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# The Sum of All the Natural Numbers from 200 to 600 (Both Inclusive) Which Are Neither Divisible by 8 Nor by 12 Is: - Mathematics

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MCQ

The sum of all the natural numbers from 200 to 600 (both inclusive) which are neither divisible by 8 nor by 12 is:

#### Options

• 1, 23, 968

• 1, 33, 068

• 1, 33, 268

• 1, 87, 332

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#### Solution

1, 33, 268

Explanation:

Sum of no. from 200 to 600

a = 200, d = 1, n = 600 - 200 + 1 = 401

"S"_401=401/2[200+600]....{"S"_"n"="n"/2("a"+"l")}

=401/2(800)=401xx400

⇒ 160400

Sum of numbers divisible by both 8 or 12

= n (8) + n (12) − n (LCM of 8 and 12)

Sum of numbers divisible by 8

=51/2[200+600]=51xx400=20400

Sum of numbers divisible by 12

=34/2(204+600)=17xx804=13668

Sum of numbers divisible by 24  .....(LCM of 8 and 12)

=17/2(216+600)=17xx408=6936

Sum of numbers divisible by 8 or 12

= 20400 + 13668 − 6936 = 27132

Sum of numbers neither divisible by 8 nor 12

= 160400 − 27132 = 133268

Concept: HCF and LCM (Entrance Exam)
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