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Modulus

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Director
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Modulus [#permalink] New post 28 Oct 2009, 15:40
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

50% (00:00) correct 50% (01:42) wrong based on 1 sessions
If n is a positive integer, which of the following is a possible value of |56 - 5n|?
A. 7
B. 9
C. 12
D. 15
E. 20

[Reveal] Spoiler:
OA B, am I suppose to expand the equation? (56-5n)^2
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Re: Modulus [#permalink] New post 28 Oct 2009, 18:35
reply2spg wrote:
If n is a positive integer, which of the following is a possible value of |56 - 5n|?

A. 7
B. 9
C. 12
D. 15
E. 20

[Reveal] Spoiler:
OA B, am I suppose to expand the equation? (56-5n)^2


= |56 - 5n|
= |(10*5) +1 - 5n|

Since n is a +ve integer, |56 - 5n| must end in either (5k + 4) or (5k - 4) or (5k + 1) or (5k - 1). Only 9 fits to the formats above. So its B.
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Senior Manager
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Re: Modulus [#permalink] New post 28 Oct 2009, 21:46
so confused with this :)
this is the best I could come up with after a coffee:

possibilities for units digit:
6-5 = 1
6-0 = 6
reversing the subtraction (as it is absolute)
5-6 = -1
15-6 = 9
10-6 = 4

only one answer option, 9, fits above
prove using -56+5(12) = -56+65 = 9
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Re: Modulus [#permalink] New post 29 Oct 2009, 03:48
Try substituting values for n and we will end with 9.

n = 13 ==> | 56-65| ==> 9

I will choose option B
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Re: Modulus [#permalink] New post 31 Oct 2009, 10:44
Substituting the values is the best approach.. and leads to option B, which is correct answer.
Re: Modulus   [#permalink] 31 Oct 2009, 10:44
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