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If x and y are positive integers, which of the following could be

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If x and y are positive integers, which of the following could be  [#permalink]

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New post 06 Mar 2019, 01:50
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Question Stats:

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If x and y are positive integers, which of the following could be the value of 1/x - 1/y?

I. 1

II. 3/4

III. 5/36

(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 positive integers, which of the following could be  [#permalink]

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New post 06 Mar 2019, 01:51
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Re: If x and y are positive integers, which of the following could be  [#permalink]

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New post 06 Mar 2019, 03:33
rohan2345 wrote:
If x and y are positive integers, which of the following could be the value of 1/x - 1/y?

I. 1

II. 3/4

III. 5/36

(A) I only

(B) II only

(C) III only

(D) I and II only

(E) II and III only



1/x - 1/y

y - x / xy.

Scan the answer choices.

I) 1

y -x / xy = 1

y -x = xy.

It is NOT possible as both x and y are positive integers.

II) y -x / xy = 3/4

4*1 = 4

4 - 1 / 4*1 = 3/4.

This option is possible.

III) y -x / xy = 5/36.


4*9 = 36.


9 - 4 / 4*9 = 5/36.

So, This option is correct.

E is the correct answer.
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If x and y are positive integers, which of the following could be  [#permalink]

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New post 06 Mar 2019, 21:07
\(\frac{1}{x} - \frac{1}{y} = \frac{y-x}{xy}\)
now given x and y are positive numbers.
hence 1/(some positive number ) is always less than equal 1 and we are subtracting two such numbers.
hence difference will be even less than 1.
Hence option 1 out .
II and III can be the options.
which can be proven by
for II x =1 and y = 4=\(\frac{y-x}{xy}\)= 3/4
for III x=4 and y =9 = \(\frac{9-4}{36} = \frac{5}{36}\)
Thus answer E. since II and III are possible
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If x and y are positive integers, which of the following could be   [#permalink] 06 Mar 2019, 21:07
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If x and y are positive integers, which of the following could be

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