Question

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

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

Answer 1

Answer: (C)

number should be of the form $4k+1$

Smallest 2 digit number that gives remainder $1$ when divided by $4$ $\Rightarrow$ $13(whenk=3)$ first term of A.P

Largest 2 digit number that gives remainder $1$ when divided by $4$ $\Rightarrow$ $97(whenk=24)$ last term of AP

Series: $13,17,21,....97$

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

$97=13+(n-1)4$

$89=(n-1)4$

$(n-1)=21$

$n=22$

Sum of series $=\frac{n}{2}$[first term + last term]

$=\frac{22}{2}[13+97]$

$=11\times \left(110\right)$

$=1210$