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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

Nice work again from

Nice work again from rajorshi (i)Obvious the value can be anything (ii)I think all must be aware of |a + b| ≤ |a| + |b| Anyhow lets try to twist it a bit and see what happens Say, 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|

The basic fundas

By understaning the follwing realtions you can answer all the above questions.

what is modulus or abosulte value

The modulus or absolute value of any number is the magnitude of that numebr. For example the modulus of the number -3 is 3 as 3 is the magnitude. The modulus of 3 is also 3. In general terms the modules of any quantity x is expressed as |x| & it is always positive. Hence

|x| = x & |-x| = x

some property based upon on modulus.

i. |x| ≥ x ii. |x – y| = |y – x| iii. |x| |y| = |x y| iv. |x - y| |x| - |y| v. |x + y| |x| - |y| vi. |x – y| |x| - |y| vii. If x > y, then |x – y| = x – y & if x < y, then |x – y| = y – x.