Question

x and y are positive integers and x + y = 11. What is the largest possible value of 1/x - 1/y ?
A. 1/30
B. 9/10
C. 1
D. 9
E. 11

Answer 1

@phi

Answer 2

what course is this ?

Answer 3

For the SHSAT

Answer 4

SH ?

Answer 5

Specialized high school admissions test

Answer 6

I did it just by using all the possible values of x and y that add up to 11. Try making a table with the x and y values ad then filling them into your equation. It's quite elementary to do it like this, but it's the easiest way, also.

Answer 7

But how can I check if it will make the largest possible value?

Answer 8

you test (1,10) , (2,9), (3,8), (4,7), (5,6)

Answer 9

it's slightly easier if you re-write
1/x - 1/y as
(y-x)/(xy)

Answer 10

and consider just the end points
(1,10) and (5,6)

Answer 11

Thank you @IMStuck and @phi