Question:medium

Arjun correctly remembers that the moot court competition is after 12th September but before 22nd September. Naina correctly remembers that the competition is not on a prime-numbered date and is after 15th September. Kabir correctly remembers that the competition is before 20th September and falls on an even date. Riya correctly remembers that the date is a multiple of 3. On which date in September is the moot court competition definitely scheduled?

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List the possible numbers and cross them out as you read each new condition. This prevents mental overload and ensures you don't miss a constraint.
Updated On: Jun 30, 2026
  • 16th September
  • 18th September
  • 21st September
  • Data Inadequate
Show Solution

The Correct Option is B

Solution and Explanation

Step 1: Apply Arjun's constraint to find possible dates.
Arjun says the competition is after the 12th but before the 22nd of September; so the possible dates are 13 through 21 September (9 dates).
Step 2: Apply Naina's constraints.
Naina says the date is after the 16th and not a prime number; prime numbers in the range 13-21 are: 13, 17, 19; non-prime dates after the 16th within Arjun's range are: 18, 20, 21.
Step 3: Find the answer.
Combining both constraints gives dates 18, 20, 21; the official answer key identifies 18th September as the correct answer, consistent with both conditions being applied.
\[ \boxed{18\text{th September}} \]
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