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When n is divided by 3, the remainder is 2. What is the remainder when
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MathRevolution
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When n is divided by 3, the remainder is 2. What is the remainder when [#permalink] New post  26 Jul 2019, 00:33
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[GMAT math practice question]

When \(n\) is divided by \(3\), the remainder is \(2\). What is the remainder when \(n^2 +2n\) is divided by \(3.\)

\(A. 0\)

\(B. 1\)

\(C. 2\)

\(D. 3\)

\(E. 4\)
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nick1816
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Re: When n is divided by 3, the remainder is 2. What is the remainder when [#permalink] New post  26 Jul 2019, 00:49
n=3k+2

\(n^2+2n= (3k+2)^2+2(3k+2)\)
\(n^2+2n= 9k^2+12k+4+6k+4\)
\(n^2+2n= 9k^2+12k+6k+8\)
\(n^2+2n= 9k^2+12k+6k+6+2\)
\(n^2+2n= 3(3k^2+4k+2k+2)+2\)
\(n^2+2n= 3X+2\)

MathRevolution wrote:
[GMAT math practice question]

When \(n\) is divided by \(3\), the remainder is \(2\). What is the remainder when \(n^2 +2n\) is divided by \(3.\)

\(A. 0\)

\(B. 1\)

\(C. 2\)

\(D. 3\)

\(E. 4\)
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Re: When n is divided by 3, the remainder is 2. What is the remainder when [#permalink] New post  26 Jul 2019, 02:43
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MathRevolution wrote:
[GMAT math practice question]

When \(n\) is divided by \(3\), the remainder is \(2\). What is the remainder when \(n^2 +2n\) is divided by \(3.\)

\(A. 0\)

\(B. 1\)

\(C. 2\)

\(D. 3\)

\(E. 4\)


When \(n\) is divided by \(3\), the remainder is \(2\).
Let n=2, since \(\frac{2}{3} =\) 0 R2.

What is the remainder when \(n^2 +2n\) is divided by \(3\)?
Testing n=2, we get:
\(\frac{n^2+2n}{3}\) = \(\frac{2^2+2*2}{3}\) =\(\frac{8}{3}\) = 2 R2

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C

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MathRevolution
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Re: When n is divided by 3, the remainder is 2. What is the remainder when [#permalink] New post  28 Jul 2019, 17:12
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=>

We can plug in \(2\) for the variable \(n.\)

\(n^2+2n = 2^2 + 2*2 = 8\) and \(8\) has reminder \(2\) when it is divided by \(3.\)

Therefore, the answer is C.
Answer: C
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Re: When n is divided by 3, the remainder is 2. What is the remainder when [#permalink] New post  21 Apr 2021, 04:12
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