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35 votes
35 votes

The expression $\large \frac{(x+y) - |x-y|}{2}$ is equal to :

  1. The maximum of $x$ and $y$
  2. The minimum of $x$ and $y$
  3. $1$
  4. None of the above
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4 Answers

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
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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
16 votes
16 votes

Hence, minimum value in both the case is the required answer.

So, option (B)

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
Answer:

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