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

A) 1190
B) 1197
C) 1210
D) None of these
Explanation

(c)
The given numbers are 13, 17, … , 97. This is an AP with the first term 13 and common difference 4. Let the number of term be $n$. Then
$97 = 13 + (n - 1)4\ \Rightarrow 4n = 88\ \Rightarrow n = 22$
Therefore, the sum of the numbers
$S = \frac{n}{2}(a + l)$
$= \frac{22}{2}\lbrack 13 + 97\rbrack = 11(110) = 1210$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.