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 Post subject: GMAT Number Theory
PostPosted: Sat Oct 22, 2011 3:21 am 
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Joined: Mon Oct 10, 2011 1:25 pm
Posts: 7
When n is divided by 5 the remainder is 3. What is the remainder when (n + 4)² is divided by 5?
A. 0
B. 1
C. 2
D. 3
E. 4

(E) When n is divided by 5 the remainder is 3. So n = 5k + 3, where k is some non-negative integer. (n + 4)² = (5k + 7)² = 25k² + 70k + 49 = 5(5k² + 14k + 9) + 4. Therefore when (n + 4)² is divided by 5 the remainder is 4. The right answer is (E).

Another option is to plug in n = 3. We can do so under an assumption that the remainder must be the same for ANY n, which yields 3 as the remainder when divided by 5.
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For the explanation to answer E, I understand how you got n = 5k + 4, but I don't get where you get (n + 4)= (5k + 7)². Where exactly did (5k + 7)² come from?


Last edited by Gennadiy on Sun Jul 15, 2012 6:27 am, edited 3 times in total.
the question itself is added


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 Post subject: Re: t.5, qt.4: number theory, remainder
PostPosted: Sun Oct 23, 2011 12:33 pm 
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Joined: Sun May 30, 2010 2:23 am
Posts: 498
Quote:
I understand how you got n = 5k + 4
We get n = 5k + 3 from the question statement, because the remainder is 3.
Quote:
Where exactly did (5k + 7)² come from?
We plug n = 5k + 3 into (n + 4)² and get
(n + 4)² = (5k + 3 + 4)²

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Furthermore, I'd like to bring your attention to 2 important moments here:
1. Representation like n = 5k + 3 is a very good simple method based on the definition of the division with a remainder.

2. In GMAT we can substitute the remainder itself, e.g. 3, instead general representation (n = 5k + 3), IF the assumption that the remainder must be the same for ANY n is TRUE (which can be easily see from the statement).


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