Solve this

[vandita24x7]

An exclusive club is trying to pick its members from the social elite. An exact election mechanism has been agreed upon that will ensure the entrance of only the most suave members from the Groups A,B,C,D,E,F,G and H. Being in or out of the club is determined by the following rules :

If A is in, then G is out.

If H is out, then B is in.

If D is out, then E is out.

If H is in, then C is in.

If B is out, then G and D are out.

Q1)  Which of the following is a complete group of people who could be in?

A)  a)   A, F, G

B)   b)   F, G, H, C, E, D

C)    c)  E, D, H, C, B

D)    d) G, D, F, E

Q2) If B is out then who MUST be in?

a)  a)    A

b)   b)   C

c)    c)   D

d)     d) E

Q3)If E and G are in the club, then what other two people must also be in the club?

a)    a)  B, A

b)    b)  G, H

c)    c)   C, F

d)    d)  D, B

Q4) If B and D are out of the club , then which of the following must be true?

a)     a) At least two people are in the club

b)     b) At least three people are in the club

c)      c) At most four people are out of the club

d)     d) At most five people are out of the club

Q5) If 7 people are in the club, then who could be out?

a)   a)   A

b)     b) B

c)     c)  E

d)     d) C

 

 

[Sumit]

Hey Vandita,
Are you posting these questions for aspiring students preparing for diff. entrance Exams or you want answer of these questions for yourself????? Plz confirm

[XIPP]

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[vandita24x7]

Hi, Sumit, its both actually, also I am preparing for MPhil entrances so want to verify my solutions in this esteemed forum. Kindly ALL of you help me in this venture, a little help is always cherished :)

XIPP, well I am confused with first option as well.But I do have sure answers for the rest.

All I want is for people to come up here, open up their great minds and find the sure answer, as its available nowhere and discussion with group of great minds is a necessity

On Sun, Oct 6, 2013 at 8:16 AM, XIPP [via Discussion forum] <[hidden email]> wrote:

The answers I think:

For Q 1.;
two answers are correct :
B)   F, G, H, C, E, D   and   D)  G, D, F, E.


Q 2. and Q 3. can't be determined as per given info+options.

Ans. of Q 4. is C)   At most four people are out of the club.Because when B is out, G & D are out and when D is out , E is out. Thus we are left with 4 members only: A C F H.

Q 5. also has no answer (i.e. we can't have 7 members in any committee.)Because, (going with options), we can't keep E or C out, as then A and B should be in and G and H must be out. If B is out, then G, D, E must also be out. We are left with A only. If A is out, then B must be in and hence H must be out. In any situation, we are left with 6 members only.  

Am I right?
Please someone verify!

Thank you.

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[Prerna Rakheja]

Hi Vandita,

My answers are:
1) c
2) b
3) d
4) a
5) a

[XIPP]

Will you please explain why these answers?

[Prerna Rakheja]

1) Check the mentioned rules for each option and eliminate.

2) B is out => H is in => C is in.
  Notice, If H is out then B is in, however if H is in then B could be either in or out; but if B is out then it must be the case than H is in.

3) E is in => D is in, Either G is in or D is in => B is in.

4) B is out => D and G are out, D is out => E is out.
    Remaining A,C,H,F. Since B is out => H is in => C is in. However we cant conclude anything about A and F.

5) For each case write the set of people who will be in and apply the rules that must be met to eliminate options in case of a contradiction.