Tricky CEM Maths question

[SuperDad3g]

Please could someone kindly assist with solving this question? I have the answer with no explanation or workings, and I can't figure out how to explain the answer to my child! Thanks for your help!

Q: There are 15 red balls, 10 white balls and 8 white balls mixed up in a bag. Tom takes the balls from the bag one by one at random. He wants to take out at least 2 balls of each colour. What is the least number of balls that Tom needs to take from the bag to guarantee doing this?

A: 27

[Tinkers]

First of all it’s not about probability as such (along you do consider that).

If you pick out 15 balls, there’s a possibly they could all be red. (Slim but possible) so to be sure you have at least two balls of each colour, think about how many more you’d need.

[SuperDad3g]

Thanks Tinkers!

I think I get it:
1. Assume first 15 are all red
2. Assume next 10 are all white
3. Then next 2 are pink (Apologies, there was a typo in my earlier note. Should be 15 red, 10 white, 8 pink)
Therefore, minimum number of balls required to guarantee that Tom picks at least 2 of each colour = 27!

[Tinkers]

Yes that’s it.

[SuperDad3g]

Hi All. I’m back with another question. Please kindly help!

Question: 12-(8-3)x2
Answer: 14

If I apply BODMAS, I workout the brackets (B) first, which gives me 5. Next, I Multiply 5 by 2 to get 10, then Subtract 10 from 12 to get 2. What am I doing wrong? Am I not applying BODMAS correctly? I assumed that BODMAS is tested in all 11+ Maths exams?

[russet]

I think the question needs another set of brackets to get 14 with the bodmas rules. You need to take the 5 from the 12, then times by 2. For this they should have put:

(12-(8-3))x2

As it stands, I make it 2 as well.

[ToadMum]

Hopefully, CEM itself would get it right on an actual paper. Or is this from a genuine CEM familiarisation booklet on a school's/ LA's website? Those are the only practice materials that CEM itself publishes.

Whoever published it, you should perhaps email them to point out that the format of the question doesn't support the answer they give?

[Tinkers]

I’d say it was 2 as well. To get 14 then the second part would need to be -2, so that subtracting -2 from 12 gets you 14.

As for BODMAS, I’m not sure what CEM say, but seem to recall (from many moons ago) that GL have been asked about this, and they say that they realise some children will have been taught it and others won’t. They structure the question so that it doesn’t matter either way, so no child is disadvantaged by knowing or not knowing BODMAS.

(While GL do this in their practice papers, other publishers weren’t doing that at the time. I don’t know if they now do or not.)

[SuperDad3g]

All - Thank you for your responses. I’ve seen written to the test provider. Awaiting their response.