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# Modulus

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Director
Joined: 12 Oct 2008
Posts: 557
Followers: 2

Kudos [?]: 149 [0], given: 2

Modulus [#permalink]  28 Oct 2009, 15:40
00:00

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? $$(56-5n)^2$$
SVP
Joined: 29 Aug 2007
Posts: 2493
Followers: 59

Kudos [?]: 576 [0], given: 19

Re: Modulus [#permalink]  28 Oct 2009, 18:35
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.
_________________
Senior Manager
Joined: 18 Aug 2009
Posts: 304
Followers: 3

Kudos [?]: 129 [0], given: 9

Re: Modulus [#permalink]  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
Manager
Joined: 15 Sep 2009
Posts: 138
Followers: 1

Kudos [?]: 18 [0], given: 2

Re: Modulus [#permalink]  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
Senior Manager
Joined: 16 Jul 2009
Posts: 262
Followers: 3

Kudos [?]: 107 [0], given: 3

Re: Modulus [#permalink]  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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