35 votes 35 votes The expression $\large \frac{(x+y) - |x-y|}{2}$ is equal to : The maximum of $x$ and $y$ The minimum of $x$ and $y$ $1$ None of the above Quantitative Aptitude gatecse-2017-set1 general-aptitude quantitative-aptitude maxima-minima absolute-value + – Arjun asked Feb 14, 2017 • edited May 29, 2019 by Pooja Khatri Arjun 9.0k views answer comment Share Follow See all 3 Comments See all 3 3 Comments reply Akash Verma 1 commented Sep 17, 2017 reply Follow Share Given expression [ (x + y) – |x – y| ] / 2 case1: x > y then, |x – y| = x - y , [ (x + y) – |x – y| ] / 2 = (x + y - (x - y) ) / 2 = y = min of x & y. case2 : x < y then, |x – y| = y - x , [ (x + y) – |x – y| ] / 2 = (x + y - (y - x) ) / 2 = x = min of x & y. So (B) option is correct. 10 votes 10 votes saipriyab commented Oct 15, 2017 reply Follow Share If we take x=4 ,y=3 value will be 3 if we take x=3 y=4 also value will be 3 so it returns minimum of x and y 1 votes 1 votes Akash Verma 1 commented Nov 12, 2017 reply Follow Share yes it gives always minimum of x & y for all values of x &y . 0 votes 0 votes Please log in or register to add a comment.
Best answer 38 votes 38 votes When $x>y, \mid x-y\mid \quad =x-y,$ if we substitute in expression we get $y.$ When $x<y, \mid x-y\mid\quad =-(x-y),$ if we substitute in expression we get $x.$ Therefore in both the case we get minimum of $(x,y).$ ANS: B rachapalli answered Feb 14, 2017 • edited May 31, 2018 by Arjun rachapalli comment Share Follow See all 6 Comments See all 6 6 Comments reply Show 3 previous comments vishnu priyan commented Jan 7, 2018 i edited by vishnu priyan Jan 7, 2018 reply Follow Share Take x=-2 y=3 $((x+y) - |x-y|)/2$ That is $((-2+3) - |-2-3|)/2$ becomes $((1) - |-5|)/2$ Then, removing mod we get $((1) - 5)/2$ ----> $(-4)/2$ --> -2! The minimum! :) 0 votes 0 votes air1ankit commented Jan 13, 2018 reply Follow Share (A) The maximum of x and y (B) The minimum of x and y PLEASE explain meanging of both 0 votes 0 votes Lakshman Bhaiya commented Jan 30, 2019 reply Follow Share $(A)$ The maximum of $x$ and $y$ $max(x,y)=max(1,2)=2$ $max(x,y)=max(3,4)=4$ $max(x,y)=max(44,24)=44$ $max(x,y)=max(100,20)=100$ $(B)$ The minimum of $x$ and $y$ $min(x,y)=min(1,2)=1$ $min(x,y)=min(100,200)=100$ $min(x,y)=min(10,2)=2$ $min(x,y)=min(101,102)=101$ 2 votes 2 votes Please log in or register to add a comment.
23 votes 23 votes The modulus function works like this: | x | = x if ( x >0) | x | = -x if (x <0 ) as it can be treated as | x - 0 | similarly here | x-y | = x-y if ( ( x-y )>0 or x>y ) and | x-y |= -( x-y ) if ( ( x-y )<0 or x<y ) so now just substitute in the equation the expression will give ( x+y - x +y )/2 = y if( x>y ) and ( x+y + x - y)/2 =x if(x<y) hence whichever is minimum that is coming as output Sanyam Lakhanpal answered Sep 17, 2017 Sanyam Lakhanpal comment Share Follow See all 0 reply Please log in or register to add a comment.
16 votes 16 votes Hence, minimum value in both the case is the required answer. So, option (B) srivivek95 answered Oct 23, 2017 srivivek95 comment Share Follow See all 0 reply Please log in or register to add a comment.
6 votes 6 votes we can simply take values and check the expression , It always gives minimum of x and y. (B) The minimum of x and y akash.dinkar12 answered Apr 12, 2017 akash.dinkar12 comment Share Follow See all 0 reply Please log in or register to add a comment.