Q12 of 14 Page 1

How many two digits numbers are divisible by 6.

The numbers divisible by 6 will form an arithmetic progression with common difference 6


First two-digit no. divisible by 6 is 12 = a1


last two-digit no. divisible by 6 is 96 = an


Therefore, we have to find number of terms in AP 12, 18, …, 96


Here, First term, a = 12


Common difference, d = 96


nth term = 96


We know, nth term of an AP is an = a1 + (n – 1)d


⇒ 96 = 12 + (n – 1)6


⇒ 84 = (n – 1)6


⇒ n – 1 = 14


⇒ n = 15


∴ 15 two-digit no are divisible by 6


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