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# What is the probability of n(n+1)(n+2) being evenly divisible by 8? 1

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Joined: 30 Jan 2018
Posts: 17
Re: What is the probability of n(n+1)(n+2) being evenly divisible by 8? 1  [#permalink]

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10 Sep 2018, 03:48

To define a probability you need a sample space or the number of all possible outcomes.
Statemetn 2 does not define if n is integer or not, hence we can not count the total no of possible cases.

Thank you.
But I still doubt option A because sample space is not clear in option A too.
for eg. If I take first 8 positive intgers as my sample space then probability will be = 3/8
And if I take first 9 positive intgers as my sample space then probability will be = 3/9=1/3

Anurag Jain
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Re: What is the probability of n(n+1)(n+2) being evenly divisible by 8? 1  [#permalink]

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10 Sep 2018, 11:33
jainanurag470 wrote:
But I still doubt option A because sample space is not clear in option A too.
for eg. If I take first 8 positive intgers as my sample space then probability will be = 3/8
And if I take first 9 positive intgers as my sample space then probability will be = 3/9=1/3

Anurag Jain

Hi, Anurag!

In the question stem pre-statements combined with statement (1), the sample space is the whole Z, in other words, the set of integers.

We are dealing with the product of ANY three consecutive integers, including negative ones, by the way!

As I mentioned, the proper way of calculating the probability asked is NOT in GMAT´s scope, but the "informal argument"
(interesting and PERFECT when (1+2) is considered) was presented in my solution.

Regards,
fskilnik.
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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
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Re: What is the probability of n(n+1)(n+2) being evenly divisible by 8? 1  [#permalink]

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11 Sep 2018, 23:22
fskilnik wrote:
jainanurag470 wrote:

Anurag Jain

Hi, Anurag!

In the question stem pre-statements combined with statement (1), the sample space is the whole Z, in other words, the set of integers.

We are dealing with the product of ANY three consecutive integers, including negative ones, by the way!

As I mentioned, the proper way of calculating the probability asked is NOT in GMAT´s scope, but the "informal argument"
(interesting and PERFECT when (1+2) is considered) was presented in my solution.

Regards,
fskilnik.

First of all thank you for the solution.
I am convinced that solution is C but OA is A.
And with your provided solution I am not convinced that solution is A.

Anurag Jain
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 936
Re: What is the probability of n(n+1)(n+2) being evenly divisible by 8? 1  [#permalink]

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12 Sep 2018, 06:14
1
jainanurag470 wrote:

First of all thank you for the solution.
I am convinced that solution is C but OA is A.
And with your provided solution I am not convinced that solution is A.

Anurag Jain

Dear Anurag,

Thank you for your contact and your strong desire to understand. That´s exactly what makes us stronger/wiser!

First of all, I believe I understand the reason you believe the answer is (C). You think something like this:

(1) If 1 <= N <= 2 , we have one answer (1/2) , but if 1 <= N <= 3 we have another answer (1/3), correct?

The rationale IS correct, but we must understand the statement (1) without being "contaminated" by the idea presented in (2)...

More explicitly: we look for the cases in which the expression n(n+1)(n+2) is divisible by 8, and using statement (1) only, we just know that n is an integer. Hence our question turns out to be:

Is n(n+1)(n+2) divisible by 8, when n is an integer? (Only considering the question stem pre-statements and statement (1) , both combined.)

Now I guess you understand that the expression n(n+1)(n+2) "runs" over infinite possibilities, because we must analyse ALL cases involved, some of them are the following:

when n = -200, we have to evaluate -200*(-199)*(-198)
when n = 0, we have to evaluate 0*1*2
when n = 1029 we have to evaluate 1029*1030*1031

In other words, we must ask ourselves the following: for EACH integer n, putting the value of the product n(n+1)(n+2) written in a small paper inside a box, (three small papers are with the numbers shown in red above) , do you understand we have infinite small papers inside the box?
(I didn´t say all numbers are different, because (-2)(-1)(0) equals (-1)(0)(1) for instance!)

If you understand that, great, because now you understand the question in blue: what is the probability that randomly choosing one small paper, you will get a number divisible by 8?

The answer IS possible to obtain, and it will be 5/8. The problem is to justify that using formal math. But, as I mentioned, this is out-of-our-scope!

I hope now things are clear!

Regards,
fskilnik.

P.S.: try my test-drive, please! Reason: students who want to understand things deeply and "as sub-product" to perform in REALLY higher-level are EXACTLY GMATH method profile...
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Re: What is the probability of n(n+1)(n+2) being evenly divisible by 8? 1   [#permalink] 12 Sep 2018, 06:14

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