11 Plus Exams Forum

Hi

Can someone please help to solve this and explain how.

20 people were surveyed at a sports centre.

5 people played both Squash and Tennis. 8 people did not play Squash. 11 people did not play tennis.

How many people dod not play either Squash or Tennis.

(a) 1
(b) 4
(c) 15
(d) 19

Thanks

Uma

Hi Uma,

5 people play both S & T;
11 people don't play T: 5 + 11 = 16 means 4 people left who must play only T.

8 people don't play S: 8 + 5 = 13 means 7 people left who must play only S.

So 4 play T, 7 play S and 5 play both = 16 leaves 4 who play neither.

Mike

It's b) 4

I used a quick 2X2 grid, with "tennis/ not tennis" along the top and "squash/ not squash" along the rows. Fill in what you know, ie 5 in the box "squash and tennis", 11 in the total for the "not tennis" column. This means there must be 9 in the total for the "tennis" column, so 4 (9-5) of these are "tennis and not squash". But we know 8 is the total "not squash" leaving 4 as the remainder "not tennis AND not squash"

Quicker to do than to explain in words!

5 people played both.

Let's call Tennis only =T
squash only =S
Neither=N

T+S+N=15 --------eqn (1)

8 did not play squash
So T+N=8 -----------Eqn(2)
T=8-N
11 did not play tennis
so S+N=11 -----------Eqn (3)
S=11-N

Substitute in Eqn 1 gives
(8-N)+(11-N)+N=15

Gives
N=4
So the number who do neither Tennis nor squash is 4 which is answer (b).

I think the ideal way to solve this would be a Venn Diagram i.e. two overlapping circles in rectangle, labelling them S and T, with 5 inserted in intersection part. If 8 did not play squash, then 12 did so you put 7 in non intersecting part of circle S. If 11 did not play tennis, then 9 did so you put 4 in non-intersecting part of circle T. You are then left with 4 to put outside circles and inside rectangle.

Yes fm - that's the way these problems are normally tackled - it's a very visual way of 'seeing' the information.

Hi

Thanks for the replies.

Yes... I have understood now. Looks easy now.

Thanks & Regards

Uma