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Monday, August 22, 2011

An Eleven Plus Problem

We have the privilege of working with some remarkably bright children. Some children seem to find the present crop of eleven plus papers rather boring. After all if you could work your way through an eleven plus paper when you were eight years old the challenge may be rather diminished by the grand old age of ten!

On our courses we meet children who are being prepared at home by their parents and other children who are working with tutors. We also have the opportunity of working with children who are trying to gain entrance to super selective schools – and accordingly have eleven plus courses that are demanding.

This is the question that the eleven plus star attempted gracefully and gladly:

Carpeting 67 cm wide is bought to cover a floor 6.7 m long and 4.9 m wide. What length of carpet will be needed if it is laid (1) lengthwise (2) crosswise?

Now children brought up in the families of carpet fitters would probably be able to cope with a question like this reasonably easily. After all, the dinner table may sometimes be regaled with tales of fitting carpets – and coping with exacting customers. We know too that when a room is carpeted from wall to all the carpet is bought in rolls – which are cut into lengths to cover the whole floor. Our eleven plus star took the question in her stride. First of all, for about ten seconds, she tried to do the question in her head – before setting the answer out neatly and logically.

Answer (1)
The width of the room is 4.9 m = 490cm.
The number of strips = 490 divided by 67 – which is 7.3 strips.
8 strips, each 6.7 m long will be needed = 53.6 m.
Therefore 54 m must be bought.

Answer (2)
The length of the room = 6.7 m = 670 cm
The number of strips = 670 divided by 67 = 10
The length needed is 10 times 4.9 m = 49 m
Therefore 49 m must be bought.

We did not, however, attempt to test her with the dilemma faced by many families who do not want to enjoy the cheaper option of a carpet going sideways.

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