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Math Revolution GMAT Instructor
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When n is divided by 4, what is the remainder? 1) When n is divided by [#permalink]
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18 Jul 2017, 01:11
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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
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When n is divided by 4, what is the remainder? 1) When n is divided by [#permalink]
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18 Jul 2017, 02:00
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) When \(n\) is divided by \(3\), the remainder is \(1\)
Lets try few numbers.
When \(n = 1\) \(1\) divided by \(3\), remainder is \(1\). \(1\) divided by \(4\), remainder is \(1\).
When \(n = 4\) \(4\) divided by \(3\), remainder is \(1\). \(4\) divided by \(4\), remainder is \(0\).
\(I\) gives multiple values of \(n\). Hence \(I\) is Not Sufficient.
2) When \(n+1\) is divided by \(4\), the remainder is \(2\)
When \(n = 1\) \(n + 1 => 1 + 1 = 2\) \(2\) divided by \(4\), remainder is \(2\). \(1\) divided by \(4\), remainder is \(1\).
When \(n = 5\) \(n + 1 => 5 + 1 = 6\) \(6\) divided by \(4\), remainder is \(2\). \(5\) divided by \(4\), remainder is \(1\).
When \(n = 9\) \(n + 1 => 9 + 1 = 10\) \(10\) divided by \(4\), remainder is \(2\). \(9\) divided by \(4\), remainder is \(1\).
When \(n\) is divided by \(4\), remainder is \(1\).
\(II\) is Sufficient.
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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, 01:00
==> 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, 06:15
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. B is the answer.
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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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21 Oct 2017, 03:27
n = 4p + x (We need to find the value of x)
(1) says, n=3q+1. We don’t know the value of q. So, INSUFFICIENT.
(2) says, n+1=4r+2 => n=4r+1. Comparing this with the original equation, we find x=1. So, SUFFICIENT.
OptionB is correct.
Please correct if I am wrong.




Re: When n is divided by 4, what is the remainder? 1) When n is divided by
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