Question

how many two digit numbers divisible by 7​

Answer 1

There are 13 two – digits number which are divisible by 7.

The 2-digit number divisible by 7 is 14, 21, 28, 35……98

The 2-digit number divisible by 7 is 14, 21, 28, 35……98The first 2-digit number which is divisible by 7 is 14

The last 2-digit number which is divisible by 7 is 98

The last 2-digit number which is divisible by 7 is 98The list of 2-digit numbers divisible by 7 are 14, 21, 28, 35……98 which forms an A.P

Consider a formula:-

T(n) = a + (n – 1)d

T(n) = a + (n – 1)dWhere

T(n) = a + (n – 1)dWherea = 14

T(n) = a + (n – 1)dWherea = 14d = 7

T(n) = a + (n – 1)dWherea = 14d = 7T(n) = 98

T(n) = a + (n – 1)dWherea = 14d = 7T(n) = 9898 = 14 + (n – 1)7

T(n) = a + (n – 1)dWherea = 14d = 7T(n) = 9898 = 14 + (n – 1)784 = 7n – 7

T(n) = a + (n – 1)dWherea = 14d = 7T(n) = 9898 = 14 + (n – 1)784 = 7n – 77n = 91

T(n) = a + (n – 1)dWherea = 14d = 7T(n) = 9898 = 14 + (n – 1)784 = 7n – 77n = 91n = 13

T(n) = a + (n – 1)dWherea = 14d = 7T(n) = 9898 = 14 + (n – 1)784 = 7n – 77n = 91n = 13

∴ There are 13 two – digits number which are divisible by 7.

• hope it helps •

Answer 2

total number of multiples of 7 (only 2 digit numbers) = (14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98) = 13

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