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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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When n is divided by 3, the remainder is 2

Theory: Dividend = Divisor*Quotient + Remainder

n -> Dividend
3 -> Divisor
a -> Quotient (Assume)
2 -> Remainders
=> n = 3*a + 2 = 3a + 2

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

\(n^2 +2n\) = n*(n+2) = (3a + 2) * (3a + 2 + 2) = (3a + 2) * (3a + 4) = \(9a^2 + 6a + 12a + 8\) = \(9a^2 + 18a + 6 + 2\) = \(3*(3a^2 + 6a + 1) + 2\)
=> \(n^2 +2n\) when divided by 3 gives \(3a^2 + 6a + 1\) as quotient and 2 as remainder

So, Answer will be C
Hope it helps!

Watch the following video to learn the Basics of Remainders

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MathRevolution
[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 \(3.\)

\(A. 0\)

\(B. 1\)

\(C. 2\)

\(D. 3\)

\(E. 4\)
­The minimum possible value of n is 2 (Which when divided by 3 is n = 2)

So,  \(n^2 +2n = 8\)

Now, REM \(\frac{8}{3} = 2\), Answer will be (C)
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