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If n is a positive integer and the greatest common divisor of n and 30

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If n is a positive integer and the greatest common divisor of n and 30 [#permalink]

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If n is a positive integer and the greatest common divisor of n and 300 is 20, which of the following is the greatest common divisor of n and 90?

A. 2
B. 5
C. 6
D. 10
E. 15
[Reveal] Spoiler: OA

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Re: If n is a positive integer and the greatest common divisor of n and 30 [#permalink]

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New post 13 Sep 2016, 02:36
GCD of n and 300 is 20. That means n and 300 has 2*2*5 as GCD.
Now the gcd for n (2*2*5*any number other than 3) and 90 (2*3*3*5) will be 2*5=10
Answer 10

Hope I'm right! Accuracy on Bunuel Problems are about 60% forme :roll: :|

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Re: If n is a positive integer and the greatest common divisor of n and 30 [#permalink]

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New post 13 Sep 2016, 02:43
Vinayak Shenoy wrote:
GCD of n and 300 is 20. That means n and 300 has 2*2*5 as GCD.
Now the gcd for n (2*2*5*any number other than 3) and 90 (2*3*3*5) will be 2*5=10
Answer 10

Hope I'm right! Accuracy on Bunuel Problems are about 60% forme :roll: :|
used same logic and got 10. What's the answer Bunuel?


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Re: If n is a positive integer and the greatest common divisor of n and 30 [#permalink]

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New post 13 Sep 2016, 05:56
From the fact that 20 is the GCD of n and 300 you can learn two things:

1) n is divisible by 20.

2) n has no more common divisors with 300 other than 2⋅2⋅5 - otherwise, those would also be included in the GCD.

In other words, if 300=3⋅2⋅2⋅5⋅5, and only 2⋅2⋅5 are common divisors for n, then n is NOT divisible by the remaining 3⋅5. In other words, we know that n is divisible by 20, but not by 3 - otherwise, the 3 would be added as a common factor to the GCD of 20 and 300. n could be 20, 40, 80, 140 (multiples of 20 that do not include a 3 or an extra 5), but not 60, 100 or 120 - otherwise, the GCD of n and 300 would be greater than 20.

Common prime factors of 20 and 90 are:

2 and 5.

This serves to POE answer choices A, B, and C: we have found a divisor of n and 90 that is greater than 2, 5, or 6. E is eliminated because n cannot be divisible by 3 (otherwise the GCD of n and 300 would be greater than 20). Therefore, 10 is the greatest common divisor

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Re: If n is a positive integer and the greatest common divisor of n and 30 [#permalink]

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New post 15 Dec 2017, 05:18
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Re: If n is a positive integer and the greatest common divisor of n and 30   [#permalink] 15 Dec 2017, 05:18
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