Find the sum of the integers which are divisible by 5 or 7 and lie between 1 and 100.

1680

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1780

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1670

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1690

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Solution

The correct option is A
1680

The numbers which are divisible by 5 will form an A.P. with a common difference of 5.
The last term will be = 100
5 + (n-1)5 =100
n = 20.
Sum of the numbers $= \frac{n}{2} (2 a + (n - 1) d)$
Sum of numbers which are divisible by 5 = 1680.
The numbers which are divisible by 7 will form an A.P. with a
common difference of 7 The last term with be =98
7 + (n-1)7 =98
n = 14
Sum of the numbers which are divisible by 7 = 735
Sum of multiples of 35 between 1 and 100
Sum of numbers which are divisible by 5 or 7 = 1680 + 735 -105
=2310.

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