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If n is a positive integer and if (n^3 - n)/(n+1) = 240, then what is the value of n?

A. 12 B. 16 C. 17 D. 20 E. 48

\(\frac{n^3-n}{n+1}=240\) --> \(\frac{n(n-1)(n+1)}{n+1}=240\) --> \(n(n-1)=240\) --> 240 is the product of two positive consecutive integers \(n-1\) and \(n\) --> \(n=16\) (16*15=240).

Answer: B.

Note that one other pair of consecutive integers satisfy \(n(n-1)=240\): -15 and -16 but we are told that n is positive hence this solution is not valid. _________________

Re: If n is a positive integer and if (n^3 - n)/(n+1) = 240, the [#permalink]

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05 Oct 2017, 18:23

Bunuel wrote:

macjas wrote:

If n is a positive integer and if (n^3 - n)/(n+1) = 240, then what is the value of n?

A. 12 B. 16 C. 17 D. 20 E. 48

\(\frac{n^3-n}{n+1}=240\) --> \(\frac{n(n-1)(n+1)}{n+1}=240\) --> \(n(n-1)=240\) --> 240 is the product of two positive consecutive integers \(n-1\) and \(n\) --> \(n=16\) (16*15=240).

Answer: B.

What is the significance of "If n is a positive integer" in this question? Would we not cancel (n+1) if n is not a positive integer?

If n is a positive integer and if (n^3 - n)/(n+1) = 240, then what is the value of n?

A. 12 B. 16 C. 17 D. 20 E. 48

\(\frac{n^3-n}{n+1}=240\) --> \(\frac{n(n-1)(n+1)}{n+1}=240\) --> \(n(n-1)=240\) --> 240 is the product of two positive consecutive integers \(n-1\) and \(n\) --> \(n=16\) (16*15=240).

Answer: B.

What is the significance of "If n is a positive integer" in this question? Would we not cancel (n+1) if n is not a positive integer?

We would but after getting \(n(n-1)=240\) we wouldn't be able to use the logic in highlighted part because if it were given that n is an integer, then \(n-1\) and \(n\) might not be consecutive integers and we would be left with quadratics to solve. We'd get the same answer though.
_________________

Re: If n is a positive integer and if (n^3 - n)/(n+1) = 240, the [#permalink]

Show Tags

05 Oct 2017, 23:05

What is the significance of "If n is a positive integer" in this question? Would we not cancel (n+1) if n is not a positive integer?[/quote]

We would but after getting \(n(n-1)=240\) we wouldn't be able to use the logic in highlighted part because if it were given that n is an integer, then \(n-1\) and \(n\) might not be consecutive integers and we would be left with quadratics to solve. We'd get the same answer though.[/quote]

Hi Bunuel

Great work, you mentioned that we might not be able to get consecutive integers, but -16 and -15 are also consecutive integers and as you have mentioned we would arrive at the same solution. I would lean towards the isolation of a single solution as the significance of the positive integer constraint. As you are well aware of, this would probably be more significant in a DS yes or no or even a DS value question.

Great work, you mentioned that we might not be able to get consecutive integers, but -16 and -15 are also consecutive integers and as you have mentioned we would arrive at the same solution. I would lean towards the isolation of a single solution as the significance of the positive integer constraint. As you are well aware of, this would probably be more significant in a DS yes or no or even a DS value question.

Thanks again for the excellent contributions.

Notice that we are not only told that n is an integer but also that n is positive: " n is a positive integer".
_________________

If n is a positive integer and if (n^3 - n)/(n+1) = 240, the [#permalink]

Show Tags

05 Oct 2017, 23:27

Bunuel wrote:

We would but after getting \(n(n-1)=240\) we wouldn't be able to use the logic in highlighted part because if it were given that n is an integer, then \(n-1\) and \(n\) might not be consecutive integers and we would be left with quadratics to solve. We'd get the same answer though.

I like the idea of plugging and not solving the quadratic equation...this saves a hell of time
_________________

"Giving kudos" is a decent way to say "Thanks" and motivate contributors. Please use them, it won't cost you anything

High achievement always takes place in the framework of high expectationCharles Kettering If we chase perfection we can catch excellenceVince Lombardi

Re: If n is a positive integer and if (n^3 - n)/(n+1) = 240, the [#permalink]

Show Tags

06 Oct 2017, 00:13

[/quote]

What is the significance of "If n is a positive integer" in this question? Would we not cancel (n+1) if n is not a positive integer?[/quote]

We would but after getting \(n(n-1)=240\) we wouldn't be able to use the logic in highlighted part because if it were given that n is an integer, then \(n-1\) and \(n\) might not be consecutive integers and we would be left with quadratics to solve. We'd get the same answer though.[/quote]

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