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*n* = (25) (*m*)?

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*n* = (25) (*m*)?

by sanju09 » Thu Mar 29, 2012 12:25 am
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
Last edited by sanju09 on Thu Mar 29, 2012 4:34 am, edited 1 time in total.
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by killer1387 » Thu Mar 29, 2012 3:44 am
are you sure something is not missing here in question? this question seems incomplete.
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by killer1387 » Thu Mar 29, 2012 3:47 am
surfing, i happened to find the correct form of question
here is the link:

https://www.manhattangmat.com/forums/mgm ... t5760.html
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by neelgandham » Thu Mar 29, 2012 4:08 am
Let m = 1111, *m* = (3*1)*(5*1)*(7*1)*(11*1)
Let n = 5511, *n* = (3*5)*(5*5)*(7*1)*(11*1) = 25 * (3*1)*(5*1)*(7*1)*(11*1) = 25 * *m*
n - m = 5511 - 1111 = 4400, Hmm. Alright, Let me try with another number

Let m = 1111, *m* = (3*1)*(5*1)*(7*1)*(11*1)
Let n = 1155, *n* = (3*1)*(5*1)*(7*5)*(11*5) = 25 * (3*1)*(5*1)*(7*1)*(11*1) = 25 * *m*
n - m = 1155 - 1111 = 44. Oops

Sanju sirjee, Is the question CORRECT :D?, or Am I missing a thing ?
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by sanju09 » Thu Mar 29, 2012 4:37 am
neelgandham wrote:Let m = 1111, *m* = (3*1)*(5*1)*(7*1)*(11*1)
Let n = 5511, *n* = (3*5)*(5*5)*(7*1)*(11*1) = 25 * (3*1)*(5*1)*(7*1)*(11*1) = 25 * *m*
n - m = 5511 - 1111 = 4400, Hmm. Alright, Let me try with another number

Let m = 1111, *m* = (3*1)*(5*1)*(7*1)*(11*1)
Let n = 1155, *n* = (3*1)*(5*1)*(7*5)*(11*5) = 25 * (3*1)*(5*1)*(7*1)*(11*1) = 25 * *m*
n - m = 1155 - 1111 = 44. Oops

Sanju sirjee, Is the question CORRECT :D?, or Am I missing a thing ?
Oh yeah! I missed a big thing. Edited :)

This account is the punishment of posting erroneous matter previously:

What must be taken out of it is that m is a 4-digit number with s in its 100th place, such that

*m* = (3^r) (5^s) (7^t) (11^u) and

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

Hence n is another 4-digit number whose 100th digit is (s + 2), and the other 3 digits are quite the same as that of m. To get the value of n - m, we can do the subtraction work as under:

n = r (s + 2) t u

m = r s t u

(-)
----------------------
n - m = [spoiler]0200
----------------------

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



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