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

Question

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

Bunuel · Answer

\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.

PareshGmat · Answer

\frac{n^3 -n}{n+1} = 240

\frac{n(n+1)(n-1)}{n+1} = 240

n^2 - n - 240 = 0

n^2 - 16n + 15n - 240 = 0

n = 16

Answer = B

Abhishek009 · Answer

\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)

JeffTargetTestPrep · Answer

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

sharadvatsey · Answer

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?

Bunuel · Answer

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.

rulingbear · Answer

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.

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.

Thanks again for the excellent contributions.

Bunuel · Answer

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

NDND · Answer

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

sharadvatsey · Answer

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. Thank you. This helps

ablatt4 · Answer

Before multiplying both sides by denominator, factor out n^3-n

n(n-1)(n+1) / n+1 = 240

n(n-1)=240

Some number multiplied by 1 less than itself = 240

Lets start by listing the factors of 240

**skipping single digit factors**

10,24
12,10
15,16

if 15*16 =240 then one of these 2 must be the answer.

B 16

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

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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My Rewards