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# When n is divided by 4 the remainder is 3. If 3n+2 is divided by 5, wh

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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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When n is divided by 4 the remainder is 3. If 3n+2 is divided by 5, wh  [#permalink]

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01 Aug 2017, 01:00
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Difficulty:

25% (medium)

Question Stats:

75% (01:06) correct 25% (01:42) wrong based on 81 sessions

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When n is divided by 4 the remainder is 3. If $$3^n+2$$ is divided by 5, what is the remainder?

A. 1
B. 2
C. 3
D. 4
E. 0

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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" Senior PS Moderator Joined: 26 Feb 2016 Posts: 3386 Location: India GPA: 3.12 Re: When n is divided by 4 the remainder is 3. If 3n+2 is divided by 5, wh [#permalink] ### Show Tags 01 Aug 2017, 01:40 MathRevolution wrote: When n is divided by 4 the remainder is 3. If $$3^n+2$$ is divided by 5, what is the remainder? A. 1 B. 2 C. 3 D. 4 E. 0 When n is divided by 4 to give us a remainder of 3, n could be 3,7,11.... $$3^n+2$$ will have the value of 29 for n=3, which when divided by 5 gives a remainder of 4. Hence, Option D(4) is the correct answer. _________________ You've got what it takes, but it will take everything you've got Senior CR Moderator Status: Long way to go! Joined: 10 Oct 2016 Posts: 1354 Location: Viet Nam When n is divided by 4 the remainder is 3. If 3n+2 is divided by 5, wh [#permalink] ### Show Tags 01 Aug 2017, 02:16 MathRevolution wrote: When n is divided by 4 the remainder is 3. If $$3^n+2$$ is divided by 5, what is the remainder? A. 1 B. 2 C. 3 D. 4 E. 0 Since $$n$$ is divided by 4 the remainder is 3, we have $$n=4k+3$$ $$\frac{3^n+2}{5}=\frac{3^{4k+3}+2}{5}=\frac{3^{4k} * 3^3 + 2}{5} =\frac{(3^4)^k * 27 +2}{5} = \frac{81^k* 2 + 2}{5}=\frac{1*2+2}{5}=4$$ The answer is D. _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7230 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: When n is divided by 4 the remainder is 3. If 3n+2 is divided by 5, wh [#permalink] ### Show Tags 03 Aug 2017, 01:29 ==> You get n=4p+3, which becomes $$3^n+2=3^{4p+3}+2=(3^4)^p(3^3)+2=(~1)^p(27)+2=(~1)(27)+2=(~7)+2=~9$$. Thus, the remainder when it is divided by 5 becomes 4. The answer is D. Answer: D _________________ 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: When n is divided by 4 the remainder is 3. If 3n+2 is divided by 5, wh   [#permalink] 03 Aug 2017, 01:29
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