## Quant Question from yahoo answer

Here is a question I found in yahoo answer w/o any answers :-) Any math guru here... X and Y are real number and |X + Y| = 100 Then (i)what is the maximum value of |X| + |Y| (ii)what is the minimum value of |X| + |Y| (iii)what is the maximum value of |X| - |Y| (iv)what is the minimum value of |X| - |Y| My answers (i)It should be infinity/indeterminate because either of X and Y can be any value and the other negative of that with 100 less (ii)should be same as 100 (iii)again it should be infinity/indeterminate (iv) Zero Then I am asking it.. just to get the confirmation

## I was thinking ,for 1 your

I was thinking , for 1 your logic is spot on for 2 from tiangle inequality you are correct again for 3 max value = 100 for 4 min value = -100 lets see my thoughts, CASE 1. therefore , when x and y are of the same sign x+y = 100 or x+y = -100 clearly the max value of |x|-|y| = 100(eg |+-100| - 0) and min value = -100 (eg 0 - |+-100|) CASE 2 : when x and y are of opposite signs and |x| >|y| lets take x> 0 becuse similar reasoning will apply for x<0 let y = -y' where y' is +ve real x-y' = 100 thus y' = x-100 let f(x) = |x| - |x-100| = x - |x -100 | since x > 0 since, y' >0 implies x-100 > 0 thus f(x)= 100 CASE 3 : when x and y are of opposite signs and |x|< |y| , let x = -x' , x' is +ve real y - x' = 100 and by the above logic, f(x) = -100 HENCE the min value of |x|-|y| = -100 and max value is 100