The sum of all two digit numbers which, when divided by 4, yield … - Vidyadip

MCQ

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

A
$1190$
B
$1197$
✓
$1210$
D
None of these

✓

Answer

Correct option: C.

$1210$

c
(c) The given numbers are $13, 17, ..... 97.$

This is an $AP$ with first term $13$ and common difference $4$.

Let the number of terms be $n$.

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

$ \Rightarrow $ $4n = 88$

$ \Rightarrow $ $n = 22$

Therefore the sum of the numbers

$ = \frac{{22}}{2}[13 + 97] = 11(110) = 1210$.

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