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==> In the original condition, there is 1 variable (n) and in order to match the number of variables to the number of equations, there must be 1 equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer. For remainder questions, you can directly substitute. Therefore, for con 1), from n=3p+1=1,4,…, the remainder when divided by 4 becomes 1=4(0)+1, which makes remainder=1, and from 4=4(1)+0, you get remainder=0, hence it is not unique and not sufficient. For con 2), from n+1=4q+2 and n=4q+1, the remainder when divided by 4 always becomes 1, hence it is unique and sufficient.

Therefore, the answer is B. Answer: B
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Re: When n is divided by 4, what is the remainder? 1) When n is divided by [#permalink]

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20 Jul 2017, 05:15

MathRevolution wrote:

When n is divided by 4, what is the remainder?

1) When n is divided by 3, the remainder is 1 2) When n+1 is divided by 4, the remainder is 2

1) \(\frac{n}{3}\) = PQ + 1 n = 4, then \(\frac{n}{4}\) has a remainder of 0. n = 7. then \(\frac{n}{7}\) has a remainder of 3. Insufficient.

2) \(\frac{(n+1)}{4}\) = QR + 2 n + 1 = 6, then n = 5, and \(\frac{n}{4}\) has a remainder of 1. n + 1 = 10, then n = 9, and \(\frac{n}{4}\) has a remainder of 1. This will always be the case => Sufficient.