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How many positive integers less than 100 are divisible by exactly

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How many positive integers less than 100 are divisible by exactly  [#permalink]

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New post 17 Apr 2020, 11:08
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Question Stats:

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How many positive integers less than 100 are divisible by exactly one of the integers 2,5,7?

(A) 39
(B) 49
(C) 59
(D) 69
(E) 79
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Re: How many positive integers less than 100 are divisible by exactly  [#permalink]

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New post 17 Apr 2020, 11:24
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Ravixxx wrote:
How many positive integers less than 100 are divisible by exactly one of the integers 2,5,7?

(A) 39
(B) 49
(C) 59
(D) 69
(E) 79


Multiple of 2 less than 100 = 49
Multiple of 5 less than 100 = 19
Multiple of 7 less than 100 = 14

Multiple of 2 and 5 less than 100 = 99/10 = 9
Multiple of 2 and 7 less than 100 = 99/14 = 7
Multiple of 5 and 7 less than 100 = 99/35 = 2

Multiples of 2 and 5 and 7 all = 1

Required numbers = 49+19+14 - 2*(9+7+2) + 3*1 = 49

ANswer: Option B
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Re: How many positive integers less than 100 are divisible by exactly  [#permalink]

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New post 17 Apr 2020, 11:45
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positive integer from 1- 100 are divisible by 2= [100/2] = 50

positive integer from 1- 100 are divisible by 5= [100/5] = 20

positive integer from 1- 100 are divisible by 7= [100/7] = 14

positive integer from 1- 100 are divisible by 10= [100/10] = 10

positive integer from 1- 100 are divisible by 14= [100/14] = 7

positive integer from 1- 100 are divisible by 35= [100/35] = 2

positive integer from 1- 100 are divisible by 70= [100/70] = 1


positive integers less than 100 are divisible by exactly one of the integers 2,5,7 = 50+20+14- 2(10+7+2) +3*1 = 49

[100 got deducted as it's divisible by 2 and 5.]


Ravixxx wrote:
How many positive integers less than 100 are divisible by exactly one of the integers 2,5,7?

(A) 39
(B) 49
(C) 59
(D) 69
(E) 79
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Re: How many positive integers less than 100 are divisible by exactly   [#permalink] 17 Apr 2020, 11:45

How many positive integers less than 100 are divisible by exactly

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