Evaluating arithmetic properties of combining prime and composite numbers
Question
Consider the following statements in respect of two natural numbers p and q such that p is a prime number and q is a composite number:
Which of the above statements are correct?
Options
1 and 2 only
2 and 3 only
1 and 3 only
1, 2 and 3
Explanation
The problem uses the permissive auxiliary verb "can be". If we can construct even a single valid integer example for a statement, it is proven correct.
Statement 1: Can p × q be odd? Yes. Multiply any odd prime by any odd composite. Let p = 3 (prime), q = 9 (composite). Product = 3 × 9 = 27 (Odd). Valid.
Statement 2: Can q/p be a prime number? Yes. Choose a composite q that is the product of two primes. Let q = 9 and p = 3. Quotient = 9 / 3 = 3 (Prime). Valid.
Statement 3: Can p + q be a prime number? Yes. Add an even prime to an odd composite. Let p = 2 and q = 9. Sum = 2 + 9 = 11 (Prime). Valid.
All three statements describe mathematically possible scenarios.
Answer: (d).
Question details
Year
2022
Paper
CSAT
Question
Q67
Section
Numerical Ability
Sub-topic
Number Properties
Type
Statement-based
Difficulty
Medium
Source hint
p is prime, q is composite
Same sub-topic — other years
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