Explanation for the Analytical Reasoning Quiz 04

This is the detailed explanation for the Analytical Reasoning Quiz 04 .

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1. “In case T and Z are the individuals serving on committee B, how many of the nine individuals should serve on committee C?”

Given:

• Committee B needs 2 members, and in this case, T and Z are on Committee B.

• Committee A needs to have exactly one more member than Committee B, which means Committee A must have 3 members.

• The total number of people is 9. If Committee B has 2 members and Committee A has 3 members, then Committee C must have the remaining members:

  • $9-(2\text{ from B}+3\text{ from A})=4\text{ members for Committee C}$.

Correct answer: 4

There are 4 members who will serve on Committee C.

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2. “Of the nine individuals, the largest number that can serve together on committee C is?”

Given:

• Committee C can have no more than 4 members because the other two committees (A and B) already take up the remaining members.

• Committee B is fixed at 2 members (as stated by the rules), and Committee A must have 3 members.

• This leaves 4 members who must serve on Committee C.

Correct answer: 4

The largest number of people that can be assigned to Committee C is 4.

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3. “In case R is the only individual serving on committee B, which among the following should serve on committee A?”

Given:

• R is the only member of Committee B. Therefore, Committee B must have one more member (since it should have exactly two members).

• T, S, and R cannot serve on Committee B (as stated in the rules).

• Thus, T and S must serve on Committee A.

Correct answer: T and S

Since T and S are the only ones who can be placed on Committee A (given the restrictions), they should serve together on Committee A.

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4. “In case any of the nine individuals serves on committee C, which among the following could not be the candidate to serve on committee A?”

Given:

• Z, Y, and X cannot serve on Committee A (as per the restrictions in the problem).

• This means any combination that includes Z, Y, or X cannot serve on Committee A.

• We need to look at each pair and see if Z, Y, or X is included:

  • X and V: X cannot serve on Committee A, so this combination is not possible.

  • Z and Y: Both Z and Y cannot serve on Committee A, so this is not allowed either.

  • Y and V: Y cannot serve on Committee A, so this pair is not allowed.

  • Z and W: Z cannot serve on Committee A, so this combination is invalid.

  • Y and U: Y cannot serve on Committee A, so this combination is also invalid.

Thus, the only pair that would not be allowed on Committee A is Z and Y because they are both restricted from serving there.

Correct answer: Z and Y

Z and Y cannot both serve on Committee A.

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5. “Among the following combinations which could constitute the membership of committee C?”

Given:

• Committee C can have members who are not restricted from serving on Committee C.

• Z, Y, and X cannot serve on Committee C (based on the restrictions).

• W, V, and U can serve on Committee C.

Let’s evaluate the options:

1. X and U: X cannot serve on Committee C (due to restriction), so this combination is invalid.

2. Y, X, and W: Y and X are restricted from Committee C, so this combination is invalid.

3. Y and T: Y is restricted from Committee C, so this combination is invalid.

4. Z, X, U, and R: Z and X are restricted from Committee C, so this combination is invalid.

5. W, V, and U: W, V, and U are all allowed to serve on Committee C, so this combination is valid.

Correct answer: W, V, and U

This is the only valid combination for Committee C.

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Summary of Correct Answers:

1. 4 – In case T and Z serve on Committee B, 4 should serve on Committee C.

2. 4 – The largest number that can serve together on Committee C is 4.

3. T and S – If R is the only member of Committee B, T and S should serve on Committee A.

4. Z and Y – Z and Y cannot serve on Committee A.

5. W, V, and U – This is the valid combination for Committee C.