Question

Assertion (A): \(7 \times 2 + 3\) is a composite number.
Reason (R): A composite number has more than two factors.

• A. Both (A) and (R) are true and (R) is the correct explanation of (A).
• B. Both A and R are true but R is not the correct explanation of A
• C. A is true but R is false
• D. A is false but R is true.

Hint:

Always perform the arithmetic operations before deciding if an expression represents a prime or composite number. Don't be fooled by the presence of prime factors like 7 and 2 in the expression.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
A composite number is a positive integer greater than 1 that has factors other than 1 and itself. A prime number has only two factors (1 and itself).
Step 2: Key Formula or Approach:
1. Solve the expression in (A).
2. Check if the result is prime or composite.
Step 3: Detailed Explanation:
1. Solve (A):
\[ 7 \times 2 + 3 = 14 + 3 = 17 \] 2. Check the result: 17 is a prime number because its only factors are 1 and 17.
3. Therefore, Assertion (A) is False.
4. Check Reason (R): By definition, a composite number must have more than two factors. This statement is True.
Step 4: Final Answer:
Assertion (A) is false, but Reason (R) is true.