If x and y are distinct single digit positive integers, what is the

Question

If x and y are distinct single digit positive integers, what is the minimum value of  \frac{(x-y)}{xy} ?

(A) -8/9
(B) 0
(C) 1/72
(D) 1/2
(E) 8/9

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hr1212 · Answer

\frac{(x-y)}{xy}  =  \frac{1}{y}-\frac{1}{x}

Minimum value of this algebra would be to minimize the first term and maximize the second term.

Minimum value of  \frac{1}{y} , would be to maximize the denominator and as y is a single positive integer => 
 \frac{1}{y}  =  \frac{1}{9}

Maximum value of  \frac{1}{x} , would be to minimize the denominator and as x is a single positive integer =>
 \frac{1}{x}  =  \frac{1}{1}

Subtracting both these values

\frac{1}{9} - 1  =  \frac{-8}{9}

Answer: A

MAN11 · Answer

shouldn't it be 1 - 1/9 as the equation is 1/y - 1/x and as you determine x = 9 and y = 1 answer should be 8/9

hr1212 · Answer

Good catch. Typo in the explanation (y should have been x and vice versa)

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