Maximum value of Quantity A will be obtained if we put least possible value of x-y in denominator. That will be minimum value of x and maximum of y.
Hence, Choice C is correct.

Yes, I have C as well. Because of the negative in x-y, plug in the least value of x (=9) with the greatest value of y (=8).

I'm sorry to revive an old topic but I disagree with the answer.
What if X = 8.5 and Y = 8?
The difference would be 1/2 = 0.5, which would duplicate the value of A, making it bigger than B.
Is there something Im missing?

Yes you are correct.
A could be actually infinity in the present state as it is NOT given that x and y are integers..


say x is 9 and y is 8.999999, $\frac{2}{x-y}=\frac{2}{9-8.999999}=\frac{2}{0.000001}=2*10^6$, way bigger than B

So editing to make it correct..
Now when we take them as integers we take minimum value of x as 9 and maximum value of y as 8
$A=\frac{2}{x-y}=\frac{2}{9-8}=\frac{2}{1}=2=B$

Please check that −2≤y≤8 means max value for y is 8 not even 8.000.......001, let alone 8.9999999, and
again for x, min vale is 9 because 9≤x≤12.

As a result, 2/(9-8)=2/1=2.
Answer is C.
_______________________________________________________________
Please let me know if I am wrong.

Yes , that is correct,
For some reason I took −2≤y≤8 as −2≤y≤9..
If it is −2≤y≤8, we have to take minimum value of x-y to get maximum of 2/(x-y)... Ans least value of x-y is 1 when x is 9 and y is 8

C
if we try all the border cases we can't seem to get x-y less than 1 in order to get A to its highest value with the lowest denominator

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