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

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New post 01 Aug 2017, 01:00
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A
B
C
D
E

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  25% (medium)

Question Stats:

67% (00:54) correct 33% (00:59) wrong based on 76 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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Re: When n is divided by 4 the remainder is 3. If 3n+2 is divided by 5, wh [#permalink]

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New post 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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New post 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.
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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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New post 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
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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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