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

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Director
Joined: 29 Aug 2005
Posts: 832
The function f is defined for each positive three-digit [#permalink]

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08 Nov 2008, 14:22
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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Intern
Joined: 04 Nov 2008
Posts: 15
Re: GMAT Set 30 - 2 [#permalink]

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08 Nov 2008, 18:03
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the answer is ( D ) 20

let m = xyz
v = x1 y1 z1
where x,x1 are hundred
y,y1 are tens
z,z1 are units

F(m) = 2^x * 3^y * 5^z
F(v) = 2^x1 * 3^y1 * 5^z1

F(m)=9 F(v)
F(m)=3^2 F(v)

2^x * 3^y * 5^z = 3^2 * 2^x1 * 3^y1 * 5^z1

now let us combine
3^2 and 3^y1
it will be 3^y1+2

2^x * 3^y * 5^z = 2^x1 * 3^(y1+2) * 5^z1

from the equation

x = x1
y = y1+2
z = z1

if M = 131
==> V = 111

F(M)=F(131) = 2^1 * 3^3 * 5^1 = 270
F(V)=F(111) = 2^1 * 3^1 * 5^1 = 30

So

M - V = 131 - 111 = 20

answer is (D)
VP
Joined: 05 Jul 2008
Posts: 1367
Re: GMAT Set 30 - 2 [#permalink]

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08 Nov 2008, 18:57
abohassan wrote:
the answer is ( D ) 20

let m = xyz
v = x1 y1 z1
where x,x1 are hundred
y,y1 are tens
z,z1 are units

F(m) = 2^x * 3^y * 5^z
F(v) = 2^x1 * 3^y1 * 5^z1

F(m)=9 F(v)
F(m)=3^2 F(v)

2^x * 3^y * 5^z = 3^2 * 2^x1 * 3^y1 * 5^z1

now let us combine
3^2 and 3^y1
it will be 3^y1+2

2^x * 3^y * 5^z = 2^x1 * 3^(y1+2) * 5^z1

from the equation

x = x1
y = y1+2
z = z1

if M = 131
==> V = 111

F(M)=F(131) = 2^1 * 3^3 * 5^1 = 270
F(V)=F(111) = 2^1 * 3^1 * 5^1 = 30

So

M - V = 131 - 111 = 20

answer is (D)

Excellent!. I got until the equations but did not realize no matter what the values are the difference is going to be only 20
SVP
Joined: 29 Aug 2007
Posts: 2452
Re: GMAT Set 30 - 2 [#permalink]

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08 Nov 2008, 18:59
1
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KUDOS
botirvoy 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

If f(m) = 9f(v), then m = xyz and v = x(y-2)z.

Since m is a 3 digit integer, xyz = 100x + 10y + z.
Similarly, v = x(y-2)z = 100x + 10(y-2) + z
so m - v = 100x + 10y + z - [100x + 10(y-2) + z] = 20

D.
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Director
Joined: 29 Aug 2005
Posts: 832
Re: GMAT Set 30 - 2 [#permalink]

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09 Nov 2008, 02:34
Excellent explanations - thank you!
OA is indeed D

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Re: GMAT Set 30 - 2   [#permalink] 09 Nov 2008, 02:34
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# The function f is defined for each positive three-digit

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