Ramu had to select a list of numbers between 1 and 1000 (including both), which are divisible by both 2 and 7. How many such numbers are there?

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SSC CPO 2022 Tier-I Official Paper (Held On 11 Nov 2022 Shift 1) [Answer Key]
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  1. 142
  2. 71
  3. 97
  4. 642

Answer (Detailed Solution Below)

Option 2 : 71
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Given:

Ramu had to select numbers between 1 to 1000 ( including both)

which are divisible by both 2 and 7 

Formula used:

an = a + ( n -  1) × d 

Where, an = last number, a = 1st term, n = number of terms, d= common difference

d = 2nd term - 1st term = 3rd term - 2nd term = 4th term - 3rd term etc.....

Calculation:

Here, it is given a list of numbers between 1 to 1000 (including both) , which are divisible by both 2 and 7

So, to be divisible by both 2 and 7, the number has to be divisible by 14 

As, we know that,

an = a + ( n - 1) × d

So, a = 1st term = 14 , 2nd term = 28 , last term = 994 

d = 2nd term - 1st term = 28 - 14 = 14 

⇒ 994 = 14 + ( n - 1) × 14 

⇒ 980  = 14n - 14 

⇒ 994 = 14n

⇒ n = 71 

Hence, there are 71 terms between 1 to 1000 (including both ) which are divisible by both 2 and 7.

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