Question

Find the sum of numbers divisible by 123 in between 1000 and 2000.
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Answer 1

Answer:

The Numbers which are divisible by 7 and 8 will be divisible by 56.

There are 18 such number between 1000 and 2000 which are divisible by 56.

But there are some numbers which are divisible by 56 as well as 3. Such numbers are divisble by 56*3 = 168.

There 6 such no. which are divisible by 168.

So, total numbers which are divisible by 7 and but not divisible by 3 = 18 - 6 = 12.

Answer 2

Numbers divisible by 123 in between 1000 and 2000.

a = 1107

d = 123

L = 1968

L = a + (n-1)d

=> 1986 - 1107 = (n-1) 123

=> 861 / 123 = (n-1)

=> n-1 = 7

=> n = 7+1

=> n = 8

S = n/2 ( 2a + (n-1)d)

=> S = 8/2 (1107+1986)

=> S = 4 × 3075

=> S = 12,300 Ans.

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