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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
What is the total number of positive integers that are less than 100 a
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05 Nov 2021, 05:32
05 Nov 2021, 05:32
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Question Stats:
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What is the total number of positive integers that are less than 100 and that have no positive factor in common with 100 other than 1?
A. 30
B. 40
C. 50
D. 60
E. 70
A. 30
B. 40
C. 50
D. 60
E. 70
Re: What is the total number of positive integers that are less than 100 a
[#permalink]
05 Nov 2021, 06:41
05 Nov 2021, 06:41
1
The positive multiples of 100 (excluding 1) are 2, 4, 5, 10, 20, 25, 50, and 100.
1) So any positive integer that has 2 as a multiple, which is basically ALL even numbers, are out.
2) All multiple of 2 are also multiples of 4 and don't need to be counted again.
3) All multiples of 5 should also be excluded, but keep in mind that we've already counted the even ones such as 10, 20, 30, etc. So counting only the odd multiples of 5, we should have another 10 numbers (such as 5, 15, 25, etc.)
4) Multiples of 10, 20, 25, and 50 should be included in both the previous buckets (multiples of 2 and 5).
5) Answer, 100 (total number of positive integers less than 100) - 50 (all even numbers) - 10 (odd multiples of 5) = 40.
Is the answer 40?
1) So any positive integer that has 2 as a multiple, which is basically ALL even numbers, are out.
2) All multiple of 2 are also multiples of 4 and don't need to be counted again.
3) All multiples of 5 should also be excluded, but keep in mind that we've already counted the even ones such as 10, 20, 30, etc. So counting only the odd multiples of 5, we should have another 10 numbers (such as 5, 15, 25, etc.)
4) Multiples of 10, 20, 25, and 50 should be included in both the previous buckets (multiples of 2 and 5).
5) Answer, 100 (total number of positive integers less than 100) - 50 (all even numbers) - 10 (odd multiples of 5) = 40.
Is the answer 40?
gmatclubot
Re: What is the total number of positive integers that are less than 100 a [#permalink]
05 Nov 2021, 06:41
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