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

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Math Expert
Joined: 02 Sep 2009
Posts: 43862
The function f is defined for all positive, three-digit integers as [#permalink]

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25 Apr 2017, 01:14
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Difficulty:

55% (hard)

Question Stats:

59% (01:06) correct 41% (01:42) wrong based on 61 sessions

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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
[Reveal] Spoiler: OA

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

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25 Apr 2017, 03:13
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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!

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Re: The function f is defined for all positive, three-digit integers as   [#permalink] 25 Apr 2017, 03:13
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