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# For any four digit number, abcd, *abcd*=

Author Message
Director
Joined: 11 Jun 2007
Posts: 914
For any four digit number, abcd, *abcd*= [#permalink]

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22 Sep 2007, 18:37
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

For any four digit number, abcd, *abcd*= (3^a)(5^b)(7^c)(11^d). What is the value of (n – m) if m and n are four-digit numbers for which *m* = (3^r)(5^s)(7^t)(11^u) and *n* = (25)(*m*)?

a) 2000
b) 200
c) 25
d) 20
e) 2

Manager
Joined: 20 Dec 2004
Posts: 177

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22 Sep 2007, 18:46
I have no idea how to approach this problem. where did u encounter this question.
_________________

Regards

Subhen

Director
Joined: 11 Jun 2007
Posts: 914

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22 Sep 2007, 18:48
subhen wrote:
I have no idea how to approach this problem. where did u encounter this question.

one of the MGMAT practice bank questions. Some of them are pretty damn difficult. This is on the 700-800 level. =\
Intern
Joined: 15 Sep 2007
Posts: 26

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22 Sep 2007, 20:36
1
KUDOS
This one is really not as difficult as it seems. here is how to approach it :

From the given equation for abcd, we can clearly see that the digits of the number, abcd are the powers to which 3,5,7,11 have been raised to.

so from *m*=(3^r)(5^s)(7^t)(11^u), we know that the four digit number "m" is "rstu" and its value is 1000r+100s+10t+u

*n*=(25)(*m*) = (25)(3^r)(5^s)(7^t)(11^u)
= (3^r)(5^(s+2))(7^t)(11^u)

Thus the four digit number "n" is "r(s+2)tu" and its value is 1000r+100(s+2)+10t+u

Finally n-m = 100(s+2) - 100s = 200
22 Sep 2007, 20:36
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