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

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Bunuel
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If x and y are positive integers, is x - y > (x+y)/2 ? (1) y < x (2) [#permalink] If x and y are positive integers, is x - y > (x+y)/2 ? (1) y < x (2)   24 Mar 2015, 04:40
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If x and y are positive integers, is x - y > (x+y)/2 ?

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

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B
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If x and y are positive integers, is x - y > (x+y)/2 ? (1) y < x (2) [#permalink] If x and y are positive integers, is x - y > (x+y)/2 ? (1) y < x (2)   24 Mar 2015, 05:44
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Bunuel wrote:
If x and y are positive integers, is x - y > (x+y)/2 ?

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

Kudos for a correct solution.


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) .
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Re: If x and y are positive integers, is x - y > (x+y)/2 ? (1) y < x (2) [#permalink] If x and y are positive integers, is x - y > (x+y)/2 ? (1) y < x (2)   24 Mar 2015, 20:16
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Bunuel wrote:
If x and y are positive integers, is x - y > (x+y)/2 ?

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

Kudos for a correct solution.


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
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Re: If x and y are positive integers, is x - y > (x+y)/2 ? (1) y < x (2) [#permalink] If x and y are positive integers, is x - y > (x+y)/2 ? (1) y < x (2)   25 Mar 2015, 00:06
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(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,
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Re: If x and y are positive integers, is x - y > (x+y)/2 ? (1) y < x (2) [#permalink] If x and y are positive integers, is x - y > (x+y)/2 ? (1) y < x (2)   30 Mar 2015, 04:26
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Bunuel wrote:
If x and y are positive integers, is x - y > (x+y)/2 ?

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

Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:
Attachment:
xminusy_explanation.png
xminusy_explanation.png [ 34.9 KiB | Viewed 4868 times ]
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Re: If x and y are positive integers, is x - y > (x+y)/2 ? (1) y < x (2) [#permalink] If x and y are positive integers, is x - y > (x+y)/2 ? (1) y < x (2)   03 Oct 2016, 05:44
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lalania1 wrote:
If x and y are positive integers, is x-y > (x+y)/2

1) y < x
2) x < 2y


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.
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Re: If x and y are positive integers, is x - y > (x+y)/2 ? (1) y < x (2) [#permalink] If x and y are positive integers, is x - y > (x+y)/2 ? (1) y < x (2)   20 Dec 2020, 01:13
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 y<x<2y. Is it that now it is clear that we can tell that x can't be more than 2y and hence we are sure that the expression can't be true or it is other way round. If y<x<2y, how are we concluding that x>3y. ( 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.

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Re: If x and y are positive integers, is x - y > (x+y)/2 ? (1) y < x (2) [#permalink] If x and y are positive integers, is x - y > (x+y)/2 ? (1) y < x (2)   20 Dec 2020, 01:44
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nuruddinies wrote:
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 y<x<2y. Is it that now it is clear that we can tell that x can't be more than 2y and hence we are sure that the expression can't be true or it is other way round. If y<x<2y, how are we concluding that x>3y. ( 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.

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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.
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Re: If x and y are positive integers, is x - y > (x+y)/2 ? (1) y < x (2) [#permalink] If x and y are positive integers, is x - y > (x+y)/2 ? (1) y < x (2)   20 Dec 2020, 01:49
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.

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Re: If x and y are positive integers, is x - y > (x+y)/2 ? (1) y < x (2) [#permalink] If x and y are positive integers, is x - y > (x+y)/2 ? (1) y < x (2)   20 Dec 2020, 05:06
Bunuel wrote:
If x and y are positive integers, is x - y > (x+y)/2 ?

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

Kudos for a correct solution.


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
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Re: If x and y are positive integers, is x - y > (x+y)/2 ? (1) y < x (2) [#permalink] If x and y are positive integers, is x - y > (x+y)/2 ? (1) y < x (2)   20 Dec 2020, 20:56
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?
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Re: If x and y are positive integers, is x - y > (x+y)/2 ? (1) y < x (2) [#permalink]
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