bb wrote:
GMAT Diagnostic Test Question 24Field: word problems (overlapping sets)
Difficulty: 750
[rating1]yellow/79353[/rating1]
Among 60 members of a club, 6p players play soccer, 11p players play tennis, 8p players play golf and 2p players play none of the games. If p players play all of the games, how many players play only one game?
(1) The number of players who play soccer and golf is half of the players who play each of the rest two games
(2) p = 3
I did not get what does mean by "rest of the two games" in st. 1?
I agree with the OA ( i.e B) assuming that statement 1 is insufficient however the number should be 33 not 36.
Rephrasing the OE:
p = 3
Soccer = 6p = 18
Tennis = 11p = 33
Golf = 8p = 24
Soccer&Tennis&Golf = p = 3
None = 2p = 6
Total = Soccer + Tennis + Golf - (Soccer&Tennis + Soccer&Golf + Tennis&Golf) - 2 (Soccer&Tennis&Golf) + None
Total = 6p + 11P + 8p - (Soccer&Tennis + Soccer&Golf + Tennis&Golf) - 2p + 2p
60 = 18 + 24 + 33 - (Soccer&Tennis + Soccer&Golf + Tennis&Golf) - 2*3 + 2*3
60 = 75 - 6 + 6 - (Soccer&Tennis + Soccer&Golf + Tennis&Golf)
60 = 75 - (Soccer&Tennis + Soccer&Golf + Tennis&Golf)
(Soccer&Tennis + Soccer&Golf + Tennis&Golf) = 15
Members playing only one game = Total - (Soccer&Tennis + Soccer&Golf + Tennis&Golf) - 2 (Soccer&Tennis&Golf) - None
Members playing only one game = 60 - 15 - 2(3) - 2*3 = 33
dzyubam wrote:
Explanation:[rating1]yellow/793532[/rating1]
Official Answer: BStatement 1 is insufficient. For simplicity's sake we will write down the formula for three overlapping sets:
Total = Soccer + Tennis + Golf - (Soccer&Tennis + Soccer&Golf + Tennis&Golf) - 2*Soccer&Tennis&Golf + None
We need to know the number inside the parentheses. Statement 1 only provides Soccer&Golf to (Soccer&Tennis + Tennis&Golf) relationship, which is not sufficient. We have one equation and two variables. Insufficient.
Statement 2 is sufficient. Knowing the value of \(p\) we can find the exact values of each group from the formula above:
60 = 18 + 24 + 33 - (Soccer&Tennis + Soccer&Golf + Tennis&Golf) - 2*3 + 2*3
60 = 75 - 6 + 6 - (Soccer&Tennis + Soccer&Golf + Tennis&Golf)
60 = 75 - (Soccer&Tennis + Soccer&Golf + Tennis&Golf)
(Soccer&Tennis + Soccer&Golf + Tennis&Golf) = 15
Now that we know the number of club members playing exactly two games, we can find the number of club members playing only one game:
Total - (Soccer&Tennis + Soccer&Golf + Tennis&Golf) - Soccer&Tennis&Golf - None =
\(60 - 15 - 3 - 2*3 = 36\)