How many two-digit numbers are divisible by 6?

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answer is C.

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Detailed Solution

We have given 2-digit numbers that are divisible by 6.
Since, two-digit numbers divisible by 6 are 12, 18, 24,....,96
As these numbers are in A.P.
So, first term a = 12 and second term

a 2 = 18

.
Applying formula and determining the common difference:

∴ d = 18 − 12 ⇒ d = 6

Let the A.P. contain n terms:

∴ a n = 96

Formula used for nth term of A.P.:

a n = a + n − 1 d

Applying the formula for nth term of A.P.:

∴ 12 + (n − 1) × 6 = 96 ⇒ 12 + 6 n − 6 = 96 ⇒ 6 + 6 n = 96

⇒ 6 n = 96 − 6 ⇒ n = 906 ⇒ n = 15

Therefore, there are 15 two-digit numbers divisible by 6.
Hence, option (3) is correct.

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