Question

Which of the following statement is incorrect ?

• A. An even number ends in 0, 2, 4, 6 or 8
• B. An odd number ends in 1, 3, 5, 7 or 9
• C. The number "8" is an irrational number
• D. The only even prime number is "2"

Hint:

All integers are automatically rational numbers because they can always be written as a fraction over a denominator of 1. Irrational numbers are reserved for non-terminating, non-repeating decimals!

Answer 1

The Correct Option is C

Concept: This question tests our understanding of classifications within the real number system, focusing on odd, even, prime, rational, and irrational numbers. Let us rigorously evaluate each statement step-by-step to isolate the false assertion.

Step 1: Evaluate statement (A) regarding even numbers.
By definition, an integer is classified as even if it is completely divisible by 2. In base-10 positional notation, any integer whose unit (last) digit is either 0, 2, 4, 6, or 8 is a multiple of 2. Hence, statement (A) is entirely correct.

Step 2: Evaluate statement (B) regarding odd numbers.
An integer is classified as odd if it is not divisible by 2. In our base-10 numerical counting framework, any integer whose unit (last) digit ends in either 1, 3, 5, 7, or 9 leaves a remainder of 1 when divided by 2. Hence, statement (B) is entirely correct.

Step 3: Evaluate statement (D) regarding prime numbers.
A prime number is a positive integer strictly greater than 1 that possesses exactly two distinct positive divisors: 1 and itself. Let us list out the initial sequence of prime numbers: \[ 2, 3, 5, 7, 11, 13, 17, 19, \ldots \] Every even integer greater than 2 can be cleanly divided by 2 in addition to 1 and itself, which automatically disqualifies it from being a prime number. Therefore, 2 stands uniquely as the single even prime number. Hence, statement (D) is entirely correct.

Step 4: Evaluate statement (C) regarding the classification of the number "8".
A real number is classified as rational if it can be written as a fraction \(\frac{p}{q}\) where both \(p\) and \(q\) are integers and \(q \neq 0\). Conversely, an irrational number cannot be expressed as a simple fraction (e.g., \(\pi\), \(\sqrt{2}\)). Let us examine the integer 8. It can be written as: \[ 8 = \frac{8}{1} \] Since it can be expressed perfectly as a ratio of two integers, 8 is a terminating, rational number. The claim that it is an irrational number is completely false. Therefore, statement (C) is the incorrect statement.