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If n is a positive integer and if (n^3  n)/(n+1) = 240, the [#permalink]
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27 May 2012, 08:27
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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
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If n is a positive integer and if (n^3  n)/(n+1) = 240, the [#permalink]
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Re: If n is a positive integer and if (n^3  n)/(n+1) = 240, the [#permalink]
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\(\frac{n^3 n}{n+1} = 240\) \(\frac{n(n+1)(n1)}{n+1} = 240\) \(n^2  n  240 = 0\) \(n^2  16n + 15n  240 = 0\) n = 16 Answer = B
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If n is a positive integer and if (n^3  n)/(n+1) = 240, the [#permalink]
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24 Nov 2015, 11:28
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 \(\frac{(n^3  n)}{(n+1)}\) = \((16 )(15)\) \(\frac{n(n^2  1)}{(n+1)}\) = \((16 )(15)\) \(\frac{n(n  1)(n+1)}{(n+1)}\)= \((16 )(15)\) \(n(n  1)\) = \((16 )(15)\) So, \(n\) = \(16\) Hence answer is definitely (B)
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Re: If n is a positive integer and if (n^3  n)/(n+1) = 240, the [#permalink]
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29 Sep 2017, 09:30
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 We can simplify the given equation: (n^3  n)/(n + 1) = 240 n(n^2  1)/(n + 1) = 240 n(n + 1)(n  1)/(n + 1) = 240 n(n  1) = 240 n^2  n  240 = 0 (n  16)(n + 15) = 0 n = 16 or n = 15 Answer: B
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Re: If n is a positive integer and if (n^3  n)/(n+1) = 240, the [#permalink]
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05 Oct 2017, 17:23
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 \(\frac{n^3n}{n+1}=240\) > \(\frac{n(n1)(n+1)}{n+1}=240\) > \(n(n1)=240\) > 240 is the product of two positive consecutive integers \(n1\) 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?



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Re: If n is a positive integer and if (n^3  n)/(n+1) = 240, the [#permalink]
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05 Oct 2017, 20:07
sharadvatsey wrote: 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 \(\frac{n^3n}{n+1}=240\) > \(\frac{n(n1)(n+1)}{n+1}=240\) > \(n(n1)=240\) > 240 is the product of two positive consecutive integers \(n1\) 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 \(n(n1)=240\) we wouldn't be able to use the logic in highlighted part because if it were given that n is an integer, then \(n1\) and \(n\) might not be consecutive integers and we would be left with quadratics to solve. We'd get the same answer though.
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Re: If n is a positive integer and if (n^3  n)/(n+1) = 240, the [#permalink]
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05 Oct 2017, 22:05
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 \(n(n1)=240\) we wouldn't be able to use the logic in highlighted part because if it were given that n is an integer, then \(n1\) 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.
Thanks again for the excellent contributions.



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If n is a positive integer and if (n^3  n)/(n+1) = 240, the [#permalink]
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05 Oct 2017, 22:10



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If n is a positive integer and if (n^3  n)/(n+1) = 240, the [#permalink]
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05 Oct 2017, 22:27
Bunuel wrote: We would but after getting \(n(n1)=240\) we wouldn't be able to use the logic in highlighted part because if it were given that n is an integer, then \(n1\) 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
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Re: If n is a positive integer and if (n^3  n)/(n+1) = 240, the [#permalink]
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05 Oct 2017, 23:13
[/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 \(n(n1)=240\) we wouldn't be able to use the logic in highlighted part because if it were given that n is an integer, then \(n1\) and \(n\) might not be consecutive integers and we would be left with quadratics to solve. We'd get the same answer though.[/quote] Thank you. This helps




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