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

To determine whether the given statements are true or false, let's analyze both the Assertion (A) and the Reason (R) individually:

1. First, evaluate the Assertion (A): \(7 \times 2 + 3\).
2. Calculate the expression:
   • \(7 \times 2 = 14\)
   • Adding 3: \(14 + 3 = 17\)
3. Now, consider whether 17 is a composite number:
   • A composite number is defined as a positive integer that has more than two distinct positive divisors.
   • The number 17 only has two factors: 1 and 17 itself, which makes it a prime number, not a composite number.
4. Thus, Assertion (A) is false.
5. Now, evaluate the Reason (R): "A composite number has more than two factors."
6. The statement accurately describes a composite number, which by definition, has more than two distinct positive integers as factors.
7. Thus, Reason (R) is true.

Given the evaluations above:

• Assertion (A) is false.
• Reason (R) is true.

Therefore, the correct answer is: "A is false but R is true."