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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
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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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66% (00:56) correct 34% (00:43) wrong based on 59 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
[Reveal] Spoiler: OA

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Re: 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, 01:40
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.
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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, 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 $$n=4k+3$$

$$\frac{3^n+2}{5}=\frac{3^{4k+3}+2}{5}=\frac{3^{4k} * 3^3 + 2}{5} =\frac{(3^4)^k * 27 +2}{5} = \frac{81^k* 2 + 2}{5}=\frac{1*2+2}{5}=4$$

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

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03 Aug 2017, 01:29
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==> 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.

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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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