Question

The sum of all two digit numbers which when divided by $4$, yield unity as reminder is

• A. $1012$
• B. $1201$
• C. $1212$
• D. $1210$

Answer 1

The correct option is D $1210$

Sum of all $2$ digit number divided by $4$ yields unity as remainder

$=13+17+21+97$

Series is in $AP$ and total are

$=a+(n-1)d=97$

4413+(n-1)4=97$

$(n-1)4=84$

$n-1=21$

$n=22$ terms

Sum $=\frac{n}{2}(2a+(n-1\left)d\right)=\frac{22}{2}(26+(21\times 4)=11(26+84)=11(110)=1210$

Answer $D$