Manchester Grammar 2013 maths Question: remainders

[Ahins]

The question below has be asked previously on the forum and the answer has been given as finding one less that a multiple of all the numbers i.e 59. I am curious to know why the answer cannot be 11 as this answer satisfies the conditions given. Can someone tell me where I could be going wrong? Many thanks


Alison has large number of pencils. When the pencils are divided by two of her friends there is one pencil left over. If they are divided by three friends there are two left over. Divided between four friends there are three left over. Between give friends there are four left over and between six friends, there are five left over. What is the smallest number of pencils that Alison could have?

[Guest55]

11 is not a 'large number' of pencils.

[Bibliovore]

This is largely because if 11 pencils are divided between five friends, there is only one left over and not four as the questions specifies.

[Guest55]

Thanks for that I missed it because of the typo.

[ToadMum]

I worked it out by trying listing (multiples of 5, plus 4), until I got to one which was a multiple of 4, plus 3. And then checked against the other requirements, obviously.

Hint - over a half century .

[Ahins]

Thanks everyone. I mis-read the question i think.