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

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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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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
[Reveal] Spoiler: OA

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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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New post 18 Jul 2017, 01:00
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.

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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New post 20 Jul 2017, 00:00
==> 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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New post 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.

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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New post 21 Oct 2017, 02:27
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.

Option-B is correct.

Please correct if I am wrong.

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Re: When n is divided by 4, what is the remainder? 1) When n is divided by   [#permalink] 21 Oct 2017, 02:27
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