Q10 of 110 Page 41

How many two digit numbers are divisible by 13?

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 = a1 – 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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