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

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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, 00:11
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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
[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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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.

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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, 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.

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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.

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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, 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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