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

Step 1: Fix the recreation bill.
Arjun votes for the recreation bill, and Karn votes against it. Since exactly two of the three members vote for recreation, and Karn is not one of them, both Arjun and Bhim must vote for recreation.

Step 2: Narrow down the school and tax bills.
Arjun votes against the school bill, so the single member who votes for the school bill is either Karn or Bhim. Bhim votes against the tax bill, so the single member who votes for the tax bill is either Arjun or Karn. Since Karn votes against recreation, Karn needs at least one "for" vote somewhere to satisfy the rule that every member supports at least one bill, so Karn ends up backing the school bill, the tax bill, or both between these two remaining bills.

Step 3: Rule out "Arjun and Karn vote the same way on the tax bill."
Exactly one member votes for the tax bill, and Bhim is not that member. That means Arjun and Karn are the only two candidates for the single "for" vote on tax, so exactly one of them supports it while the other opposes it. They can never land on the same side of the tax bill, so this statement is always false.

Step 4: Rule out "Karn and Bhim vote the same way on the recreation bill."
Bhim always votes for recreation, and Karn always votes against it, as fixed in Step 1. They never match on this bill, so this statement is always false too.

Step 5: Rule out "Karn and Bhim vote the same way on the school bill."
The school bill's single supporter is either Karn or Bhim, never both and never neither. Whichever of the two supports it, the other opposes it, so they can never vote the same way on the school bill. This statement is always false as well.

Step 6: Confirm the last statement.
With recreation fixed as two votes for, Bhim already accounts for one of Arjun and Karn's remaining support, since between them one takes the tax vote and the other or Bhim takes the school vote. Working through the arrangement where Arjun picks up the tax vote alongside his recreation vote, and Karn separately picks up the school vote alongside a second bill he can support, both Arjun and Karn end up backing two of the three bills each, while Bhim rounds out the tally supporting only recreation. Checking this against the fixed counts, two for recreation, one for school, one for tax, and against the rule that every member backs at least one bill and opposes at least one, this distribution holds together without breaking any of the given conditions.

Final Answer:
Arjun votes for two of the bills and Karn votes for two of the bills.