Rahul, Samuel, Tony, Uday, and Xavier met for a reunion, 15 years

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.

• 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 · Accepted Answer

Official Solution:

• Tony and Rahul — No. Both are heavy, but the swing allows at most one heavy person.

• Tony and Uday — No. If Tony is on the ride, Xavier cannot ride. Without Xavier, Uday cannot ride.

• Rahul and Xavier — Yes. Rahul is heavy, Xavier is lean. No conditions are violated.

Correct answer:

Tony and Rahul  "No"

Tony and Uday  "No"

Rahul and Xavier  "Yes"

Bunuel · Answer

Official Solution:

• Rahul is not guaranteed. A valid group like Samuel, Xavier, and Uday excludes him.
 
• Samuel is not guaranteed. A valid group like Rahul, Xavier, and Uday excludes him.
 
• Tony is not guaranteed. A valid group like Samuel, Xavier, and Uday excludes him.
 
• Uday is not guaranteed. A valid group like Samuel, Xavier, and Rahul excludes him.
 
• Xavier is guaranteed. If he’s excluded, Uday is also out. That leaves only Samuel, Rahul, and Tony—but Rahul and Tony are both heavy, which isn’t allowed. So every valid group must include Xavier. For example, Rahul, Xavier, and Uday is a valid group.

Correct answer:

If exactly three of the five friends were to go on the swing ride, and all constraints were met, who is guaranteed to be one of the three?

"Xavier"

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"

samarpan.g28 · Answer

1. If exactly two of the five friends were to go on the swing ride, and all constraints were met, select Yes if a pair could have gone together. Otherwise, select No. 
A. Tony and Rahul: Both are heavy-weighted, so NO.
B. Tony and Uday: Uday can go only if Xavier goes, but the ride will have only 2 people, so NO.
C. Rahul and Xavier: They have no restrictions, so YES.

NO, NO, YES.

2. If exactly three of the five friends were to go on the swing ride, and all constraints were met, who is guaranteed to be one of the three? 
If Rahul rides and Tony does not ride, then the other 2 friends can be Samuel and Xavier, or Uday and Xavier. Xavier is a constant.
If Rahul and Tony do not ride, then Uday, Xavier and Samuel can ride.
If Tony rides and Rahul does not ride, then no possible combinations are made.
Only Xavier is common in all groups.

Xavier.

3. 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? 
From the last question's solution. Tony cannot ride.

Tony.

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Rahul, Samuel, Tony, Uday, and Xavier met for a reunion, 15 years

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