Question

The sum of all two-digit odd positive numbers is equal to

• A. 2235
• B. 2745
• C. 2475
• D. 2385

Answer 1

The correct option is C 2475

The sequence of all the two-digit odd positive numbers are 11, 13, 15, 17, …, 99.
Clearly, they form an AP with first term (a) = 11, common difference (d) = 2 and last term (l) = 99
Let the number of terms be n.
Last term of the AP, l = a + (n –1)d
$\Rightarrow a+(n-1)d=99$
$\Rightarrow 11+(n-1)\times 2=99$
$\Rightarrow (n-1)=44$
$\Rightarrow n=45$
Sum of n terms, $S_n=\frac{n}{2}(a+l)$
$\Rightarrow S_n=\frac{45}{2}(11+99)$
$\Rightarrow S_n=45\times 55=2475$
Thus, the sum of all two-digit odd positive numbers is 2475.
Hence, the correct answer is option (3).