How many two-digit numbers are divisible by 6 ? A) 12 B) 15 C) 10

1.	How many two-digit numbers are divisible by 6 ? A) 12 B) 15 C) 10 D) 17
Answer» Correct option is (B) 15 First two-digit number which is divisible by 6 is 12 and last two-digit number which is divisible by 6 is 96. 12, 18, 24, ........., 96 is the A.P. of two-digit numbers which are divisible by 6. \(\therefore a=12,a_n=96,d=a_2-a_1=18-12=6\) Now, \(a_n=a+(n-1)d\) \(\Rightarrow96=12+(n-1)6\) \(\Rightarrow6(n-1)=96-12=84\) \(\Rightarrow n-1=\frac{84}6=14\) \(\Rightarrow n=14+1=15\) Hence, there are 15 two-digit numbers which are divisible by 6. Correct option is B) 15

How many two-digit numbers are divisible by 6 ? A) 12 B) 15 C) 10 D) 17

Answer»

Correct option is (B) 15

First two-digit number which is divisible by 6 is 12 and last two-digit number which is divisible by 6 is 96.

12, 18, 24, ........., 96 is the A.P. of two-digit numbers which are divisible by 6.

\(\therefore a=12,a_n=96,d=a_2-a_1=18-12=6\)

Now, \(a_n=a+(n-1)d\)

\(\Rightarrow96=12+(n-1)6\)

\(\Rightarrow6(n-1)=96-12=84\)

\(\Rightarrow n-1=\frac{84}6=14\)

\(\Rightarrow n=14+1=15\)

Hence, there are 15 two-digit numbers which are divisible by 6.

Correct option is B) 15