First slide

Arithmetic progression

Question

The number of numbers lying between 100 and 500 that are divisible by 7 but not by 21 is

Moderate

A

57
B

19
C

38
D

None of these

Solution

The numbers between 100 and 500 that are divisible by 7 are 105, 112, 119, 126, 133, 140, 147, …, 483, 490, 497.
Let such numbers be n.
Then, $497 = 105 + (n - 1) \times 7; or n = 57$ .
The numbers between 100 and 500 that are divisible by 21 are 105, 126, 147, …, 483.Let such numbers be m.
Then 483 = 105 + (m – 1) × 21; or m = 19.
Hence, the required number = n – m = 57 – 19 = 38.

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