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# What is the remainder when 3^50 is divided by 4?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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What is the remainder when 3^50 is divided by 4?  [#permalink]

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06 Dec 2016, 00:56
00:00

Difficulty:

15% (low)

Question Stats:

74% (00:58) correct 26% (01:07) wrong based on 104 sessions

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What is the remainder when $$3^5^0$$ is divided by 4?

A. 0 B. 1 C. 2 D. 3 E. -1

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Intern Joined: 15 Nov 2015 Posts: 26 Location: Netherlands Schools: HEC Dec '17 (II) GMAT 1: 730 Q47 V44 GPA: 3.99 What is the remainder when 3^50 is divided by 4? [#permalink] ### Show Tags Updated on: 06 Dec 2016, 07:45 1 2 Rewrite $$3^{50}$$ as $$(3^{2})^{25} = 9^{25}$$. $$9^{25} = (8+1)^{25}$$. Now $$8^{25}$$ will always be divisible by 4 and leaves remainder 0. $$1^{25}$$ = 1 and leaves remainder 1. Answer B. Originally posted by koenh on 06 Dec 2016, 01:26. Last edited by koenh on 06 Dec 2016, 07:45, edited 2 times in total. Board of Directors Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 4342 Location: India GPA: 3.5 WE: Business Development (Commercial Banking) Re: What is the remainder when 3^50 is divided by 4? [#permalink] ### Show Tags 06 Dec 2016, 07:11 MathRevolution wrote: What is the remainder when $$3^5^0$$ is divided by 4? A. 0 B. 1 C. 2 D. 3 E. -1 $$3^{50} = 9^{25}$$ $$\frac{9}{4}$$ = Remainder 1 So, $$9^{25}$$ , will have remainer as 1 Answer will be (B) 1 _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6821 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: What is the remainder when 3^50 is divided by 4? [#permalink] ### Show Tags 08 Dec 2016, 00:44 ==> The units digit of $$3^n$$ is the repetition of $$3-->9-->7--->1-->3-->9-->7-->1$$, so you get $$50=4*12+2$$. Thus, from $$3^5^0=3^4^*^1^2^+^2$$ --> $$~3^2=~9$$, the units digit becomes 9, and if you divide it by 4, from $$9=4*2+1$$, the remainder becomes 1. 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$149 for 3 month Online Course"
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Re: What is the remainder when 3^50 is divided by 4?  [#permalink]

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22 Aug 2018, 11:59
hat is the remainder when 3^50 is divided by 4?

A. 0 B. 1 C. 2 D. 3 E. -1

unit digit of powers of 3 follows a pattern of 4 (3,9,7,1)
So we divide 50/4=2 remainder which means power of 2 will be there
3 power 2= 9

Option B (1)
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Re: What is the remainder when 3^50 is divided by 4?  [#permalink]

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26 Aug 2018, 17:22
MathRevolution wrote:
What is the remainder when $$3^5^0$$ is divided by 4?

A. 0 B. 1 C. 2 D. 3 E. -1

Since 3 = 4 - 1, we can think 3 as “-1” when it’s divided by 4. Therefore, the remainder when 3^50 is divided by 4 is same as the remainder when (-1)^50 is divided by 4. So the remainder is (-1)^50 = 1.

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Re: What is the remainder when 3^50 is divided by 4? &nbs [#permalink] 26 Aug 2018, 17:22
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