Question

10. Sum of the odd numbers from 1 to 2019 both inclusive, is divisible by
A) only 100
B) only 101
C) both 100 and 101
D) neither by 100 nor by 101​

Answer 1

Answer:

option (c) is correct

Step-by-step explanation:

Sum of the odd numbers from 1 to 2019 both inclusive, is divisible by

A) only 100

B) only 101

C) both 100 and 101

D) neither by 100 nor by 101​

Clearly, the numbers 1,3,5,...............2019

form an A.P with common difference 2.

Here,

First term, a=1

Last term, l=2019

$\text{Number of terms },n=\frac{l-a}{d}+1$

$\implies\:n=\frac{2019-1}{2}+1$

$\implies\:n=\frac{2018}{2}+1$

$\implies\:n=1009+1$

$\implies\:n=1010$

$\text{Sum of the A.P },S_n=\frac{n}{2}[a+l]$

$\implies\:S_n=\frac{1010}{2}[1+2019]$

$\implies\:S_n=\frac{1010}{2}[2020]$

$\implies\:S_n=(1010)(1010)$

$\implies\:S_n=101\times\:101\times\:100\:\text{which is divisible by both 100 and 101}$

Answer 2

Answer:

C) both 100 and 101

Step-by-step explanation:

10. Sum of the odd numbers from 1 to 2019 both inclusive, is divisible by

A) only 100

B) only 101

C) both 100 and 101 ✓

D) neither by 100 nor by 101