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n and k are positive integers. If n=(22)(3)(53)/15k, is n<k?

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n and k are positive integers. If n=(22)(3)(53)/15k, is n<k? [#permalink]

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n and k are positive integers. If n=(2^2)(3)(5^3)/15k, is n<k?
1) n<10
2) k>4

*An answer will be posted in 2 days.
[Reveal] Spoiler: OA

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Last edited by MathRevolution on 13 Jun 2016, 01:09, edited 1 time in total.

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n and k are positive integers. If n=(22)(3)(53)/15k, is n<k? [#permalink]

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New post 13 Jun 2016, 01:08
If we modify the original condition and the question, we get n=100/k, k=100/n. If we substitute this into n<k?, the question becomes n<100/n?, n^2<100=10^2?, n<10?. Hence, the correct answer is A.

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Re: n and k are positive integers. If n=(22)(3)(53)/15k, is n[#permalink]

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New post 13 Jun 2016, 05:45
MathRevolution wrote:
n and k are positive integers. If n=(2^2)(3)(5^3)/15k, is n<k?
1) n<10
2) k>4

*An answer will be posted in 2 days.

Both sufficient


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Re: n and k are positive integers. If n=(22)(3)(53)/15k, is n<k? [#permalink]

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Re: n and k are positive integers. If n=(22)(3)(53)/15k, is n<k? [#permalink]

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New post 23 Sep 2017, 11:10
How did the substitution occur?

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Re: n and k are positive integers. If n=(22)(3)(53)/15k, is n<k? [#permalink]

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New post 24 Sep 2017, 10:13
Madhavi1990 wrote:
How did the substitution occur?


simplify the eq: it comes down to n = 300/k

1. n<10 to make that happen k>30
2. k>4 so k=5 n=60... keep going and k=31 n<10 so we have multiple values

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Re: n and k are positive integers. If n=(22)(3)(53)/15k, is n<k? [#permalink]

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New post 24 Sep 2017, 11:26
Simplifying question stem:
\(n=\frac{(4*3*5*5*5)}{(5*3)k}\)
\(n=\frac{100}{k}\)

Statement 1: n<10
Rewrite question stem as \(k=\frac{100}{n}\)
For 0<n<10, k will be more than n.-----------Sufficient

Statement 1: k>4
Rewrite question stem as \(n=\frac{100}{k}\)
For k=100, n=1.................Is n<k? Yes
For k=5, n=20................Is n<k? No----------Insufficient

Answer is A
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Re: n and k are positive integers. If n=(22)(3)(53)/15k, is n<k?   [#permalink] 24 Sep 2017, 11:26
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