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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, 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
[Reveal] Spoiler: OA

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Director Joined: 04 Dec 2015 Posts: 696 Location: India Concentration: Technology, Strategy Schools: ISB '19, IIMA , IIMB, XLRI WE: Information Technology (Consulting) When n is divided by 4, what is the remainder? 1) When n is divided by [#permalink] ### Show Tags 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. Answer (B)... _________________ Please Press "+1 Kudos" to appreciate. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5048 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: When n is divided by 4, what is the remainder? 1) When n is divided by [#permalink] ### Show Tags 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 3 month Online Course"
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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.

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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.

Option-B 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   [#permalink] 21 Oct 2017, 03:27
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