Question 1
Tournament participants: Purvi, Matthew, Raelynn, Vipul
Given the following clues:
1. Purvi is younger than Matthew
2. Matthew is younger than Raelynn
3. Raelynn is younger than Vipul
4. Each person is exactly 4 years older than the person immediately younger than them.
5. Raelynn is 27 years old.
Determine Matthew's age.
Step 1: From clues 1-3, the age order from youngest to oldest is:
Purvi → Matthew → Raelynn → Vipul
Step 2: From clue 4, each consecutive person differs by exactly 4 years.
So if youngest = x, then: Purvi=x, Matthew=x+4, Raelynn=x+8, Vipul=x+12
Step 3: From clue 5, Raelynn (the 3rd) = 27
Therefore, x + 8 = 27
Solving: x = 27 - 8 = 19
Step 4: All ages are:
• Purvi = 19
• Matthew = 23
• Raelynn = 27
• Vipul = 31
Step 5: Matthew is the 2nd.
Therefore, Matthew = 23
Purvi → Matthew → Raelynn → Vipul
Step 2: From clue 4, each consecutive person differs by exactly 4 years.
So if youngest = x, then: Purvi=x, Matthew=x+4, Raelynn=x+8, Vipul=x+12
Step 3: From clue 5, Raelynn (the 3rd) = 27
Therefore, x + 8 = 27
Solving: x = 27 - 8 = 19
Step 4: All ages are:
• Purvi = 19
• Matthew = 23
• Raelynn = 27
• Vipul = 31
Step 5: Matthew is the 2nd.
Therefore, Matthew = 23