Please help me solve the below quant question:
If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?
A. 1/4
B. 3/8
C. 1/2
D. 5/8
E. 3/4
Quant question query.
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B
n(n+1)(n+2) needs to be divisible by 8
n will be divisible by 8 for 96/8 = 12 times for e.g. 8,16,24….
n+1 will be divisible by 8 for 96/8 = 12 times for e.g. 7,15,23…
n+2 will be divisible by 8 for 96/8 = 12 times for e.g. 6,14,22…
total favorable output = 12 + 12 +12 = 36
total output = 96
prob = 36/96 = 3/8
Ans: D ” we will get 60 possible outcomes for a random number betw 1-96 for which n(n+1)(n+2) is divisible by 8 and total no.of outcomes = 96 so 60 /96 = 5 /8
kindly post right answer
Out of All cases if n is odd then multiple will not be divided by 8 otherwise for any even n, multiple will be divided by 8.
Total no. of cases = 96
total no. of even no. = 46
therefore probability will be 1/2
Ans C
Probablility is Sample Space/Total Outcomes hence,
1. We have 96 integers in the total outcome
2. Sample space includes numbers such as 1.2.3; 2.3.4; 3.4.5; 4.5.6; 5.6.7; 6.7.8; 7.8.9; 8.9.10; 9.10.11; 10.11.12 etc etc
Firstly, whenever we have a multiple of 8 as ‘n’ the expression n.(n+1).(n+2) is divisible by 8. Hence we have 12 such expressions.
Secondly, whenever we have one of these multiple of 8 as ‘(n+1)’, the expression is divisible by 8. Again we have 12 such cases.
Thirdly, whenver we have even numbers as ‘n’ and ‘(n+2)’, the expression will be divisible by 8. We have total 48 such expressions but we will subtract 12 from them as we have already considered them in the first case. So the total cases are 36.
Hence our sample space: 12+12+36 = 60 and
60/96 = 5/8. Hence answer is ‘D’