A numbers problem I cant seem to solve....

[kirtanasrin]

If 'n' is an integer between 1 and 96 (both inclusive) What is the probability that N*(N+1)*(N+2) will be divisible by eight..

1*2*3= 6
2*3*4=24 - divisible by eight
3*4*5=60
4*5*6=120 - divisible by eight
.and so on
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.
This way u identify that every alternate multiplication yeilds a number divisible by eight and also for n integers there are n-2 combination ( Eg, if n =1 or 2 or3 or 4 or 5 or 6 u have 4 combinations -1*2*3,2*3*4,3*4*5,4*5*6 )
.
.
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With these assumtions i dint get the answer . please tell me where im going wrong or if theres another approach to it .....

[pach2212]

If 'n' is an even number, then the product is divisible by 8. There are 47 even numbers between 1 to 96 excluding 96.

If 'n' is one less than the multiple of 8, then the product is divisible by 8. There are 11 numbers that suit the condition.

So we have 47 + 11 = 58 values of 'n'

Hence the probability will be 58 / 96 = 29 / 48.

Correct me if I am wrong.

[Swiss_boy]

Why did you exclude 96??

[pach2212]

Why did you exclude 96??

The triplets that I am referring to will be:

when n=2 ; (2,3,4)
when n=4 ; (4,5,6)

and so on...

when n=96 ; (96,97,98)

But, 97 and 98 are not included in the list

It is from 1 to 96.

Or is it that the value of 'n' that is from 1 to 96? If this is the case, add 1 to 47, and subtract from my score

[kirtanasrin]

If 'n' is an even number, then the product is divisible by 8. There are 47 even numbers between 1 to 96 excluding 96.

If 'n' is one less than the multiple of 8, then the product is divisible by 8. There are 11 numbers that suit the condition.

So we have 47 + 11 = 58 values of 'n'

Hence the probability will be 58 / 96 = 29 / 48.

Correct me if I am wrong.

I did not get what u mean . From what i understood ... the value of 'n' is from 1 - 96 both inclusive .

Anyway the answer is .625 or 62.5% Please tell me how .

[River Side]

ok.. i just did it the brute force way.. only possible if u have time.. if u don't.. then as is usual for me.. i just guess and move on..

anywho.. just laying down the table..

1*2*3 = nope
2*3*4 = divisible by 8
every even value for n results in a product divisible by n so total 48

BUT if u reach 7.. the next number is 8 and so the product will be divisible by 8... so here we have an odd number resulting in the possible outcome too..

but not all odd numbers.. as pach2212 pointed out.. only odd numbers that are one less than a multiple of 8 result in a product divisible by 8 cuz they also have (n+1)= multiple of 8 in their product set..

now count how many would they be? just write out the table for 8

8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96

and all odds one less than these that we need to count are

7, 15, 23, 31, 39, 47, 55, 63, 71, 79, 87, 95 = 12 options.

so we have a total of 48+12 desired outcomes out of possible 96

60/96 * 100 = 62.5%

[check.stone]

Is this PS or DS? Be more frustrating as a DS I think.

I think Pachman's method is the quickest way to get the ans. All even gives us 48/96.

Then we know if n is 1 less than a multiple of 8, then n+1 is divisible by 8. There are 12 multiples(x) of 8 and same number of (8-1)x in 96.

So 48+12 -> 60/96. Only n needs to be 1-96. Good question.

[Swiss_boy]

I am not sure if I could have answered this in a real GMAT test..

Very nice one..

Whats the source?

[thankont]

Nice question. We can go like this too:
multiples of 8 from 1 to 96 = 12
starting with odd number = 48
so 48 - 12 = 36 starting with odd and excluding mult. of 8
so including mult. of 8 is 96-36 = 60 so p=60/96

[kirtanasrin]

Nice question. We can go like this too:
multiples of 8 from 1 to 96 = 12
starting with odd number = 48
so 48 - 12 = 36 starting with odd and excluding mult. of 8
so including mult. of 8 is 96-36 = 60 so p=60/96

Nice question indeed ,a lil tougher than the usual GMAT level ...
The question was posted by someone in Scoretop.com