Confusing Pattern Question.

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unavailable4now

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I stumbled across a Vague question in my 11+ mock maths paper today (I already finished the paper) which I found difficult and didn't attempt.
The question was "The number on the left becomes the number on the right find the missing number with the question mark"
2➡7
3➡9
5➡?
6➡19
Please could someone help.
 
What topics have been covered that might be applicable to this?

I hope you recognize that this sort of thing is a puzzle, not mathematics, as all you can do is to GUESS what the rule might be, which at best is science (inferring a "best" explanation). IF the context implied a particular kind of rule, then it might become mathematics. So this is not worth attempting if you don't quickly see an answer (e.g. a linear function).
 
unavailable4now said:
I stumbled across a Vague question in my 11+ mock maths paper today (I already finished the paper) which I found difficult and didn't attempt.
The question was "The number on the left becomes the number on the right find the missing number with the question mark"
2➡7
3➡9
5➡?
6➡19
Please could someone help.
Click to expand...
with three points given - what the highest degree of polynomial you could fit through all those points?
 
Someone gave me this. Try it.

[MATH]a_n = \frac{n^2}{3} + \frac{n}{3} + 5[/MATH]
[MATH]a_5 =\ ? [/MATH]
 
mario99 said:
Someone gave me this. Try it.

[MATH]a_n = \frac{n^2}{3} + \frac{n}{3} + 5[/MATH]
[MATH]a_5 =\ ? [/MATH]
Click to expand...
It's not a good idea to depend on people "giving" you answers. That's why we avoid doing so:

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SK's suggestion leads to this answer: You can expect that a quadratic function can match the data (any three points define one), so suppose the function has the form [MATH]ax^2 + bx + c[/MATH], plug in the three data points, and solve for a, b, and c. You'll get the answer you were "given" -- but you'll also know how to get it yourself next time.

Note that if the class to which this problem was given covered this technique, then the problem might be valid - that's part of the context I asked about. But there may well be other formulas that would work as well, and they should be considered correct, too! And in fact, there will be a cubic equation that will yield any value you fill in for f(5), so you could pick any answer you like, as long as you prepare to justify it!
 
Dr.Peterson said:
What topics have been covered that might be applicable to this?

I hope you recognize that this sort of thing is a puzzle, not mathematics, as all you can do is to GUESS what the rule might be, which at best is science (inferring a "best" explanation). IF the context implied a particular kind of rule, then it might become mathematics. So this is not worth attempting if you don't quickly see an answer (e.g. a linear function).
Click to expand...
Patterns
 
Dr.Peterson said:
It's not a good idea to depend on people "giving" you answers. That's why we avoid doing so:

Posting Guidelines (Summary)

Welcome to our tutoring boards! :) This page summarizes main points from our posting guidelines. As our name implies, we provide math help (primarily to students with homework). We do not generally post immediate answers or step-by-step solutions. We don't do your homework. We prefer to help...
www.freemathhelp.com

SK's suggestion leads to this answer: You can expect that a quadratic function can match the data (any three points define one), so suppose the function has the form [MATH]ax^2 + bx + c[/MATH], plug in the three data points, and solve for a, b, and c. You'll get the answer you were "given" -- but you'll also know how to get it yourself next time.

Note that if the class to which this problem was given covered this technique, then the problem might be valid - that's part of the context I asked about. But there may well be other formulas that would work as well, and they should be considered correct, too! And in fact, there will be a cubic equation that will yield any value you fill in for f(5), so you could pick any answer you like, as long as you prepare to justify it!
Click to expand...
I don't understand this please can you help me step by step.
 
That makes no sense, given that they say "The number on the left becomes the number on the right": This is a function problem, relating the number on the left to the number on the right, not a sequence problem relating only the numbers in the right column. Observe that the numbers on the left do not increase by 1 each time (4 is skipped), so they are not sequence indices.

The term "pattern" has no mathematical definition. That is not a mathematical topic, unless specific types of "pattern" are under discussion.
 
No, I don't know what the "correct" answer would be. See post #2, where I said there is no one answer, because in principle they might have a different pattern in mind than whatever pattern you perceive.

The answer proposed in #4, without explanation (and explained in #5) is a possible answer; but if polynomial functions are not something you have been taught, then it is not likely. There may be something else entirely, that I'm not seeing; or the problem may just be faulty.

Here is an example of another possibility: multiply the input by 3, and then add 1 if the input was even. Then the answer is 15.

Can you ask about whether the problem is correct? Or about what topic you learned is meant to be applied?
 
There is some circumstantial evidence that the quadratic function may be what was intended. If you graph (or just make a table of) that function, like this:
1597975944184.png
you can see that the value 4, which they skipped, is one of the inputs that do not produce integer outputs. When an answer provides an explanation for an odd feature of a problem, it seems more likely.

But, as I've suggested, this only makes sense as an answer if that class for which this is a practice test covers something about quadratic functions, or finding polynomial functions given a few points, or something along these lines. As a random "find this pattern" problem, it would be entirely illegitimate in a mathematics course. I'm still waiting for a solid answer to my question about what was covered.
 
unavailable4now said:
I stumbled across a Vague question in my 11+ mock maths paper today (I already finished the paper) which I found difficult and didn't attempt.
The question was "The number on the left becomes the number on the right find the missing number with the question mark"
2➡7
3➡9
5➡?
6➡19
Please could someone help.
Click to expand...
I have given up reading these posts.
Here is a solution.
Define f(x) = ax^2 + bx + c (I used three variables since there were 3 points given)
Now on one hand f(2) = 4a + 2b + c and on the other hand f(2) = 7 (given). So 4a + 2b + c =7
f(3) = 9a +3b + c = 9
f(6) = 36a + 6b + c = 19.

Now solve this system of equations. Do this!

You will get a = 1/3, b = 1/3 and c = 5.

So f(x) = (1/3)x^2 + (1/3)x + (5).

Now f(5) = 15. This is one such answer to what 5 can be paired with. OK?
 
Last edited:
I think that reply #2 is the best we can do to what is clearly a nonsense question.
At best it is a contest question that has multiple possible answers.
A clearer set of objectives may have saved the question. But no, that did not happen.
So no one answer works.
 
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