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

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Manager
Joined: 08 Aug 2008
Posts: 228
The function f is defined for each positive three-digit [#permalink]

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05 Nov 2008, 12:01
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) = 9f(v), then m-v = ?
A. 8
B. 9
C. 18
D. 20
E. 80

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Manager
Joined: 08 Aug 2008
Posts: 228

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05 Nov 2008, 12:04
i guessed the answer as D.

since 2,3,5 are all primes, the corresponding digits would remain same for units and hundredths except for tens which would be +2 and thus the diffrence as 20.

However, i would like to know if there is another way to solve it.
Thanks.
Manager
Joined: 30 Sep 2008
Posts: 111

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06 Nov 2008, 05:13
prasun84 wrote:
i guessed the answer as D.

since 2,3,5 are all primes, the corresponding digits would remain same for units and hundredths except for tens which would be +2 and thus the diffrence as 20.

However, i would like to know if there is another way to solve it.
Thanks.

I suppose yours is the quickest way

as $$f(m) = 9f(v) so y_{m} - y_{v} = 2, x_{m} = x_{v}, z_{m} = z_{v}$$

$$m - v = 100x_{m} + 10y_{m} + z_{m} - 100x_{v} + 10y_{v} + z_{v} = 10y_{m} - 10y_{v} = 10*2 = 20$$
Director
Joined: 14 Aug 2007
Posts: 704

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06 Nov 2008, 05:48
prasun84 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) = 9f(v), then m-v = ?
A. 8
B. 9
C. 18
D. 20
E. 80

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

2^(x-a) * 3 ^(y-b) * 5^(z-c) = 3^2

x-a =0
y-b = 2
z-c = 0

20

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This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

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Re: Func   [#permalink] 06 Nov 2008, 05:48
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# The function f is defined for each positive three-digit

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