If xy 0 and both x and y are even numbers, is x y?

Question

If xy > 0 and both x and y are even numbers, is x > y?

(1) x > y - 2
(2) |x - y| > 4

Chetan's  questions

chetan2u · Answer

OE to follow.. xy>0..... x and y are even... 1) x>y-2 x+2>y So y y Insufficient 2) |x-y|>4 We cannot say if y>x or x>y but surely x eq{y} Insufficient Combined.. We know from statement I that either x=y or X>y But statement II tells us that x eq{y} So only possibility x>y Sufficient C

harish1986 · Answer

The answer is C . since xy>0; here is my list of values

from statement 1:
x=-2; y= -8
x=4; y =4

statement 1 is insufficient

from statement 2:
x=-2; y=-8
x=-8; y=-2
x=2; y=8
x=8; y=2

statement 2 is insufficient

combining both makes it sufficient. C

deepverma · Answer

Xy>0 means either x ND y r both -ve or both are positive. 
1) not sufficient.as x can be bigger/smaller than y or equal
2) sufficient: x-y >4 or y-x <- 4; for both +ve ND -ve x> y

AnswerB

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chetan2u · Answer

you will have to recheck highlighted portion |x-y|>4 two cases 1) x-y\geq{0} x-y>0 2) x-y<{0} -(x-y)>4.......y-x>4 both x-y >4 and y-x <- 4 are SAME

GmatDaddy · Answer

Given: 
both x and y are even numbers
xy>0: This means both x & y have same sign.

Statement 1: x>y-2

Case 1 both x,y >0
eg 8>6-2
x>y Yes

Case 2: both x,y<0
eg -8>-8-2
x>y No
Hence  Insuficient

Statement 1: |x-y|>4
that means the distance between x & y is 4, but we dont know their relative positions.
Hence  Insufficient.

Considering both Statement 1 &2
10>6-2

Sufficient.

Answer: C

deepverma · Answer

Ya got it. thanks. Should be x-y >4 or x-y < -4 ND not sufficient.
Combining 1)ND 2) gives ultimate x-y > 4 which means x>y . So answer is C

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VodkaHelps · Answer

How does the "even" information come into play?

Once I consider 2 conditions together, it was hard to see if it satisfies x > y. 
x -y > -2 AND |x- y| > 4

I had to guess it is C because I picked a pair of different sign x and y ( x=-5, y =1) and it could not satisfy both conditions -> probably they must be same sign. Kinda not sure about this one.

TariqOmar · Answer

In the posted solutions above where A is determined as insufficient, there was the assumption that X can equal y.
My question is , when you are told x and y are even number(s), doesn't that mean that these numbers are different numbers?

Gmatprep550 · Answer

Understood why A and B is not an answer but still not able to understand why C is an answer,  GmatDaddy  could you please elaborate how both equation together are sufficient.

GmatDaddy · Answer

We have to judge if X>Y such that both the conditions mentioned in Statement 1 and 2 are met.. If you will try to choose values accordingly, you will see that X>Y Eg: We know from 2 that the difference between X and Y is 4. Now select values of X and Y such that X>Y-2 ie YY is Yes 6<2+2, this equality is absurd. similarly the other case when both X and Y are -ve

amresh09 · Answer

Given xy>0 (Same signs). we have to check x>y or x-y>0?

St 1: x>y-2, x-y>-2. Insufficient as x-y could be negative, zero or greater than 0.

St 2: x-y>4 or x-y<-4. Insufficient as Inequality 1 gives us Yes answer while Inequality 2 gives us No Answer.

Combining st 1 & 2, we have three inequalities:
x-y>-2
x-y>4
x-y<-4

From here on, if anyone can explain how both statements together are sufficient it would help me in error correction. Please explain algebraic approach.

chetan2u · Answer

xy>0..... x and y are even... 1) x>y-2 x+2>y So y y 2) |x-y|>4 We cannot say if y>x or x>y but x eq{y} Insufficient Combined.. We know from statement I that either x=y or X>y But statement II tells us that x eq{y} So only possibility x>y Sufficient C

ankitamundhra28 · Answer

Hi chetan2u From St.2, how did you derive x<>0? If x = 0 & y = -6, Modulus (0-(-6)) = 6 ==> 6>4 x<>0 can be derived from the question stem itself, because xy>0. So what value is statement 2 adding here? Didn't quite get it... Awaiting your explanation.. Thanks. Also, is this a 700+ level question?

chetan2u · Answer

Hi...
Although combined too I have worked on  x
eq{y}  but have mentioned 0 instead of y...
 x
eq{y}  is correct as x-y cannot be 0

VaCeFe · Answer

I arrived in the same point with the 3 equations and I combined the two first equations: x-y>-2 x-y>4 >>> 2x - 2y > 2 >>> x - y > 1 >>> x > y +1 The only way to satisfy x > y +1 is when x>y. I think I didn't use those information:

x and y are even and xy > 0, so we know y and x are different to zero and or both are positive or both are negative. Or am I missing some step and should I had used ?

bumpbot · Answer

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If xy > 0 and both x and y are even numbers, is x > y?

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If xy > 0 and both x and y are even numbers, is x > y?

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