BE ODD
If y is odd, then y+1 must be EVEN
This means that x(y+1) = x(some EVEN integer) = EVEN
So, x(y+1) is definitely even
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

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Re: If x and y are integers, is the value of x(y + 1) even?  [#permalink]

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In my opinion, this type of problem is super easy if you really understand what you're being asked, and then re-frame the question to be more straightforward.

Original Question: Is x(y+1) even?

For x(y+1) to be even, either "x", or "y+1" must be even. So we're really asking, "Is either "x" or "y+1" even?

Well, we can simplify that even further. If "y+1" is even, then "y" is odd. So the new question becomes:

"Do we know whether either "x" is even, or "y" is odd?

A.) x and y are prime numbers.

Remember that "2" is a prime number, so "x" could be the even number 2, or it could be the odd number 3,or 5, or 7, etc. Same goes for "y".

This is not enough information to answer the question: "Do we know whether either "x" is even, or "y" is odd?

INSUFFICIENT.

B.) y > 7

This tells us nothing about "x," and it does not tell us whether "y" is even or odd. (There are many even and odd numbers greater than 7. For example, 8 is even, and 9 is odd.)

This is not enough information to answer the question: "Do we know whether either "x" is even, or "y" is odd?

INSUFFICIENT.

C.) If we know that "x" and "y" are prime, AND we know that "y" is greater than 7, then we know that "y" is NOT 2, and therefore "y" is odd. (every prime number above 2 is odd). Since we know that "y" is odd...

This is enough to answer the question "Do we know whether either "x" is even, or "y" is odd?

SUFFICIENT.

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Re: If x and y are integers, is the value of x(y + 1) even?  [#permalink]

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hi chetan2u

Since the question does not say positive or negative integers,but just says "integers". Can we assume that st2 is insufficient because "x" can be negative?

Or in gmat does "integers" mean we should test positive only?
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Re: If x and y are integers, is the value of x(y + 1) even?  [#permalink]

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blitzkriegxX wrote:
hi chetan2u

Since the question does not say positive or negative integers,but just says "integers". Can we assume that st2 is insufficient because "x" can be negative?

Or in gmat does "integers" mean we should test positive only?

Hi,

Negative or positive does not influence whether the outcome would be odd or even, since we have both negative odd/even and positive odd/even numbers.

Statement 2 says Y>7, it does not say whether Y is odd or even (also no info is given about X), If y=8 & X=odd, then product is odd and If Y=9 and X=odd, Product is even. Since we get both odd and even numbers based on st-2, it is insufficient.

In ''GMAT'', i generally check for both positive and negative numbers if the question stem says ''integers''.

Thanks
Manager  S
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GMAT 1: 490 Q39 V18 GMAT 2: 640 Q47 V30 GMAT 3: 670 Q50 V31 GMAT 4: 700 Q49 V36 GPA: 4
Re: If x and y are integers, is the value of x(y + 1) even?  [#permalink]

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Ashokshiva wrote:
blitzkriegxX wrote:
hi chetan2u

Since the question does not say positive or negative integers,but just says "integers". Can we assume that st2 is insufficient because "x" can be negative?

Or in gmat does "integers" mean we should test positive only?

Hi,

Negative or positive does not influence whether the outcome would be odd or even, since we have both negative odd/even and positive odd/even numbers.

Statement 2 says Y>7, it does not say whether Y is odd or even (also no info is given about X), If y=8 & X=odd, then product is odd and If Y=9 and X=odd, Product is even. Since we get both odd and even numbers based on st-2, it is insufficient.

In ''GMAT'', i generally check for both positive and negative numbers if the question stem says ''integers''.

Thanks

Hey!

Thanks!
I assumed that even/odds can only be for 0 and positive numbers!
Math Expert V
Joined: 02 Aug 2009
Posts: 7981
Re: If x and y are integers, is the value of x(y + 1) even?  [#permalink]

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blitzkriegxX wrote:
hi chetan2u

Since the question does not say positive or negative integers,but just says "integers". Can we assume that st2 is insufficient because "x" can be negative?

Or in gmat does "integers" mean we should test positive only?

Hi,

Integers mean both positive and negative integers and both negative and positive integers.
Also, even integers can be both positive and negative.

0 is even but neither positive nor negative.
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Re: If x and y are integers, is the value of x(y + 1) even?  [#permalink]

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fozzzy wrote:
If x and y are integers, is the value of x(y + 1) even?

(1) x and y are prime numbers.
(2) y > 7

Why is the answer C I'm getting E aren't there multiple cases when the statements are combined?

#1
x=2 ,y=3
yes even
x=3,y=2
not even
not sufficient
#2
value of x missing
not sufficient
from 1& 2
irrespective of value of x if x& y are both prime no and y>7 ie its always odd so x ( odd+1) ; even integer
IMO C
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Joined: 07 Nov 2016
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GMAT 1: 760 Q51 V42 Re: If x and y are integers, is the value of x(y + 1) even?  [#permalink]

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fozzzy wrote:
If x and y are integers, is the value of x(y + 1) even?

(1) x and y are prime numbers.
(2) y > 7

Why is the answer C I'm getting E aren't there multiple cases when the statements are combined?

St 1 :

Case 1 : x = 2, y = 3 yes

Case 2 : x = 3, y = 2 no

Not Sufficient

St 2 :

x = 8, y = 9 yes

x = 3, y = 8 no

Not Sufficient

St 1 + St 2

y is a prime number > 7

y is definitely odd, and hence (y + 1) will be definitely even

Definite Yes

Sufficient

Choice C
_________________ Re: If x and y are integers, is the value of x(y + 1) even?   [#permalink] 28 Jan 2019, 04:51
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