GATE CSE 2017 Set 1 | Question: GA-8

Question

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

• A. The maximum of $x$ and $y$
• B. The minimum of $x$ and $y$
• C. $1$
• D. None of the above

Comments

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.

---

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

---

yes it gives always minimum of x & y for all values of x &y  .

Answer 1

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

Comments

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! :)

---

(A) The maximum of x and y                                         (B) The minimum of x and y

PLEASE explain meanging of both

---

$(A)$ 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 $y$

 $min(x,y)=min(1,2)=1$

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

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

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

Answer 2

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

Answer 3

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

So, option (B)

Answer 4

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