How many numbers between 300 and 1000 are divisible by 7?

Question

Question

This question was previously asked in

NTPC CBT-I (Held On: 9 Jan 2021 Shift 1)

Answer 1

Given condition:

Numbers between 300 and 1000 are divisible by 7.

Concept:

Arithmetic Progression

a_n = a + (n - 1)d

Calculation:

The first number that is divisible by 7 (300 - 1000) = 301

Likewise: 301, 308, 315, 322...........994

The above series makes an AP,

Where a = 301, Common Difference/d = 308 - 301 = 7 and Last term (an) = 994

⇒ an = a + (n - 1)d

⇒ 994 = 301 + (n - 1)7

⇒ (994 - 301)/7 = n - 1

⇒ 693/7 + 1 = n

⇒ 99 + 1 = n

⇒ n = 100

∴ There are 100 numbers between 300 and 1000 which are divisible by 7.