MGS 2008 Question

[kateJ]

I would really appreciate help with how to explain the following question which appears in the 2008 MGS paper ( Paper 2 )

Q5

A newspaper is made up from double sheets of paper, placed on top of each other, and then folded down the middle.
For example, an 8-page newspaper is made from two double sheets. The outer one consists of the pages numbered 1, 2, 7 and 8. The inner one, which is tucked inside the outer, consists of the pages numbered 3, 4, 5 and 6.
(a) In a 16-page newspaper, what other three numbers are on the double sheet with page 3 on it?
_ANS: 4,13,14

(b) In a 24-page newspaper, what other three numbers are on the double sheet with page 18 on it?
ANS: 7,8,17

(c) In another newspaper, pages 7 and 42 are on the same double sheet. How many pages does this newspaper have?
ANS:48

I know there must be an easier way of explaining this without having to draw out the pages, but I'm lost right now.

Thank you

[moved]

I had great fun with four girls that I tutored playing with newspapers. It's a really good reasoning question that opens their minds to other reasoning possibilities.

Fold up paper and have fun; another bridge built in the brain.

[ConcernedDad]

I would really appreciate help with how to explain the following question which appears in the 2008 MGS paper ( Paper 2 )

Q5

A newspaper is made up from double sheets of paper, placed on top of each other, and then folded down the middle.
For example, an 8-page newspaper is made from two double sheets. The outer one consists of the pages numbered 1, 2, 7 and 8. The inner one, which is tucked inside the outer, consists of the pages numbered 3, 4, 5 and 6.
(a) In a 16-page newspaper, what other three numbers are on the double sheet with page 3 on it?
_ANS: 4,13,14

(b) In a 24-page newspaper, what other three numbers are on the double sheet with page 18 on it?
ANS: 7,8,17

(c) In another newspaper, pages 7 and 42 are on the same double sheet. How many pages does this newspaper have?
ANS:48

I know there must be an easier way of explaining this without having to draw out the pages, but I'm lost right now.

Thank you

Practical learning as suggested by moved is great fun, and will help retain the concepts for much longer time.

Another way of solving is to write page numbers in two rows : Front to Back, and Back to Front

Front to Back : 1, 2, 3, 4, 5, 6, ….…….19, 20, 21, 22, 23, 24
Back to Front : 24, 23, 22, 21, 20, 19, …………6, 5, 4 3, 2, 1

Each double sheet has four pages :2 pages from front to back, and 2 pages back to front - as underlined above.

[kateJ]

Thank you very much for your suggestions.

I explained it by drawing lines as pages and numbering them. Not sure how a ten year old with strict time constraints could think of a solution though.

More practice methinks of this type of question....

[gdf]

The two numbers on any given side of a sheet of newspaper will always add up to the same value. In the given example, in a 8 page newspaper the outer sheet is made up of 1, 2, 7 and 8. Therefore, 1 and 8 are on the same side of the sheet and add up to 9. The same goes for 2 and 7(add up to 9). You also have to bear in mind that a sheet will always start with the lowest odd number for a given set of pages.

By applying this logic then on a 16 page newspaper the page numbers should add up to 17. So to find what is on the sheet with page 3, you would minus 3 from 17=14. Then, because 3 is the lowest odd number on the sheet (the other possible odd numbers being on the either side of 14. So 13 and 15), go to the next page which is 4 and minus 4 from 17=13.

Giving you 4,13,17

The other question talked about pages 7 and 42 being on the same sheet. If we add these page numbers up, we get 49. This is also the sum of page 1 and page 48.

Hope that helped..

[kateJ]

Wow! That's brilliant.

Thank you