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If x is a positive integer and y is a negative integer, what

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Director
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If x is a positive integer and y is a negative integer, what [#permalink] New post 26 Mar 2007, 03:46
If x is a positive integer and y is a negative integer, what is the largest possible value of 1 / (x - y)?

a)1/4

b)1/2

c)2/3

d)3/4

e)1
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 [#permalink] New post 26 Mar 2007, 04:30
(B) for me :)

we want that x-y is the most little possible.... In case of integers with x positive and y negative, the solution is to take x = 1 and y = -1. :)

Note that:
> 1 is impossible
> 2/3 and 3/4 are also ruled out because x and y are integers... It's not possible to have 2 or 3 in numerator (in case of simplified solution ;) ) :)
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 [#permalink] New post 26 Mar 2007, 06:40
If x is a positive integer and y is a negative integer, what is the largest possible value of 1 / (x - y)?

Largest possible value of a fraction means largest possible numerator and smallest possible denominator

numerator is 1, fixed
denominator is x-y --> miminimze [smallest difference between x and y]

best value would be if x-y is a really small fraction. However, as stated in the problem, x and y are both integers --> the difference is an integer.
Therefore, best difference is value of 1 [x-y=1]

Since x is positive and y is negative, it is impossible to have x-y=1 because smallest +ive is 1 and largest -ive is -1 and hence the difference is 2

Best case, or as we may say the largest possible value for 1/(x-y) is 1/2

Answer is B
  [#permalink] 26 Mar 2007, 06:40
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If x is a positive integer and y is a negative integer, what

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