Odd GCSE Maths Question

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Odd GCSE Maths Question

#1  Postby LjSpike » May 14, 2016 2:28 pm

I was doing a past paper, and not even my maths teacher could work out the answer, she said she was going to check the mark scheme, but I was wondering if anyone here could work it out. (The answer will be an integer).
The Question:
Martin thinks of 2 numbers.
The HCF (Highest common factor) of the numbers is 6.
The LCM (Lowest common multiple) of the numbers is 15.


I did the working out of firstly, factors of 15:
1, 15, 3, 5.

Now, at this point I would normally go to see which numbers there have a factor of 6, so you can rule out 3 of the numbers...
1, 3 and 5 as they are lower then 6, thus cannot have a factor of 6.

Now, were left with 15. There is 2 problems here.
1) 15 Is not a multiple of 6 (thus 6 is not a factor of it).
2) We only have 15, yet martin was thinking of 2 numbers.


Slip up by the exam board in question making, or did we miss something horrifically obvious? :scratch:
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Re: Odd GCSE Maths Question

#2  Postby Thommo » May 14, 2016 2:40 pm

No integer solutions to that as presented.

1. If 6 is a factor of two numbers then they are both even (since 2 is also a factor of both numbers as 2 is a factor of 6).
2. If 15 is a common multiple of two numbers then they are both odd (since any integer multiplied by an even integer is even).

Therefore we have a contradiction - both the numbers are both even and odd. So there are no solutions.
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Re: Odd GCSE Maths Question

#3  Postby LjSpike » May 15, 2016 7:56 am

Thommo wrote:No integer solutions to that as presented.

1. If 6 is a factor of two numbers then they are both even (since 2 is also a factor of both numbers as 2 is a factor of 6).
2. If 15 is a common multiple of two numbers then they are both odd (since any integer multiplied by an even integer is even).

Therefore we have a contradiction - both the numbers are both even and odd. So there are no solutions.


Thats a very good point as well. Its a rather unusual question.
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Re: Odd GCSE Maths Question

#4  Postby RobM » May 15, 2016 8:11 am

I looked for this on the web and I have seen the question with different wording which makes a solution possible.
Martin thinks of 2 numbers.
The HCF (Highest common factor) of the numbers is 6.
The LCM (Lowest common multiple) of the numbers is a multiple of 15.
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Re: Odd GCSE Maths Question

#5  Postby Thommo » May 15, 2016 2:00 pm

RobM wrote:I looked for this on the web and I have seen the question with different wording which makes a solution possible.
Martin thinks of 2 numbers.
The HCF (Highest common factor) of the numbers is 6.
The LCM (Lowest common multiple) of the numbers is a multiple of 15.


Yeah, that would do it. Infinitely many solutions to that (most of them trivial). 12 and 30 is (I think) the lowest non trivial solution.
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Re: Odd GCSE Maths Question

#6  Postby VazScep » May 15, 2016 2:44 pm

Thommo wrote:
RobM wrote:I looked for this on the web and I have seen the question with different wording which makes a solution possible.
Martin thinks of 2 numbers.
The HCF (Highest common factor) of the numbers is 6.
The LCM (Lowest common multiple) of the numbers is a multiple of 15.


Yeah, that would do it. Infinitely many solutions to that (most of them trivial). 12 and 30 is (I think) the lowest non trivial solution.
What are you taking to be a trivial solution?
Here we go again. First, we discover recursion.
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Re: Odd GCSE Maths Question

#7  Postby Thommo » May 15, 2016 3:04 pm

VazScep wrote:
Thommo wrote:
RobM wrote:I looked for this on the web and I have seen the question with different wording which makes a solution possible.
Martin thinks of 2 numbers.
The HCF (Highest common factor) of the numbers is 6.
The LCM (Lowest common multiple) of the numbers is a multiple of 15.


Yeah, that would do it. Infinitely many solutions to that (most of them trivial). 12 and 30 is (I think) the lowest non trivial solution.
What are you taking to be a trivial solution?


Where one of the numbers is the HCF or the multiple. E.g. 6 and 30 works.
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