Question

13. How many three-digit numbers are divisible by 7?
14. How many multiples of 4 lie between 10 and 250?

Answer 1

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13. The first three - digit number which is divisible by 7 is 105 and last three digit number which divisible by 7 is 994.

This is an A.P. in which a = 105, d = 7 and 1 = 994.

Let the number of terms be n then tn = 994.

nth term of A.P. = tn = a + (N - 1)d

994 = 105 + (n - 1)7

889 = 7(n - 1) => n - 1 = 127

n = 127 + 1 = 128

Ans:- There are 3 digits numbers which are divisible by 7.

14. The first multiple of 4 beyond 10 is 12.

The multiple of 4 just below 250 is 248.

∴ The A.P. is given by : 12, 16, ..... , 248

Here, a = 12 and d = 4.

Let the number of terms = n

∴ Using Tn = a + (n - 1) d, we get

Tn = 12 + (n - 1) × 4

=> 248 = 12 + (n - 1) × 4

=> (n - 1) × 4 = 248 - 12 = 236

=> n - 1 = 236/4 = 59 => N = 59 + 1 = 60

Thus, the required number of multiples = 60.

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