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Question

If x denotes the value of the sum of the integers lying between 1 and 100 which are divisible by either 3 or 7. The value of X equals

A
5050
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B
3000
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C
4068
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D
2208
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Solution

The correct option is C 2208
Divisible by 3:3,6,9,12,.....,99
A.P with a=3,d=3,an=99,n=?
an=a+(n1)d
99=3+(n1)3
96=3n3
3n=99
n=33
Sum =n2(2a+(n1)d)
=n2(a+an)=332(3+99)
=33(51)=1683
Divisible by 7:7,14,..98
98=7+(n1)7
91=7n7
7n=98
n=14
Sum =7(7+98)=7×105=735
Divisible by both 3 & 7, i.e., by 21,
21,42,63,84
Sum =63+147=210
Total sum=1683+735210
=2208.

1165383_1245759_ans_a6ac49f7c0ef4bc8ababc8459bf54de4.jpg

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