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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
edited | 2.7k views

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
edited by
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substitute 6,-2 it is giving -2 as answer
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Yes -2 is the minimum
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..?? i did not get.. plz elaborate
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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! :)
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(A) The maximum of x and y                                         (B) The minimum of x and y

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$(A)$ 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 $y$

$min(x,y)=min(1,2)=1$

$min(x,y)=min(100,200)=100$

$min(x,y)=min(10,2)=2$

$min(x,y)=min(101,102)=101$

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

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

So, option (B)

we can simply take values and check the expression , It always gives minimum of x and y.
(B)   The minimum of x and y

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