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# GMAT Diagnostic Test Question 24

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GMAT Diagnostic Test Question 24 [#permalink]

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06 Jun 2009, 23:03
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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
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Re: GMAT Diagnostic Test Question 24 [#permalink]

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02 Jul 2009, 07:53
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Explanation:
 Rating:

Statement 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 =
$$60 - 15 - 3 - 2*3 = 36$$
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Re: GMAT Diagnostic Test Question 24 [#permalink]

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10 Aug 2009, 22:18
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can u plz elaborate a bit more..im confused with the explanation given..

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

uve written this equation fr S1

then u hav used

Statement 2 is sufficient. Knowing the value of 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

this for S2..

it wuld b grt if u culd throw sum light n this topic..

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Re: GMAT Diagnostic Test Question 24 [#permalink]

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11 Aug 2009, 01:07
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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..

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

uve written this equation fr S1

then u hav used

Statement 2 is sufficient. Knowing the value of 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

this for S2..

it wuld b grt if u culd throw sum light n this topic..

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Re: GMAT Diagnostic Test Question 24 [#permalink]

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22 Aug 2009, 13:57
I found confusing the wording of statement 1.
"...is half of the players who play each of the rest two games"
Wonder if any high scorer would find it confusing.

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Re: GMAT Diagnostic Test Question 24 [#permalink]

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23 Aug 2009, 09:18
powerka wrote:
I found confusing the wording of statement 1.
"...is half of the players who play each of the rest two games"
Wonder if any high scorer would find it confusing.

got the same problem here. The description is weird.
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Re: GMAT Diagnostic Test Question 24 [#permalink]

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23 Aug 2009, 09:32
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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?
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Re: GMAT Diagnostic Test Question 24 [#permalink]

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23 Aug 2009, 10:50
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.
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Re: GMAT Diagnostic Test Question 24 [#permalink]

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23 Aug 2009, 21:53
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.

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Re: GMAT Diagnostic Test Question 24 [#permalink]

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23 Aug 2009, 22:22
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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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Re: GMAT Diagnostic Test Question 24 [#permalink]

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23 Aug 2009, 23:12
I always draw a diagram to help understanding this kinda question.

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Re: GMAT Diagnostic Test Question 24 [#permalink]

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06 Sep 2009, 01:46
defeatgmat wrote:
I always draw a diagram to help understanding this kinda question.

What would that look like for this question?

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Re: GMAT Diagnostic Test Question 24 [#permalink]

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18 Oct 2009, 13:40
blue4rain wrote:
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.

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

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Re: GMAT Diagnostic Test Question 24 [#permalink]

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12 Nov 2009, 19:15
Venn diagrams are the best way to go for this one... Though it eats up time doing so.

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Re: GMAT Diagnostic Test Question 24 [#permalink]

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14 Dec 2009, 07:34
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)

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Re: GMAT Diagnostic Test Question 24 [#permalink]

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14 Dec 2009, 08:44
vasyl27 wrote:
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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Re: GMAT Diagnostic Test Question 24 [#permalink]

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16 Dec 2009, 00:14
bb wrote:
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.

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:
 Rating:

Statement 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 =
$$60 - 15 - 3 - 2*3 = 36$$

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Re: GMAT Diagnostic Test Question 24 [#permalink]

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18 Feb 2010, 13:03
I agree with "each of rest two games" being confusing. What exactly does that mean? Please rephrase this if you can. Thanks.

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Re: GMAT Diagnostic Test Question 24 [#permalink]

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25 Feb 2010, 10:17
BarneyStinson wrote:
vasyl27 wrote:
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

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Re: GMAT Diagnostic Test Question 24 [#permalink]

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02 Apr 2010, 18:23
bb wrote:
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

(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
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Re: GMAT Diagnostic Test Question 24   [#permalink] 02 Apr 2010, 18:23

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