Question

If the sets A and B are defined as
$A=\{x:x=2n,n\in N,n<100\}B=\{x:x=3n,n\in N,n<100\}$
then, the number of elements in $A\cap B$ is

• A. 16
• B. 198
• C. 33
• D. 59

Answer 1

The correct option is C 33

$A=\{x:x=2n,n\in N,n<100\}=\{2,4,6,8,.....,198\}B=\{x:x=3n,n\in N,n<100\}=\{3,6,9,12,....,297\}\mathrm{The}\mathrm{elements}\mathrm{in}A\cap B\mathrm{are}\mathrm{the}\mathrm{common}\mathrm{multiples}\mathrm{of}2\mathrm{and}3\mathrm{which}\mathrm{are}\mathrm{less}\mathrm{than}199.\mathrm{Common}\mathrm{multiples}\mathrm{of}2\mathrm{and}3\mathrm{are}\mathrm{multiple}\mathrm{of}6.\mathrm{So}A\cap B\mathrm{will}\mathrm{contain}\mathrm{multiples}\mathrm{of}6\mathrm{less}\mathrm{than}199.\therefore A\cap B=(x:x=6n,n\in N,x<199\}A\cap B=(6,12,18,24,....,198\left\}n\right(A\cap B)=33$