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The function f is defined for each positive three-digit

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Manager
Joined: 24 Jun 2017
Posts: 91

Kudos [?]: 13 [0], given: 123

The function f is defined for each positive three-digit [#permalink]

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09 Aug 2017, 16:56
The easiest way for me was:
take v=100 as the least possible 3 digits positive integer and plug it into the function
f(v)=2^1*3^0*5^0= 2*1*1=2
Then we know that f(m) = 9*f(v)
so f(m) = 18
it's obvious that we keep 5^0 in order to get 1, then what are prime factors for 18, it's 2 and 3^2
then the 3 digits number is m=120

120-100=20

works like a charm for all that kind of questions

Kudos [?]: 13 [0], given: 123

Intern
Joined: 28 May 2014
Posts: 30

Kudos [?]: 1 [0], given: 83

Schools: ISB '17, NUS '17
Re: The function f is defined for each positive three-digit [#permalink]

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01 Sep 2017, 09:30
Hi Bunuel,

My question here is how you can write 2^a x 3^b x 5^c = 100a + 10b + c. Is this a property, if yes then why 120 three digit positive integer is not as per this property.

Kudos [?]: 1 [0], given: 83

Intern
Status: Target 760
Joined: 20 Aug 2014
Posts: 10

Kudos [?]: 5 [0], given: 2

Location: India
Concentration: Strategy, Economics
GPA: 3.25
WE: Corporate Finance (Investment Banking)
Re: The function f is defined for each positive three-digit [#permalink]

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15 Oct 2017, 08:18
Orange08 wrote:
The function f is defined for each positive three-digit integer n by $$f(n) = 2^x3^y5^z$$ , where x, y and z are the hundreds, tens, and units digits of n, respectively. If m and v are three-digit positive integers such that $$f(m)=9*f(v)$$ , then $$m-v=$$ ?

(A) 8
(B) 9
(C) 18
(D) 20
(E) 80

2^x3^y5^z is the function: If you caught the above highlighted clue from the question stem you are through. Since the differential is of 3^2 means that at the tens position, 10*2 is the additional figure to the overall number, m. Thus, M-V=10(x+2)-10x = 20

Kudos [?]: 5 [0], given: 2

Re: The function f is defined for each positive three-digit   [#permalink] 15 Oct 2017, 08:18

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