Question

Let $A=\{1,2,3,.......50\}$ and $B=\{2,4,\mathrm{6.......100}\}$ .The number of elements $(x,y)\in A\times B$ such that $x+y=50$

• A. $24$
• B. $25$
• C. $50$
• D. $75$

Answer 1

The correct option is A $24$

The elements will be
$(2,48),(48,2)$
$(4,46),(46,4)$
:
:
$(2n,50-2n),(50-2n,2n)$
Now we have
$2,4,6,\mathrm{8...}$ upto $48$
This forms an A.P
The number terms is $24$.