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If x and y are integers and x>y, then what is the value of x-y?

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mangamma
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If x and y are integers and x>y, then what is the value of x-y? [#permalink] New post   28 Apr 2019, 08:43
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If x and y are integers and x>y, then what is the value of x-y?

(1) 0.5 < ((x−y)^2)/5 < 1

(2) -1 < 2y < 2 < 2x < 5
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D
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m1033512
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Re: If x and y are integers and x>y, then what is the value of x-y? [#permalink] New post   28 Apr 2019, 09:02
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IMO D

from.statement 1

we get , (x-y)^2 = 4

and x-y=+2 or -2

but x>y given so x-y can only be 2

sufficient


statment 2

after simplifying
we get y = 0 and x = 2

sufficient

IMO D

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nick1816
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If x and y are integers and x>y, then what is the value of x-y? (1) 0 [#permalink] New post   22 Jun 2020, 11:53
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Statement 1-

x>y, hence x-y>0

\(2.5 < (x-y)^2 < 5\)
1.6< (x-y) < 2.2

Since x, and y are integers, x-y must also be an integer.

x-y =2

Sufficient

Statement 2 -

-1 < 2y < 2 or -0.5 <y <1

Since y is an integer, y=0

2 < 2x < 5 or 1<x<2.5

Since x is an integer, x=2

x-y=2

Sufficient
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Re: If x and y are integers and x>y, then what is the value of x-y? [#permalink] New post   25 Jun 2020, 05:40
Expert Reply
mangamma wrote:
If x and y are integers and x>y, then what is the value of x-y?

(1) 0.5 < ((x−y)^2)/5 < 1

(2) -1 < 2y < 2 < 2x < 5


If you let k = x - y, and multiply the inequality in Statement 1 throughout by 5, you get

2.5 < k^2 < 5

and since k is a positive integer, k must be 2.

From Statement 2, if y is an integer, and -1 < 2y < 2, dividing by 2 we find -1/2 < y < 1, and y must be 0. If x is an integer and 2 < 2x < 5, similarly 1 < x < 2.5, and x must be 2. So we can find both x and y from Statement 2 and answer any question about them.

So the answer is D.
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Re: If x and y are integers and x>y, then what is the value of x-y? [#permalink] New post   25 Jun 2020, 08:27
Quote:
(1) 0.5 < ((x−y)^2)/5 < 1

Simplifying
5/2 < (x-y)^2 < 5
Taking square root
\(\sqrt{2.5}\) < |x-y| < \(\sqrt{5}\)
taking approx readings
1.05 < |x-y| < 2.1
x-y could be -2 or 2 as c-y is positive, hence x-y = 2
Sufficient


Quote:
(2) -1 < 2y < 2 < 2x < 5

dividing by 2
-0.5 < y < 1< x < 2.5
y = 0, x = 2
x-y = 2
Sufficient

D is correct
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Re: If x and y are integers and x>y, then what is the value of x-y? [#permalink] New post   21 Jan 2022, 20:54
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Re: If x and y are integers and x>y, then what is the value of x-y? [#permalink]
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