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If x and y are integers such that x > y, which of the following CANNOT

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If x and y are integers such that x > y, which of the following CANNOT  [#permalink]

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New post 20 Dec 2015, 05:40
00:00
A
B
C
D
E

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If x and y are integers such that x > y, which of the following CANNOT be a positive integer?

I. y(y – x)
II. y(x – y)
III. (x - y)/(y - x)

A. I only
B. II only
C. III only
D. I and II only
E. II and III only

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Re: If x and y are integers such that x > y, which of the following CANNOT  [#permalink]

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New post 20 Dec 2015, 05:51
Bunuel wrote:
If x and y are integers such that x > y, which of the following CANNOT be a positive integer?

I. y(y – x)
II. y(x – y)
III. (x - y)/(y - x)

A. I only
B. II only
C. III only
D. I and II only
E. II and III only



lets see the three equations..
I. y(y – x)
if both x and y are negative number, y will be -ive and y-x, as numeric value of y will be more than x,will also be -ive... so out

II. y(x – y)
if both x and y are +ive number, y will be +ive and x-y will also be positive... so out

III. (x - y)/(y - x)
either one of the numerator and denominator will be -ive and the other +ive..
so will always be -ive

we need not see any further after checking for II as all choices except C are eliminated..
ans C
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: If x and y are integers such that x > y, which of the following CANNOT  [#permalink]

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New post 29 Sep 2017, 08:34
1
When X>Y,
These are the possible cases

X Y
+ -
+ 0
+ +
- -

The question is asking CANNOT be positive, we will prove CAN be positive and eliminate that answer.

I. y(y – x)
If both are negative the result will be positive, hence eliminate answer choices a and d.
II. y(x – y)
If both are positive the result will be positive, hence eliminate answer choice b and e.
III. (x - y)/(y - x)

Answer is C, which is the only choice left.
Re: If x and y are integers such that x > y, which of the following CANNOT &nbs [#permalink] 29 Sep 2017, 08:34
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