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

Question

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

Bunuel · Answer

________________________
Please add options. Thank you.

KSBGC · Answer

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.

globaldesi · Answer

\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

ihasan · Answer

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

The way I approached is that 1/x - 1/y is always going to be less than 1.

Hence any fraction could be obtained by putting different positive integer values of x and y.

So I check for the option with fraction less than 1 and chose it to be correct as that could be the value of (1/x-1/y)

Is my understanding correct ? though my answer was correct.

I did not try to solve II and III for x and y - As mentioned in above responses.
3/4 i.e. x = 1, y = 4 OR
5/36 i.e. x = 4, y = 9

bumpbot · Answer

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

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GMAT Problem Solving (PS) Questions

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

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