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GMAT Instructor
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If q is the sum of all factors of 8184, then what is the [#permalink]
 16 Sep 2006, 02:58
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If q is the sum of all factors of 8184, then what is the units digit of q?
(A) 0 (B) 1 (C) 4 (D) 7 (E) none of these
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VP
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Its A. Thanks to Cicerone 
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The path is long, but self-surrender makes it short;
the way is difficult, but perfect trust makes it easy.
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GMAT Instructor
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How could this be done without Cicerone's formula, (which is very nice, by the way)?
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Intern
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kevincan wrote: How could this be done without Cicerone's formula, (which is very nice, by the way)?
I am sorry, I can't find Ciceone's formula. Can someone help?
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GMAT Instructor
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VP
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kevincan wrote: How could this be done without Cicerone's formula, (which is very nice, by the way)?
This is the way it was sujjested..
8184 = 2^3*3^1*11^1*31^1
= (2^4)-1/(2-1) * (3^2)-1/(3-1)* (11^2)-1/(11-1) * (31^2)-1/31-1
= 15*4*some number*...
unit's digit is 0
_________________
The path is long, but self-surrender makes it short;
the way is difficult, but perfect trust makes it easy.
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Senior Manager
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I am happy that people r using the formula given by me to answer these questions. I am sure that formulae like these will help us to save time in the exam, keep rocking folks, Regards,
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Averages Accelerated:Guide to solve Averages Quickly(with 10 practice problems)
Last edited by cicerone on 25 Sep 2008, 01:08, edited 1 time in total.
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Senior Manager
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I get 1 or 7?
Factors of 8184 = 2^3 * 3^1 * 11^1 * 31^1
So either 2+3+11+31 = 47 So units digit is 7
OR
2+2+2+3+11+31 = 51 So units digit 1
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VP
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cicerone wrote: I am happy that people r using the formula given by me to answer these questions. I am sure that formulae like these will help us to save time in the exam,
keep rocking folks,
Regards,
sure cicerone...it would definetely save a huge chunk of time
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Senior Manager
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AHHHHH, I've seen the light.
I read as sum of smallest factors, not ALL factors. D'oh!
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VP
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Re: PS: Units digit of q [#permalink]
17 Sep 2006, 06:38
kevincan wrote: If q is the sum of all factors of 8184, then what is the units digit of q?
(A) 0 (B) 1 (C) 4 (D) 7 (E) none of these
The factors are 31*11*3*2^3
If we take only fatcors that are not repetitive then it is 7.
If we can take all the 3 2's in 2^3 the it is 1
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Senior Manager
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trivikram, I think I fell into this trap. It asks for the sum of ALL of the factors so 8184, 4092.......1
I think!
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VP
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Thanks to Kevin for giving such wonderful questions
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