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

Question

(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?

Bunuel · Accepted Answer

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.

Answer: C.

Hope it's clear.

BrentGMATPrepNow · Answer

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

Answer:  C

fozzzy · Answer

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

Archit143 · Answer

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

grimm1111 · Answer

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.

Answer is C.

blitzkriegxX · Answer

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?

Ashokshiva · Answer

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

blitzkriegxX · Answer

Hey!

Thanks! 
I assumed that even/odds can only be for 0 and positive numbers!

chetan2u · Answer

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.

Archit3110 · Answer

#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

ksrutisagar · Answer

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

Ravixxx · Answer

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

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

Solution: 
x(y + 1) even means that at least x or (y+1) must be even. 
so if x is odd, y must be odd (odd+1=even).

(1) x and y could be 2,3,5,7... not sufficient
(2) y could be 8,9,10,11... not sufficient.

together: 
 if y>7 and it is a prime number means that y is odd. 
 
so (y+1) is even. 
x(odd or even)(even) = even.

Sufficient.

GDT · Answer

VeritasKarishma

Just a small query here

As we are not told whether x and y are distinct, so we can consider them to be same also, correct?

Thanks in advance!

KarishmaB · Answer

Yes, they can be same too. The question does not say that they need to be distinct.

AwesomeYao · Answer

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

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

(1) if x=3 and y=2, then x(y+1) is odd. If x=5,y=3, then x(y+1) is even. Hence, this condition alone is not sufficient
(2) if x=2 and y=11, then x(y+1) is even. If x=3 and y=11, then x(y+1) is odd. Hence, this condition alone is not sufficient

Combine (1) and (2), for any prime number y greater than 7, y is odd, so y+1 is even. if x=2, x(y+1) is even. for any other prime number, x is odd, so x(y+1) is even. Sufficient

bumpbot · Answer

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

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

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