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The function f is defined for all positive, three-digit integers as

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The function f is defined for all positive, three-digit integers as  [#permalink]

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New post 25 Apr 2017, 02:14
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The function f is defined for all positive, three-digit integers as \(f(x)=(2^a)(3^b)(5^c)\), where a, b, and c are the hundreds, tens, and units digits, respectively, of x. What is m−n?


(1) \(f(m)=8f(n)\)

(2) \(n=111\)

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Re: The function f is defined for all positive, three-digit integers as  [#permalink]

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New post 25 Apr 2017, 04:13
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S1. f(m)=8f(n)

f(m) = 2^3 f(n)

f(x) = 2^a * 3^b * 5^c

so, we now know that only a is different in f(m) and f(n), b and c are same.
we also know that a in f(m) is 3 greater than a in f(n).

a is the hundreds digit of the number. So, if m=401, n =101 or m=996, n=696

m-n in all case would be 300.

Sufficient!

S2. No mention of m.

Insufficient!

Hence, answer will be A.
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Re: The function f is defined for all positive, three-digit integers as  [#permalink]

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New post 10 Sep 2018, 09:11
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Re: The function f is defined for all positive, three-digit integers as &nbs [#permalink] 10 Sep 2018, 09:11
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