GMAT Diagnostic Test Question 24

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.

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.

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.

can someone please explain why the formula is:

Total = Soccer + Tennis + Golf - (Soccer&Tennis + Soccer&Golf + Tennis&Golf) - 2*Soccer&Tennis&Golf + None,

in particular, why it is - 2*Soccer&Tennis&Golf


aren't we using the formula that

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)

and so Total = P(A u B u C) + complement (P(A u B u C) )

= Soccer + Tennis + Golf - (Soccer&Tennis + Soccer&Golf + Tennis&Golf) + Soccer&Tennis&Golf + None,

thanks.

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.

I always draw a diagram to help understanding this kinda question.

What would that look like for this question?

Agree with you - there are 33 and not 36 players who only played one game - Good to see probabilistic people here

Venn diagrams are the best way to go for this one... Though it eats up time doing so.

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?

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

I agree with "each of rest two games" being confusing. What exactly does that mean? Please rephrase this if you can. Thanks.

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

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

(2) 60 = 25(3) - double
=> double = 15
1 game: total - double - triple(x) [i guess not 2x] - N
= 60 - 15 - 3 - 2(3)
=> 60 - 24 = 36

Hence, B