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GMAT Diagnostic Test Question 24 Field: word problems (overlapping sets) Difficulty: 750

Rating:

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 but not tennis is half the number of players who play any other combination of two sports (2) p = 3

A. Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient B. Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient D. EACH statement ALONE is sufficient E. Statements (1) and (2) TOGETHER are NOT sufficient
_________________

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:

Thank you, there was a typo in the OE. I've corrected that. +1 for you!

First of all, we have to remember that we don't have to find the exact values in DS questions. We should save time and move on to the next question once we know that the info we have is sufficient.

There was a typo that I've fixed in the OE. The final value is different now, but the answer is still B.

arvs212 wrote:

can u plz elaborate a bit more..im confused with the explanation given..

I found confusing the wording of statement 1. "...is half of the players who play each of the rest two games" I had to read the explanation above to understand it. Wonder if any high scorer would find it confusing.

I found confusing the wording of statement 1. "...is half of the players who play each of the rest two games" I had to read the explanation above to understand it. Wonder if any high scorer would find it confusing.

got the same problem here. The description is weird.
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suppose there are: s: players only play soccer t: only tennis g: only golf x: only play soccer and golf y: only play soccer and tennis z: only play tennis and golf p: play all the three.

we can have: a) s+t+g+x+y+z+p+2p=60 ==> s+t+g+x+y+z=60-3p ==>> a1) 2*(s+t+g)+2*(x+y+z)=120-6p b) s+x+y+p=6p c) t+y+z+p=11p d) g+x+z+p=8p

from b) c) d), we have bcd) s+t+g+2*(x+y+z)=22p

use equation a1)- bcd), we can get: s+t+g=120-28p=36

Answer is B for this question, but it seems dzyubam's calculation is not correct. Or am I wrong?

I agree with flyingbunny. Number of players that play only one game is 36, not 33.

Demonstration using the first explanation as base.

Total = Soccer + Tennis + Golf - (Soccer&Tennis + Soccer&Golf + Tennis&Golf) - 2*Soccer&Tennis&Golf + None => 60 = 6*3 + 8*3 + 11*3 - (Soccer&Tennis + Soccer&Golf + Tennis&Golf) - 2*3 + 2*3 => (Soccer&Tennis + Soccer&Golf + Tennis&Golf) = 15 => Number of players playing two games only is 15.

Therefore, number of players playing one game only = Total - 2only - 3only - none = Total - (Soccer&Tennis + Soccer&Golf + Tennis&Golf) - Soccer&Tennis&Golf - None = 60 - 15 - 3 - 6 = 36

First explanation makes a mistake on the last step by counting "3only" twice, when it should be counted once.

Overlapping sets exercises are so simple yet is so easy to get confused with them.
_________________

Each formula is a different way of expressing the same equality.

Let me reprhase Total = Soccer + Tennis + Golf - (Soccer&Tennis + Soccer&Golf + Tennis&Golf) - 2*Soccer&Tennis&Golf + None as Total = Soccer + Tennis + Golf - (ONLY Soccer&Tennis + Soccer&Golf + Tennis&Golf) - 2*ONLY Soccer&Tennis&Golf + None, Note that the expression between parenthesis does not include the intersections of Soccer&Tennis, Soccer&Golf, and Tennis&Golf. To make it easier, refer to the graph posted by flyingbunny above. Total = s + t + g - y - x - z - 2p + 2P

Meanwhile, P(A u B u C) : P(A) + P(B) + P(C) – P(A n B) – P(A n C) – P(B n C) + P(A n B n C) is the same as saying Total = Soccer + Tennis + Golf - (Soccer&Tennis + Soccer&Golf + Tennis&Golf) + ONLY Soccer&Tennis&Golf + None, In this case the intersections of "Soccer&Tennis + Soccer&Golf + Tennis&Golf" are included. This expression counts/substracts the intersections thrice, so it is necessary to add it once. Using the nomenclature of the graph, this one could be written as: Total = s + t + g - (y+p) - (x+p) - (z+p) + p + 2P

You can use either formula. It depends on personal preference. Data provided and question asked should tilt the balance for using one or the other.
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People, it never says in the wording of the problem that "6p people play ONLY soccer", "11p people play ONLY tennis" etc. To me this wording sounds like 6p includes people who play solely soccer, as well as others who play soccer in a combination (e.g. soccer + tennis).

Given the above, I would say that we can't find the solution, given the information provided (E)

People, it never says in the wording of the problem that "6p people play ONLY soccer", "11p people play ONLY tennis" etc. To me this wording sounds like 6p includes people who play solely soccer, as well as others who play soccer in a combination (e.g. soccer + tennis).

Given the above, I would say that we can't find the solution, given the information provided (E)

Exactly, I'd go with E as well. In my understanding of the question, where [INT] represents Intersection. n(S) = 6p, n(T) = 11p, n(G) = 8p, n(S [INT] G [INT] T) = p, n(None) = 2p. The equation for total should be 60 = n(S) + n(T) + n(G) - [ n(S [INT] T) + n(S [INT] G) + n(T [INT] G)] + n(S [INT] G [INT] T) + n(None)

Both statements are insufficient to solve the above equation. what's the OA?
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GMAT Diagnostic Test Question 24 Field: word problems (overlapping sets) Difficulty: 750

Rating:

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.

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:

Rating:

Official Answer: B

Statement 1 is insufficient. For simplicity's sake we will write down the formula for three overlapping sets:

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:

People, it never says in the wording of the problem that "6p people play ONLY soccer", "11p people play ONLY tennis" etc. To me this wording sounds like 6p includes people who play solely soccer, as well as others who play soccer in a combination (e.g. soccer + tennis).

Given the above, I would say that we can't find the solution, given the information provided (E)

Exactly, I'd go with E as well. In my understanding of the question, where [INT] represents Intersection. n(S) = 6p, n(T) = 11p, n(G) = 8p, n(S [INT] G [INT] T) = p, n(None) = 2p. The equation for total should be 60 = n(S) + n(T) + n(G) - [ n(S [INT] T) + n(S [INT] G) + n(T [INT] G)] + n(S [INT] G [INT] T) + n(None)

Both statements are insufficient to solve the above equation. what's the OA?

OA is B. we need to find the number of people who play exactly two games so from the equation 60 = n(S) + n(T) + n(G) - [ n(S [INT] T) + n(S [INT] G) + n(T [INT] G)] + n(S [INT] G [INT] T) + n(None) reduces to n(S [INT] T) + n(S [INT] G) + n(T [INT] G) = 6p+11p+8p+2p+p-60 if p=3 then we can solve this hence B

GMAT Diagnostic Test Question 24 Field: word problems (overlapping sets) Difficulty: 750

Rating:

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

A. Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient B. Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient D. EACH statement ALONE is sufficient E. Statements (1) and (2) TOGETHER are NOT sufficient

Total = S+T+G - double -2(x) + N: S=soccer; T=tennis; double=no of those playing 2 games; x = No of those playing all 3 games; N=none 60 = 6p+11p+8p - double -2(x) + 2p 60 = 25p - double - 2p + 2p

(1) 60 = 25p - double.......... Notwithstanding its interpretation, (1) introduces another variable relating 2-games players INSUFF