11 Plus Exams Forum

Please advise the quicker way for doing this question.

Question: A milkman and a Baker deliver to the same house . In a period of 28 days , the milkman calls every second day and the baker every third day. They meet at the house twice in the first 7 days. How many more times do they meet during the 4 week period ?
Answers; 1) 6
2) 5
3) 4
4) 7-- my son did educated guess-- this is wrong answer
5) 3 -- correct answer

i tried explaining him

for milkman dates --1,3,5,7,9,11,13,15,17,19,21,23,25,27,29
Baker dates -------1,4,7,10,13,16,19,22,25,28

Matching dates 1,7,13,19,25,---- 1,7 already met , so 3 more days .


If there is any quicker way for doing this .. kindly advise.

With regards,
Jyoti

If you search the maths section for milkman and baker you'll find several explanations.

Hi Jyoti!

It's about the Lowest Common Multiple of 2 and 3, i.e. 6. You need a sequence of numbers every 6 numbers (six days). The first two can only be 1 and 7 to fit into the first week. After that just keep adding 6 before you run out. ( After day 7, there are only 21 days left; 6 x 3= 18, the biggest multiple of 6 less than or equal to 21; so the answer is 3.)

This may help your child visualise the problem:

Cut out 2 strips of graph paper. On the first colour every second square, on the second colour every third square. The child can then see that they line up every 6 squares and that even if you move the bottom one along one square relative to the one above, they still meet once every 6 squares. They can then also see the coloured squares have to be lined up on day 1 in order to meet twice in the first week.

You could then go on to strips with squares 4, 5 and 6 coloured so they get the idea or why it is the lowest common multiple. (Interestingly it also shows that in some positions numbers with common factors will not line up, eg 2 and 4 days starting on odd and even numbers)

Many thanks, this was really a great help.

With regards