I19-06

Question

Rahul, Samuel, Tony, Uday, and Xavier met for a reunion, 15 years after graduating. During the reunion, they observed that only Rahul and Tony had gained significant weight, while the other three had remained lean. To celebrate, they are considering going on a popular swing ride in town.Due to combined space and weight constraints, the swing could accommodate a maximum of three people, with no more than one person of heavy build.The friends had the following personal conditions for going on the swing:
 
• Uday would ride only if Xavier also rides.
 
• Xavier would not ride if Tony is on the same ride.
 
• Samuel would ride only if he would be one of exactly three people riding.

Bunuel · Answer

Official Solution: • Rahul is not guaranteed to be excluded. A valid group like Rahul, Xavier, and Uday includes him. • Samuel is not guaranteed to be excluded. A valid group like Samuel, Xavier, and Uday includes him. • Tony must be excluded. If Tony is included, Xavier cannot be included. Then Uday is also out. That leaves Samuel, Rahul, and Tony—but Rahul and Tony are both heavy, which violates the swing rule. • Uday is not guaranteed to be excluded. A valid group like Samuel, Xavier, and Uday includes him. • Xavier is not guaranteed to be excluded. He is required in all valid groups. Correct answer: If exactly three of the five friends were to go on the swing ride, and all constraints were met, who is guaranteed not to be one of the three? "Tony"

Bunuel · Answer

This MSR question and its solutions have been completely revised and improved.

AnkitSinghaniya · Answer

I did not quite understand the solution. if Rahul, Xavier and Uday form a 3-man team, then Samuel will be left with just Tony, which violates the last constraint that says Samuel must be a part of 3-man team.

Bunuel · Answer

Samuel’s rule is that  if he rides, then the group must consist of exactly three people . It does not mean that if he doesn’t ride, some kind of leftover “team” has to be formed.

So if Rahul, Xavier, and Uday go together, then Samuel and Tony simply don’t ride at all. Samuel’s condition is not violated, because he is not on the swing in that case. The only time we need to check Samuel’s rule is when he is actually part of the riding group. That’s why a team of Rahul, Xavier, and Uday is perfectly valid.

bagarwal11 · Answer

I like the solution - it’s helpful.

I19-06

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