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An infinite number of correct answers
mini me + poo
From a SATS key stage 2 (i.e. for 6-7 year olds) practice question...

Poll #1386206 What answer would you give?

Harry multiplied two numbers together. His answer was 120. Which two numbers could he have multiplied together?

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Wow, way to ask a non-specific question! I'm assuming the kids will get points for any two numbers that have a product of 120, though. Otherwise that's just cruel.

Yes, you get a point (or you would, if this weren't a practice question) for any correct answer. But which answer people pick is quite interesting.

Bugger you've hidden the responses ;)

I specifically said I was only dealing in integers.

That's also quite hard for a KS2 child - they only really seem to have started multiplication tables by then. I'm not sure I could have done that at 6 or 7 cos we didn't do tables properly till I was about 8 when I crunched through them rapidly and got my stupid certificate out of the way.

If you said integers, did you consider answers like -6*-20?

No, you got me on those.

I've never understood why minus numbers behave that way.

I'll show you next time we're in the same place. The short answer is: draw a graph of -2x against x and it should be clear!

It's OK, I don't think I really need to know why. Multiplying minus numbers in my head isn't something I need to do regularly, anyway.

Yeah, I wanted to avoid biasing answers. I'll post something about the answers tomorrow or so, but the first five people asked 'in real life' here gave five different (correct) answers.

I was expecting Paul to say something like '120 pi and 1 / pi' :)

I await your answers with interest.

I definitely want to see what the mathmos answered and see if my poor little brain can make sense of it without going *boom*.

I think I gave good answer :-)

(1,120),(2,60),(3,40),(4,30),(5,24),(6,20),(8,15),(10,12) are the positive integers.
While (-1,-120),(-2,-60),(-3,-40),(-4,-30),(-5,-24),(-6,-20),(-8,-15),(-10,-12) are the negative integer solutions,
also (x,120/x) where x is a rational number,
also irrational solutions such as (120^1/2,120^1/2),
also transcendental numbers such as (Pi, 120/Pi),(e,120/e).
also complex numbers, such as (120i, -i).

I suppose the most general answer would be something like (x, 120/x) where x is a complex number a +bi where a and b are real numbers and a+bi <> 0. But this does seem a bot beyond the comprehension of most 5-6 yeat olds.

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I'd give the quickest answer I could think of and then move on to see if the other questions were any more challenging

But then I'm not 6

An infinite number of correct answers. But also a larger infinite number of wrong answers presumably?

I would not have had a clue about that when I was 6.

I had 30x40 as one but knew it looked too big and had to do it on paper :) I got 10x12 ok at once. I think that was the expected answer if they do tables. Ten times table is one of the first you learn, isn't it?

You weren't the only one to say 30x40.

I'm not sure they do 10x as a formal table, but yes, it's an early one although there are some children in te age range who won't have done much wth numbers greater than a 100 yet.

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