CAT 2016 | Question: 73

Question

$A, S, M$ and $D$ are functions of $x$ and $y$, and they are defined as follows.

• $A(x, y) = x + y$
• $M(x, y) = xy$
• $S(x,y)= x-y$
• $D(x,y)= x/y, y\neq 0$

What is the value of $M(M(A(M(x, y), S(y, x)), x), A(y, x))$ for $x = 2, y = 3$?

• A. $60$
• B. $140$
• C. $25$
• D. $70$

Answer 1

Given that,

• $A(x,y)=x+y$
• $M(x,y)=xy$
• $S(x,y)=x−y$
• $D(x,y)=x/y;y\ne0$

Now, the value of $M(M(A(M(x,y),S(y,x)),x),A(y,x))$ for $x=2,y=3:$

$\Rightarrow M(M(A(M(2,3),S(3,2)),2),A(3,2))$

$\Rightarrow M(M(A(6,1),2),5)$

$\Rightarrow M(M(7,2),5)$

$\Rightarrow M(14,5)$

$\Rightarrow 70$

Correct Answer $:\text{D}$