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# If q is the sum of all factors of 8184, then what is the

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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, 01:58
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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
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.

GMAT Instructor
Joined: 04 Jul 2006
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Kudos [?]: 167 [0], given: 0

How could this be done without Cicerone's formula, (which is very nice, by the way)?
Intern
Joined: 23 Aug 2006
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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?
GMAT Instructor
Joined: 04 Jul 2006
Posts: 1266
Followers: 24

Kudos [?]: 167 [0], given: 0

VP
Joined: 21 Aug 2006
Posts: 1026
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Kudos [?]: 21 [0], given: 0

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.

Senior Manager
Joined: 28 Aug 2006
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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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Last edited by cicerone on 25 Sep 2008, 00:08, edited 1 time in total.
Senior Manager
Joined: 20 Feb 2006
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Kudos [?]: 7 [0], given: 0

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
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
Senior Manager
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AHHHHH, I've seen the light.

I read as sum of smallest factors, not ALL factors. D'oh!
VP
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Re: PS: Units digit of q [#permalink]  17 Sep 2006, 05:38
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
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!
VP
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Thanks to Kevin for giving such wonderful questions
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