x and y are integers, is x even 1. x(y + 1) is even 2. (x +

Question

x and y are integers, is x even

1. x(y + 1) is even
2. (x + 2)(y + 4) is even

giddi77 · Answer

This is a headache Bhai! I think C.

1. x(y+1) = even

If (x,y) = (1,1) the above can be even. 
if (x,y) = (2,2) the above is definitely even. So INSUFF!

2. (x+2)(y+2) = even
 if (x,y) = (1,3) the eqn can be even
 if (x,y) = (2,3) the eqn is still even. So INSUFF!

Combing both: Here comes the trouble (I don't have a neat approach)
O= odd
E = even
I came up with a truth table type apparoach

x y x(y+1) (x+2)(y+4)
O O True False
O E False True
E O True True
E E True True 

So when x is odd, both (1) and (2) cannot be true at the same time. Hence x must be even. Hence C.

Sorry about my vague explanation, but this the best I could come up with.

shahnandan · Answer

E.

stmt 1,

take x=2 y=3
2(3+1)=8 conditon satisfied, X is even

take x=y=3
3(3+1)- 12 condition satisfied X isNOT even insuff

stmt2,

x=3
y=2
(3+2) (2+4) =30, condition satisfied, X NOT even

x=2
y=3
4.7=28 , condition satisfied, X NOT even insuff

combining,
x=2
y=0
both conditions satisfied, X even

x=y=3
both conditions satisfied, X NOT even

Hence E

allabout · Answer

1) x(y+1) even, so either x, y+1, or both are even => insuff

2) Either x, y or both are even or 0 =>insuff

1+2) 

If y is odd, then 

- acc. to 1., x can but must not be even (can't be 0)
- combined with 2. it must be even

If y is even, then

- acc. to 1. x must be even
- acc. to 2. x can be even, odd or 0

C it is, as far as I can see

shahnandan · Answer

oops..sorry, realized I made a mistake towards the end (x=y=3) this doesnt satifythe equation..answer should be C

sperumba · Answer

my answer is C too.. 

Good questions Bhai.

vivek123 · Answer

Should be "C" V good Q Bhai :good

ywilfred · Answer

1. x(y+1) is even -> x can be even, y+1 can be even, or both can be even. Insufficient.
2 (x+2)(y+4) -> insufficient for the same reason.

Using both, (y+1) = even and (y+4) is even

Note that (y+1) and (y+4) are opposites. 

If y is odd, then (y+1) = even and (y+4) is odd.
If (y+4) is odd -> (x+2) has to be even -> x is even (which makes st1 okay as well)

Now, if y is even, then (y+1) = odd, (y+4) = even
(y+1) is odd -> x has to be even -> x+2 is even but it doesn't matter since (y+4) is even. 

Both cases, x is even.

Ans C

ywilfred · Answer

The truth table way is interesting. It's amazing how you transform digital electronics to math

giddi77 · Answer

You got me here ywilfred! I am a Chip Design Engineer! I am gald you liked it.

lhotseface · Answer

C.....no gate logic involved...

1. x(y + 1) is even........................INSUFF (y+1) could be even. 2. (x + 2)(y + 4) is even....................INSUFF (y+4) could be even. 2. Simplifying, we get (x+2)(y+4) = xy + 4x + 2y + 8 is EVEN. From I, xy + y is EVEN. xy + 4x + y + y + 8 = EVEN Substituting, xy + y as even, we get Even + 4x + y + 8 = EVEN. => y = EVEN - EVEN - 4X -8 => y = EVEN. Since y is EVEN, y+1 is ODD. From statement I, x(y+1) = even and if y+1 is ODD, then x is EVEN...SUFF.

x and y are integers, is x even 1. x(y + 1) is even 2. (x +

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