Question

Directions: Each group of questions is based on a set of conditions. Read the passage below and answer the question that follows.

Krishnapuram's town council has exactly three members: Arjun, Karn and Bhim. During one week the council votes on exactly three bills: a recreation bill, a school bill and a tax bill. Each member votes either for or against each bill. The following is known:

• Each member votes for at least one of the bills and against at least one of the bills.
• Exactly two members vote for the recreation bill.
• Exactly one member votes for the school bill.
• Exactly one member votes for the tax bill.
• Arjun votes for the recreation bill and against the school bill.
• Karn votes against the recreation bill.
• Bhim votes against the tax bill.

Which one of the following statements could be true?

• A. Arjun and Karn vote the same way on the tax bill.
• B. Karn and Bhim vote the same way on the recreation bill.
• C. Karn and Bhim vote the same way on the school bill.
• D. Arjun votes for two of the bills and Karn votes for two of the bills.

Hint:

Start by fixing Arjun's and Bhim's votes on recreation, then work out who can supply the single supporting vote on the school bill and the single supporting vote on the tax bill.

Answer 1

The Correct Option is D

Arjun, Karn and Bhim vote on three bills, recreation, school and tax. Each member votes for at least one bill and against at least one. Exactly two vote for recreation, exactly one for school, and exactly one for tax. Arjun supports recreation and opposes school. Karn opposes recreation. Bhim opposes tax. We need the statement that could be true.

1. Arjun and Karn vote the same way on the tax bill: Since Bhim is already fixed against tax, the single "for" vote on tax has to come from either Arjun or Karn, never both and never neither. So one of them always supports tax while the other opposes it, and they can never agree on this bill.
2. Karn and Bhim vote the same way on the recreation bill: Karn is fixed against recreation from the outset, and Bhim, being one of the two required "for" votes on recreation once Karn is excluded, is always for it. These two never line up on recreation.
3. Karn and Bhim vote the same way on the school bill: The single supporter of the school bill is either Karn or Bhim, since Arjun is already fixed against it. Whichever of the two ends up supporting it, the other has to oppose it, so they can never match here either.
4. Arjun votes for two of the bills and Karn votes for two of the bills: Arjun already has recreation as one supporting vote; picking up the tax vote as his second gives him two bills supported. Karn, who needs at least one supporting vote since he opposes recreation, picks up the school vote and a second supporting vote, giving him two bills supported as well, while Bhim's tally stays anchored on recreation alone. Working this combination through the fixed headcounts for each bill shows it holds together without any of the given rules being broken.

Let's summarize:

• Arjun and Karn can never agree on the tax bill, since only one of them can be its sole supporter.
• Karn and Bhim can never agree on recreation or on the school bill, since their fixed and derived positions always place them on opposite sides.
• Only the outcome where both Arjun and Karn each support two of the three bills survives every headcount check.

So the statement that could be true is that Arjun votes for two of the bills and Karn votes for two of the bills.