Anyone able to solve this exam question?

[bartonian]

Three whole numbers when added together make 20. When multiplied together they make 300. What are the numbers?

I can't do this and it is now driving me mad. I have split 300 into its factors of 2 2 3 5 5, but I can't use them to make 3 numbers that add up to 20, even sneaking in a -1 somewhere.

Exactly - we have spent hours on it. But would they put a question that doesn’t work on an exam paper? (past paper, so people actually sat it)

Will have a think.

Could have two negative and one positive number as those would multiply to make a positive number.

Are you allowed to use negative numbers?

Is it -10, 0 and 30?

no, because it would then be -300. bugger.

That won't work as they will be 0 multiplied together

No, it would be zero. Even more bugger.

Also not sure whether negative numbers are whole numbers or not.

Surely this must be a misprint somewhere?

What is the past paper?

negative numbers are whole numbers, I'm pretty certain

can it include brackets?

Just found a definition that said whole number are only positive, integers include the negative one too, but I don't think its do able with just positive ones?? What age was this for, and if you have the specific paper we can maybe check if it was an actual mistake?

@noblegiraffe will hopefully come and help.

is this definitely in base 10?

It'd work if it had to add up to 21, not 20, any chance it was copied wrong at some point OP?

I don’t think it can be done. It works with 4 numbers- 10, 5, 3, 2 but I can’t find three that work.

in base 4:
-2, -2, and 30 (12 in base 10) works:
-2 + -2 + 30 = 20 and -2 x -2 x 30 = 300 . In decimal:
-2 + -2 + 12 = 8 and -2 x -2 x 12 = 48

I think it will be 2 negative numbers and one positive. So that the 2 negative multiplied together become a positive. Not the answer, but approaching it....
27-4-3=20
27 x -4 x -3= 324

What is the exact question?

I like Ifailed's base 4 answer, because there's definitely no way to do it in base 10 (which you can prove by an exhaustive search if you really want to)

If you type the exact question into Google you might find the mark scheme if it's from a past paper.

This is driving me nuts. I NEED to know the answer!

Is this a GCSE past paper?

I think it's a misprint.

DS says it's not doable!