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Question

There are five men - A, B, C, D and E, six women P, Q, R, S, T and Z. A, B, and R are advocates. S, Q, P, D and C are doctors and the rest are teachers. A team has to be selected from these eleven persons subject to the following conditions:
(I) A, P and Z have to be together.
(II) B cannot go with D or R.
(III) E and Q have to be together.
(IV) C and T have to be together.
(V) D and P cannot go together.
(VI) C cannot go with Q.
If the team formed consists of two male advocates, two lady doctors and one teacher, the members of the team can be:

The correct answer is
A,B,P,Z,S

This problem involves selecting a team based on specific roles and adherence to several conditions. Let's break down the information provided.

Understanding the Professions

We have 5 men (A, B, C, D, E) and 6 women (P, Q, R, S, T, Z).

Their professions are defined as follows:

  • Advocates: A, B (men) and R (woman).
  • Doctors: D (man) and S, Q, P, C (women).
  • Teachers: E (man) and T, Z (women).

Here's a summary table:

Category Male Members Female Members
Advocates A, B R
Doctors D S, Q, P, C
Teachers E T, Z

Team Composition Requirements

The team must consist of:

  • Two male advocates.
  • Two lady doctors.
  • One teacher.

Analysis of Conditions

The team selection is subject to the following rules:

  • (I) A, P, and Z have to be together. If one is selected, all must be selected.
  • (II) B cannot go with D or R. If B is in the team, D and R must be out.
  • (III) E and Q have to be together. If one is selected, the other must be selected.
  • (IV) C and T have to be together. If one is selected, the other must be selected.
  • (V) D and P cannot go together. If D is selected, P must be out, and vice versa.
  • (VI) C cannot go with Q. If C is selected, Q must be out, and vice versa.

Evaluation of Options

Let's check each option against the team composition and the conditions:

Option 1: A, B, P, Z, S

  • Members: A (Male Adv), B (Male Adv), P (Lady Dr), Z (Teacher), S (Lady Dr).
  • Composition Check: 2 Male Advocates (A, B), 2 Lady Doctors (P, S), 1 Teacher (Z). This matches the requirement.
  • Conditions Check:
    • (I) A, P, Z are all included. (OK)
    • (II) B is included. D and R are not included. (OK)
    • (III) E and Q are not included. (OK)
    • (IV) C and T are not included. (OK)
    • (V) D is not included. (OK)
    • (VI) C and Q are not included. (OK)
  • Result: This option satisfies all conditions and composition requirements.

Option 2: A, B, P, Q, Z

  • Members: A (Male Adv), B (Male Adv), P (Lady Dr), Q (Lady Dr), Z (Teacher).
  • Composition Check: 2 Male Advocates (A, B), 2 Lady Doctors (P, Q), 1 Teacher (Z). This matches the requirement.
  • Conditions Check:
    • (III) Q is included, but E is not. This violates the condition that E and Q must be together. (FAIL)
  • Result: This option is invalid.

Option 3: B, E, Q, R, S

  • Members: B (Male Adv), E (Teacher), Q (Lady Dr), R (Female Adv), S (Lady Dr).
  • Composition Check: Only 1 Male Advocate (B) is included. The requirement is 2 Male Advocates. (FAIL)
  • Result: This option is invalid.

Option 4: A, P, R, S, Z

  • Members: A (Male Adv), P (Lady Dr), R (Female Adv), S (Lady Dr), Z (Teacher).
  • Composition Check: Only 1 Male Advocate (A) is included. The requirement is 2 Male Advocates. (FAIL)
  • Result: This option is invalid.

Conclusion

Only Option 1 successfully meets all the specified criteria for team composition and adheres to all the given conditions.

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Important Questions from Puzzle (Notes)

  1. Four individuals - P, Q, R and S - are suspects in a theft case. They make the following statements :
    P says: "Q is guilty."
    Q says: "R is guilty."
    R says: "P is innocent."
    S says: "I am innocent"
    If it is known that exactly one of them is guilty, and only the guilty person lies (all innocent people tell the truth), then who is the guilty one?
  2. Read the following informations and answer the question given below :
    A total of nine cards consisting of four kings, four queens and one joker are distributed among three persons P, Q and R such as :
    I. Q has two cards, P has three cards and R has four cards.
    II. Person, who has maximum number of cards, does not have the joker.
    III. Each one has atleast one king while Q has two kings.
    Who has three queens ?
  3. Consider the following information regarding a 3-digit PIN.

    The correct PIN is

  4. A boatman on a bank of a river has to carry a dog, a cat and a container full of milk to the other bank in a boat, one at a time. The cat cannot be left alone with the milk or with the dog on either bank. What is the minimum number of times the boatman has to cross the river to carry all to the other bank?
  5. How many minimum number of times water must be poured from a fully filled vessel of 12 litre capacity to an empty vessel of 8 litre capacity to transfer 6 litres of water while an empty vessel of 5 litre capacity is also available for use?
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