Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
n(n+1)(n-1) is divisible by 8 if any or all of its terms are divisible by 8.
Lets assume X=[1,96];
The probability P that X is divisible by 8 is P = 1/8.
X could be equal to n or (n-1) or (n+1), so there are 3 possible favorable outcomes out of 8 possible outcomes.
I'd go with C 1/2
We need the expression n(n+1)(n-1) to contain 2^3 to be divisible by 8
Plug in 1, 2, 3, 4... and you will see that every other 2nd number starting with 1 will have 2^3 in it. _________________
the total cases : 96
for all multiples of 8 we have 3 triplets i.e in total 12 * 3 = 36 triplets
for all odd multiples of 4 we have 2 triplets so 12 *2 = 24
OA is E.
the key here is to determine the favorable outcomes for the task: either 12x3, either 12x2, either 12 events
12 12 12
The total sum of favorable outcomes is 12x3 + 12x2 + 12 = 72
So it is 72/96 = 3/4.
we are choosing a number n from 1 to 96. If we choose n=1, then we have (n-1)(n)(n+1)=0. However, 0/8 is still 0. 0 is divisible by 8. then next odd number is 3 in which case (n-1)(n)(n+1) would be 2*3*4 = 24, which is divisble by 8. Same is the case with 5...so on - totalling to 48 of them that are divisible by 8.
I didn't quite get your reference to 2.
I feel that the question will have NO ambiguity if it reads n(n+1)(n+2)
gayathri, the result set is (1,2,0) meaning that when you take 1, you get 1*(1+1)*(1-1) = 1*2*0 = 0
0 IS a multiple of 8
Hence, take every odd number from the domain, 1 to 96, you will have a number divisible by 8 and there are 48 of those. But as Venksune explained, every even number that is a multiple of 8 will also give a result divisible by 8 and there are 12 of those.