Q. 105.0( 2 Votes )

# How many two digit numbers are divisible by 13?

Answer :

The two digits form the A.P.: 10, 11, 12 … 99.

The two digit numbers that are divisible by 13 form the A.P.: 13, 26, 39 … 91.

Here, first term, a = 13

__We know that common difference, d = a _{1} – a.__

∴ d = 26 – 13 = 13

And last term, l = 91

__We know that l = a + (n – 1) d.__

⇒ 91 = 13 + (n – 1) (13)

⇒ 91 – 13 = (n – 1) (13)

⇒ 78 = (n – 1) (13)

⇒ 78/13 = (n – 1)

⇒ 6 = n – 1

⇒ n = 6 + 1 = 7

∴ There are 7 two digit numbers that are divisible by 13.

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