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Golfers

by Ashujain » Fri Jun 22, 2012 2:29 am
1/3 of golfers also play tennis. 3/5 of tennis players also surf. 4/7 of surfers also ski. If a golfer is selected at random, is the chance that that golfer also skis greater than 1/2 ?

1) All golfers who do not play tennis also surf.
2) All tennis players also play golf.

OA: E
But I am getting C as answer.
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by jcnasia » Fri Jun 22, 2012 5:09 am
Here's how I solved the problem...

Statement 1:

Case 1:
15 Golfers: Andrew, Ben, Carla, Della, Ella, F, G...O
5 Tennis players: Andrew, Ben, Carla, Della, Ella
14 Surfers: Andrew, Ben, Carla, and F, G, ... 0, and Pamela
Skiers: Andrew, Ben, Carla, F, G, H, I, J
8 of the golfers also ski so the chance is > 1/2

Case 2:
15 Golfers: Andrew, Ben, Carla, Della, Ella, F, G...O
5 Tennis players: Andrew, Ben, Carla, Della, Ella
14 Surfers: Andrew, Ben, Carla, and F, G, ... 0, and Pamela
Skiers: Andrew, Ben, Carla, F, G, H, I, Pamela
7 of the golfers also ski so the chance is < 1/2

Statement 2:

Case 1:
15 Golfers: Andrew, Ben, Carla, Della, Ella, F, G ...O
5 Tennis player: Andrew, Ben, Carla, Della, Ella
7 Surfers: Andrew, Ben, Carla, Pamela, Quin, Ryan, Sara
16 Skiers: Andrew, Ben, Carla, Della, Ella, ... O, Pamela
So all the golfers also ski.

Case 2:
15 Golfers: Andrew, Ben, Carla, Della, Ella, F, G ...O
5 Tennis player: Andrew, Ben, Carla, Della, Ella
7 Surfers: Andrew, Ben, Carla, Pamela, Quin, Ryan, Sara
4 Skiers: Pamela, Quin, Ryan, Sara
So none of the golfers also ski.

Statement 1 & 2:

Case 1:
15 Golfers: A...O
5 Tennis players: A...E
14 Surfers: F...O, P...S
10 Skiers: F...O
So 2/3 golfers also ski.

Case 2:

15 Golfers: A...O
5 Tennis players: A...E
28 Surfers: F...O, P...S, T...Z, AA..GG
20 Skiers: N...GG
So 2/15 golfers also ski.

So Statement 1 and 2 together are insufficient.
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by Anurag@Gurome » Fri Jun 22, 2012 6:04 am
Ashujain wrote:1/3 of golfers also play tennis. 3/5 of tennis players also surf. 4/7 of surfers also ski. If a golfer is selected at random, is the chance that that golfer also skis greater than 1/2 ?

1) All golfers who do not play tennis also surf.
2) All tennis players also play golf.
One thing we should note that "1/3 of golfers also play tennis" doesn't mean number of players who play tennis is 1/3 of the number of the golfers. There may be some other people who play tennis but do not play golf.

So for now, let us assume,
  • Number of golfers = G
    Number of tennis players = T
    Number of surfers = F
    Number of skiers = K
Evidently each statement individually is not sufficient as we cannot establish any definite relation between the golfers and skiers. Let us analyze both statements together,

From statement 2, all tennis players play golf. Hence, T = G/3
From statement 1, all golfers who do not play tennis also surf.
Hence, F = 3T/5 + 2G/3 + f = 3(G/3)/5 + 2G/3 + f = G/5 + 2G/3 + f = 13G/15 + f
Where, f = number of players who neither plays golf nor tennis but surfs

Now, K = (4F/7 + k)
Where, k = number of players who does not surfs but skis.

Hence, we can see that the number of golfers who also skis depends upon f and k also, which we do not have any idea of.

Not sufficient

The correct answer is E.
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by dhonu121 » Fri Jun 22, 2012 6:17 am
If we had to find the chance that golfer also skies, what is the formula that we would have used ?
As in, what quantity was supposed to come in the denominator ?
The numerator would have number of golfers who ski.
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by veneetvishal » Fri Jun 22, 2012 6:51 am
The way i solved was:
To start lets take the no. of golfers as 105(LCM of 3,5,7)
Hence, no. of golfers who play tennis: 35 + some other tennis players
No. of surfers who also play tennis and golf: 21+ some other surfers
No. of skiers who also surf,play tennis and golf : 12 + some other skiers

Now for probability to be true, the total no. of skiers (12+some other skiers) should be less than 24.

Since we cannot find the "some other skiers" information, answer is E.
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by jcnasia » Fri Jun 22, 2012 6:56 am
dhonu121 wrote:If we had to find the chance that golfer also skies, what is the formula that we would have used ?
As in, what quantity was supposed to come in the denominator ?
The numerator would have number of golfers who ski.
The denominator is # of golfers.
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