Help anyone? (doubling, cube numbers)

[MCLC]

Can someone give me some guidance on how to work out the following:

A teacher fills a large tank of water over a period of time. She starts with 1 cup of water on day one. Every day she doubles the amount of water in the tank. For example, at the end of day two there are two cups of water in the tank. After three days there are four cups, etc. If it takes 28 days to exactly fill the tank, on which day was the tank a quarter full?



What is the largest cube number divided by the highest common factor of 8 and 12?

[Guest55]

A teacher fills a large tank of water over a period of time. She starts with 1 cup of water on day one. Every day she doubles the amount of water in the tank. For example, at the end of day two there are two cups of water in the tank. After three days there are four cups, etc. If it takes 28 days to exactly fill the tank, on which day was the tank a quarter full?

28 days full
27 days half full ... does that help?

[Guest55]

What is the largest cube number divided by the highest common factor of 8 and 12?

What on earth does this mean?

Does it mean HCF of 8 and 12 [which is 4] has to go into the cube number or what?

[MCLC]

Thanks Guest. Re the first question - how did you work out the tank was half full on day 27?

Second question - I have no idea! The answer is 16 on the sheet.

[ToadMum]

Thanks Guest. Re the first question - how did you work out the tank was half full on day 27?

Second question - I have no idea! The answer is 16 on the sheet.

Every day she doubles the amount of water in the tank.

So, however much water there is in the tank on a given day, the day before there was half as much.

Was the second question actually printed as you have reproduced? If so, it was written by someone with very poor English, if it meant enough to them to get any kind of answer. Was there a choice of numbers, which included the cube number 64 (4×4×4)? The question only makes sense if 64 is there to be chosen (that is, the largest cube number from a selection of numbers) - the real 'largest cube number' is obviously very much larger than 64.

'What cube number do you make from the highest common factor of...?' perhaps

[MCLC]

Thank you both!

Yes the question was printed that way.
It's a multiple choice question with options of:

16
8
4
2
24.

Answer is 16.

[Guest55]

It's a poorly worded question - the HCF of 8 and 12 is 4.

16 is not a cube! 8 is the only cube in that list ... where does this question come from??!!

[ToadMum]

To get the answer '16':

Which number is the result of dividing a cube number by the highest common factor of 8 and 12?'??

[MCLC]

Both questions are from a paper which was given out by a mock provider.

[ToadMum]

Both questions are from a paper which was given out by a mock provider.

The water question is fine.

If the wording of the HCF question would make me hope that they don't offer tuition in English...