Find the sum of the integers which are divisible by 5 or 7 and lie between 1 and 100.
A
1680
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B
1780
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C
1670
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D
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 =n2(2a+(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.