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# Seven students are trying out for the school soccer team, on which the

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Manager
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Seven students are trying out for the school soccer team, on which the [#permalink]

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12 Jan 2015, 22:19
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Difficulty:

95% (hard)

Question Stats:

51% (01:51) correct 49% (01:11) wrong based on 225 sessions

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Seven students are trying out for the school soccer team, on which there are three available positions: fullback, sweeper, and goalie. Each student can only try out for one position. The first two students are trying out for fullback. The next two students are trying out for sweeper. The remaining three students are trying out for goalie. However, the fourth student will only play if the second student is also on the team, and the third student will only play if the fifth student is on the team. How many possible combinations of students are there to fill the available positions?

A 3
B 5
C 7
D 10
E 12
[Reveal] Spoiler: OA
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Re: Seven students are trying out for the school soccer team, on which the [#permalink]

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12 Jan 2015, 23:13
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Hi PathFinder007,

This question uses what's called "Formal Logic" (a concept that you would see repeatedly on the LSAT, but rarely on the GMAT). You can answer it with some drawings and careful note-taking.

Based on the information in the prompt, we have seven players (A,B,C,D,E,F,G). We're asked for the total groups of 3 that can be formed with the following restrictions:

1) Only 1 player per position
2) A and B are trying out for fullback
C and D are trying out for sweeper
E, F and G are trying out for goalie
3) D will only play if B is also on the team
C will only play if E is also on the team

The big restrictions are in the two 'formal logic' rules....
-We can put E with ANYONE, but we can only put in C if E is ALSO there.
-We can put B with ANYONE, but we can only put in D if B is ALSO there.

By extension....
D can NEVER be with A (because then B would not be in the group)
C can NEVER be with F or G (because then E would not be in the group)

As such, there are only a few possibilities. We can have...
ACE
BCE
BDE
BDF
BDG

[Reveal] Spoiler:
B

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Manager
Joined: 30 Apr 2017
Posts: 88
Re: Seven students are trying out for the school soccer team, on which the [#permalink]

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29 Oct 2017, 06:45
EMPOWERgmatRichC wrote:
Hi PathFinder007,

This question uses what's called "Formal Logic" (a concept that you would see repeatedly on the LSAT, but rarely on the GMAT). You can answer it with some drawings and careful note-taking.

Based on the information in the prompt, we have seven players (A,B,C,D,E,F,G). We're asked for the total groups of 3 that can be formed with the following restrictions:

1) Only 1 player per position
2) A and B are trying out for fullback
C and D are trying out for sweeper
E, F and G are trying out for goalie
3) D will only play if B is also on the team
C will only play if E is also on the team

The big restrictions are in the two 'formal logic' rules....
-We can put E with ANYONE, but we can only put in C if E is ALSO there.
-We can put B with ANYONE, but we can only put in D if B is ALSO there.

By extension....
D can NEVER be with A (because then B would not be in the group)
C can NEVER be with F or G (because then E would not be in the group)

As such, there are only a few possibilities. We can have...
ACE
BCE
BDE
BDF
BDG

[Reveal] Spoiler:
B

GMAT assassins aren't born, they're made,
Rich

tough one!
is there any algebraic solution for this?
is it possible we see such a question n real Gmat???
Director
Joined: 29 Jun 2017
Posts: 512
GMAT 1: 570 Q49 V19
GPA: 4
WE: Engineering (Transportation)
Seven students are trying out for the school soccer team, on which the [#permalink]

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23 Dec 2017, 07:10
soodia wrote:
EMPOWERgmatRichC wrote:
Hi PathFinder007,

This question uses what's called "Formal Logic" (a concept that you would see repeatedly on the LSAT, but rarely on the GMAT). You can answer it with some drawings and careful note-taking.

Based on the information in the prompt, we have seven players (A,B,C,D,E,F,G). We're asked for the total groups of 3 that can be formed with the following restrictions:

1) Only 1 player per position
2) A and B are trying out for fullback
C and D are trying out for sweeper
E, F and G are trying out for goalie
3) D will only play if B is also on the team
C will only play if E is also on the team

The big restrictions are in the two 'formal logic' rules....
-We can put E with ANYONE, but we can only put in C if E is ALSO there.
-We can put B with ANYONE, but we can only put in D if B is ALSO there.

By extension....
D can NEVER be with A (because then B would not be in the group)
C can NEVER be with F or G (because then E would not be in the group)

As such, there are only a few possibilities. We can have...
ACE
BCE
BDE
BDF
BDG

[Reveal] Spoiler:
B

GMAT assassins aren't born, they're made,
Rich

tough one!
is there any algebraic solution for this?
is it possible we see such a question n real Gmat???

Let me try ->
a1a2 for F
a3a4 for S
a4-7 for G
a1 a2 a3 a4 a5 a6 a7 be the candidates { a4 will be there when a2 is there and a 3 when a5 is there => LOCK a2 and a5 in mind or paper}
F ------S ------G
a1-----a3-----a5,a6,a7 => 3 ways
a2-----a4-----a6,a7 only => 2 ways

total 5 ways - SHORT and SWEET -
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Last edited by sahilvijay on 23 Dec 2017, 09:34, edited 1 time in total.
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Joined: 02 Aug 2009
Posts: 5663
Re: Seven students are trying out for the school soccer team, on which the [#permalink]

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23 Dec 2017, 07:28
PathFinder007 wrote:
Seven students are trying out for the school soccer team, on which there are three available positions: fullback, sweeper, and goalie. Each student can only try out for one position. The first two students are trying out for fullback. The next two students are trying out for sweeper. The remaining three students are trying out for goalie. However, the fourth student will only play if the second student is also on the team, and the third student will only play if the fifth student is on the team. How many possible combinations of students are there to fill the available positions?

A 3
B 5
C 7
D 10
E 12

three category..
1) Full back - $$F_1 , F_2$$.... NO restrictions
2) sweeper - $$S_3, S_4$$...
$$S_3$$ plays if $$G_5$$ plays
$$S_4$$ plays if $$F_2$$ plays
so restrictions for BOTH
3) Goalie - $$G_5, G_6,G_7$$... No restrictions

so lets look at the sweeper as the restrictions are there
let $$S_3$$play so ANY of two F and $$G_5$$ in G .... so $$1*2*1=2$$ ways
let $$S_4$$ play so $$F_2$$ in F and ANY of three in G .... so $$1*1*3=3$$ ways

Total = 2+3=5 ways
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Re: Seven students are trying out for the school soccer team, on which the   [#permalink] 23 Dec 2017, 07:28
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