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Need help
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
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
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!
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).
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.