If x and y are positive integers, is x - y (x+y)/2 ? (1) y

Question

If x and y are positive integers, is x - y > (x+y)/2 ?

(1) y < x
(2) x < 2y

Kudos for a correct  solution .

Lucky2783 · Answer

is x - y > (x+y)/2 ? is x >3y ? (1) y < x Insufficient. X=4,Y=2 No. X=4, Y=1 Yes. (2) x < 2y Sufficient as we have to find whether x>3y (note x,y are positive) .

peachfuzz · Answer

rephrased, the question is x > 3y ?

Statement 1:
if x=1, y=1, no
if x=100, y=1 yes
Insufficient

Statement 2:
x < 2y
less than 2y is never larger than 3y
Sufficient

Answer: B

lipsi18 · Answer

(X+Y)<2(X-Y)?

1. X>Y; X,Y=2,1(No) = 4,1(Yes); Not sufficient
2. X<2Y; above equation will never satisfy;sufficient

Hence answer is B

Thanks,

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION: xminusy_explanation.png

abhimahna · Answer

Reframing the question , we are asked if x > 3y

Statement 1 : x > y. Insufficient.

Statement 2 : 2y > x, If 2y > x, then obviously x is not greater than 3y as x and y are both positive integers. -- SUFFICIENT.

nuruddinies · Answer

Sorry guys I'm developing a very basic doubt. If x<2y, how are we concluding that x>3y. Combining both the statements, we get a range of X, which is y3y. ( Or we are now sure that x can't be more than 3y) therefore we can say that the expression of the question can be evaluated. Kindly enlighten. Posted from my mobile device

Bunuel · Answer

Notice that we are told that x and y are positive integers. The question asks: is x > 3y? Now, (2) says that x < 2y. If x < 2y and x and y are positive integers, then x cannot be greater than 3y, so we have a NO answer to the question: is x > 3y? Hope it's clear.

nuruddinies · Answer

Thanks Brunel, my baiscs improved.

We need to answer either component,whether the expression is true or not. So we conclude that expression is unture, with the help of second statement. I was looking for trueness only. Perhaps due to my intrinsic characters 😀 Thanks once again.

Posted from my mobile device

callmeDP · Answer

x - y > (x+y)/2 2x - 2y > x + y x > 3y ? 1. y < x, but we want to if 3y < x ; thus not sufficient. 2. x < 2y, thus definitely 3y < x ; is not possible hence NO. Sufficient. IMO B

Aharonhillel · Answer

I am confused how number 2 is always sufficient.

What if X = 3 and y = 2. If that is the case 3 < 2(2) aka: 3 <4

However, 3-2 > 5/2 is fasle

1 is not greater than 2.5. Doesn't this prove B as false?

If x and y are positive integers, is x - y > (x+y)/2 ? (1) y < x (2)

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