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Junior | Next Rank: 30 Posts
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by nagar.sandeep » Wed Sep 08, 2010 9:04 am
Hi,

Can you please explain me the solution of the following question:

The function f is defined for each positive three-digit integer n by f(n) = 2x3y5z, 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

Any help will be appreciated.

Thanks,
Sandeep.
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by Maciek » Wed Sep 08, 2010 12:34 pm
Hi Sandeep!

n = 100*x + 10*y + z
f(n) = 2x*3y*5z
f(m) = 9f(v)
m-v = ?

2xm*3ym*5zm = 9*2xv*3yv*5zv
xm*ym*zm = 9*xv*yv*zv
let us plug in numbers:
v = 991
xm*ym*zm = 9*9*9*1
xm = 9, ym = 9, zm = 9
m - v = 8
v = 919
xm*ym*zm = 9*9*1*9
m - v = 80

It is ambiguous for me. Can you find an error either in my calculation or in my approach?

Hope it helps!
Best,
Maciek
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by sanju09 » Wed Sep 08, 2010 10:39 pm
nagar.sandeep wrote:Hi,

Can you please explain me the solution of the following question:

The function f is defined for each positive three-digit integer n by f(n) = 2x3y5z, 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

Any help will be appreciated.

Thanks,
Sandeep.

@Sandeep,

Your post could confuse many if proper care is not taken while copy pasting your post. Remember, many expressions including subscripts and superscripts change their shape when brought to this edit box. The correct definition of the function, as per my evaluation here, must be f(n) = 2^x3^y5^z. Please take care while posting.

If m = 100 p + 10 q + r and v = 100 a + 10 b + c, then

2^p3^q5^r = 3^2(2^a3^b5^c) = 2^a3^(b + 2)5^c

That means, m and v are such that p = a, q = b + 2, and r = c, an example for m and v is m = 287 and v = 267, m - v = [spoiler]20, always.

D[/spoiler]
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
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by nagar.sandeep » Fri Sep 10, 2010 8:09 pm
Hi Maciek,

Sorry buddy, I did some copy paste mistake.
in the acutal question the equation was
f(n) = 2^x3^y5^z.

Thanks,
Sandeep

Maciek wrote:Hi Sandeep!

n = 100*x + 10*y + z
f(n) = 2x*3y*5z
f(m) = 9f(v)
m-v = ?

2xm*3ym*5zm = 9*2xv*3yv*5zv
xm*ym*zm = 9*xv*yv*zv
let us plug in numbers:
v = 991
xm*ym*zm = 9*9*9*1
xm = 9, ym = 9, zm = 9
m - v = 8
v = 919
xm*ym*zm = 9*9*1*9
m - v = 80

It is ambiguous for me. Can you find an error either in my calculation or in my approach?

Hope it helps!
Best,
Maciek
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