Goldman Sachs Interview Question
Software Engineer / Developershi,
i think its 9:
5 6 7 8 8 8 8 8... if you observe the difference between the 1st no and last no is 3, then the second and the second from last is 2, and so on ... until it becones 8-8 = 0.
So if we need to preserve tht order, i guess a 9 shud be placed as the next number.
I think the number must be 8 again, becoz your observation till 8-8=0 is correct till 8-8=0 an symmetry is there. So to this series if I add and 8 again then the difference between the 1st no and last no is 3, then the second and the second from last is 2, and so on ... until it becomes 8-8 = 0, and one middle number can be any thing(in this case it is 8).
Not enough data. Or the question is ambiguous. If it is 9, then the question should be "What is the FIRST and LAST number in this give series so far?".. which in this case will be 5 and 9 to preserve 4, 3, 2, 1, 0. But it can also be 4 and 8 to preserver 4, 3, 2, 1, 0. So the answer can also be 8. These questions are to see how strong your observation can be.. there isn't any right answer. If you just say 9 by itself, it doesn't make sense because it cannot preserve the order -> 5 6 7 8 8 8 8 8 9:
9-5 = 4
8-6 = 2
8-7 = 1
8-8 = 0
8
there is no sequence. 8, 0, 1, 2, 4
7
the first three differences were 1. (5 6 7 8)
the next three differences were 0. (8 8 8 8)
so the next three differences should be -1. (7 6 5 4)
if v add the 1st and the 4th no. the result is =5+8=13
and then add 2nd and 5th no. the result is=6+8=14
now keep adding the next no. with 6th no. result is =7+8=15
then 8+8=16
to continue the counting we add 8+x=17
so x=17-8=9
so next no. of series will b 9
5 6 7 8 8 8 8 _ = 5 6 7 8 8 8 8 9
Dear gaurav your idea is excellent , but u dont u think that you should use whole string
to use whole series 5678 8888 we should add 1st and the 5th no. the result is =5+8=13
and then add 2nd and 6th no. the result is=6+8=14
now keep adding the next no. with 7th no. result is =7+8=15
then last 8+8=16
so if we want any number here it should be 9 and if we ask to add next number too then it will be 10
if v add the 1st and the 5th no. the result is =5+8=13
and then add 2nd and 6th no. the result is=6+8=14
now keep adding the next no. with 7th no. result is =7+8=15
then 8+8=16
to continue the counting we add 8+x=17
so x=17-8=9
so next no. of series will b 9
5 6 7 8 8 8 8 8 _ = 5 6 7 8 8 8 8 8 9
I would do expected value for this brain teaser since it is very subjective to say which number comes first. Which means you would have to assume the same probability for each number. The sum of all numbers is 58. You divide it by 8 assuming that each of the has the probability of 1/8 (8 data entries). You will get 7.25 as your final answer. I don't think you can go wrong with this answer.
answer is 9. The numbers given are the first numbers that appear after the decimal point when converted from these fractions: 1/2, 2/3, 3/4, 4/5, 5/6, 6/7, 7/8, 8/9, and 9/10.
5 6 7 8 8(t1+3) 8(t2+2) 8(t3+1) 8(t4+0) 11(t5+3) 10(t6+2) 9(t7+1) 8(t8+0)...............
series - 5 6 7 8 8 8 8 8 ........
if we observe there are four different AP series which have different d = 3,2,1,0.
first 5 8 ... difference 3
second 6 8 .... difference 2
third 7 8 ... difference 1
fourth 8 8 ... difference 0
so next step should be 11
5 6 7 8 8 8 8 8 11 10 9 8 .............
any comments
The numbers given are the first numbers that appear after the decimal point when converted from these fractions: 1/2, 2/3, 3/4, 4/5, 5/6, 6/7, 7/8, 8/9, and 9/10.
- YetAnotherCoder October 02, 2008http://www.puzz.com/1001/series17.htm