Numerical Sequence Brain Strain

[Bill_Lumbergh]

Hi All,

I am working on some mathematical testing, some of which involves solving numerical sequences. While I have literally done hundreds so far, there are a few that I just cannot figure out. I have the answers, but even with the answers, I cannot figure out the mathematical logic behind it. Any number geniuses here able to help?

Questions
1. 48 46 42 38 xx
2. xx 19 23 29 31 (not a prime number sequence as 17 was not an option in the multi choice answers)
3. 628 54 311 30 627 55 298 xx
4. 24 16 40 27 73 61 29 xx
5. 6 6 8 12 12 24 20 xx 36

Answers
1. 32
2. 15
3. 21
4. 90
5. 20

Any help would be greatly appreciated

Bill

 

[tkhunny]

Without the answers given, there are literally infinitely many solutions to each of these.
Without additional constraints, there are literally infinitely many solutions to each of these.

On the first, 32 is as good an option as any other value.

Have you considered they might be two sequences alternating?
Have you considered they might not be mathematical at all?

 

[Steven G]

I think the answer to the 1st one is (-1/6)n^4 + 2n^3 + (-53/6)n^2 + 13n +41

 

[Bill_Lumbergh]

Hi tkhunny,

Thanks for the reply. They are mathematical in the sense that they are the application of logical or deductive reasoning to numerical sequences. In some cases there could be a infinite number of possible answers, but given the answers are multiple choice, the logical one from those presented is chosen as correct. The problem for me is that even with the answers, I cannot figure out the logical arithmetic reason for the choice.

Bill

 

[Dr.Peterson]

They are mathematical in the sense that they are the application of logical or deductive reasoning to numerical sequences. In some cases there could be a infinite number of possible answers, but given the answers are multiple choice, the logical one from those presented is chosen as correct. The problem for me is that even with the answers, I cannot figure out the logical arithmetic reason for the choice.

I wouldn't call this logic at all! Possibly inductive, or really abductive, reasoning could be involved, but not deductive! Really, these are lateral thinking exercises, and I think they are totally invalid for testing mathematical thinking. (The best mathematicians would be the least likely to be willing to answer them!)

But if answering them depends on the choices, why didn't you show us the choices? Maybe if you do, we can see how they make sense.

 

[Steven G]

6 6 8 12 12 24 20 xx 36

It seems that the pattern is 2 repeated numbers followed by a non repeated. So I would pick 20 for xx

I do not see a pattern of how they get those numbers.

 

[tkhunny]

...In some cases there could be a infinite number of possible answers...

No, in ALL cases there ARE infinitely many answers to such a question. This is what makes the exercise illogical; although it does give some practice in pattern recognition and various interpolation and extrapolation techniques.

In the case of your five specific problems, and the five specific answers from which to choose, one can construct a rule for ALL FIVE answers to fit ALL FIVE questions. It simply is not appropriate to suggest that a single answer necessarily applies to a single sequence.

Here's one of my favorite examples:

0
14
17
18
24
25
27
32
34
38
39
45
46
47
49
49
49
49
50

What's THE next number? What's THE rule?