Adam buys 6 bags of white balloons.

Chen buys 3 bags of red balloons.

Adam says, ‘I have four times as many balloons as Chen.’

Explain why Adam is correct.

How hard can it be? After all, this is a maths question for kids in year 6. It’s question 12 in Mathematics paper 3: Reasoning, from the May 2017 SATs test, and it can earn you one mark. But there’s a high probability you’ll get it wrong, whether you’re an 11-year-old or a degree-level mathematician.

Explain why Adam is correct. There’s the catch. ‘Explain.’ Explain? How about these explanations:

“Because his mum and dad pay for a maths tutor.”

“Adam is a fictional character so is neither correct nor incorrect, but the question states he is correct, so it must be so, as the author is always right.”

“Because he has a lot more pocket money than Chen and can afford to buy 4 times as many balloons.”

“Because the question setters would have been careful not to get the question wrong.”

“Because Adam has been brought up never to tell a lie.”

…and so on.

But none of these will get a mark, so let’s cut to the maths.

Adam has 6 x 24 balloons, which is 144, and Chen has 3 x 12, which is 36.

Is that sufficient explanation? I have no idea. Maybe. Is it necessary to also point out that 144 divided by 36 is 4, so Adam is right? Or is it obvious enough at this point?

Perhaps a more intuitive approach would be to spot that the white balloon bags have twice as many balloons as the red bags, and coupled with the fact that Adam buys twice as many bags as Chen, he is bound to end up with 4 times as many balloons, greedy Adam.  Will that get you the mark?

No idea really, so let’s turn to the advice in the marking schemes document provided by the government’s Standards & Testing Agency (STA). They’ll know, as it’s their question.

Go on, challenge yourself

Here are some of the sample answers, right and wrong, that you’ll find in that document. I challenge you to sort these into correct and incorrect answers. Can you find the two that are correct?

  • A: Adam buys twice as many bags of twice as many balloons.
  • B: 24 is double 12 and 6 is double 3, so it’s doubled twice.
  • C: 36 × 4 = 144
  • D: Chen buys half the amount of bags and each bag has half the number of balloons, so he has 1/4 of the amount.

How did you get on?

Scroll down for the answer…

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Well if you answered C and D, congratulations. According to the STA, answers A and B do not sufficiently explain why Adam is correct yet, somehow, C and D would get you the mark.

Note that answer C makes no reference to how the number 36 is arrived at. Note also that answer D does not explain the relationship between the 1/4 and ‘four times as many’.

Now for a harder question: Explain why the STA is correct.