The Question is from neet-botany plant-growth-and-development , and it was created by the author Mr. NARESH KUMAR K

Question

Chooses the incorrect statement

Mr. NARESH KUMAR K · Accepted Answer

## CORE INFORMATION
✓ **Answer**: D
## CONCEPT FRAMEWORK
	**Primary Concept**: Divisibility Rules
	**Related Topics**: Prime numbers, Composite numbers, Factors, Multiples
	**Prerequisites**: Basic arithmetic and number theory
## SOLUTION PATHWAY
**Given Information**:
	Multiple-choice question about divisibility.
**Method & Steps**:
	1. Analyze each statement and determine its validity based on divisibility rules.
	2. Identify the incorrect statement.
## OPTION ANALYSIS
[A] ✓: Prime numbers greater than 2 are odd
Reasoning: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.  Even numbers are divisible by 2.  Since the only even prime number is 2, all other prime numbers must be odd. 
[B] ✓: A number divisible by 9 is divisible by 3
Reasoning: 9 is a multiple of 3 ($9 = 3 	imes 3$).  Therefore, any number divisible by 9 must also be divisible by 3.
[C] ✓: A number divisible by 2 and 3 is divisible by 6
Reasoning: 2 and 3 are coprime (their greatest common divisor is 1).  If a number is divisible by two coprime numbers, it is also divisible by their product.  Thus, a number divisible by both 2 and 3 is divisible by $2 	imes 3 = 6$.
[D] :x: A number divisible by 2 and 4 is divisible by 8
Reasoning: While numbers divisible by 8 are also divisible by 2 and 4, the converse is not always true.  For example, 12 is divisible by both 2 and 4 but not by 8.  A number is divisible by 8 if the last three digits are divisible by 8, or if it is divisible by both 2 and 4 *and* the quotient when divided by 4 is even.
## LEARNING AIDS
	**Common Mistakes**:
		1. Confusing the rules of divisibility: Carefully review the rules for each divisor.
		2. Assuming the converse is true:  Just because A implies B, it doesn't mean B implies A. 
	**Quick Tips**:
		1. Divisibility by $2^n$: A number is divisible by $2^n$ if its last $n$ digits are divisible by $2^n$.
		2. Prime factorization: Breaking down numbers into their prime factors can help understand divisibility.

Mr. NARESH KUMAR K · Answer

Prime numbers greater than 2 are odd

Mr. NARESH KUMAR K · Answer

A number divisible by 9 is divisible by 3

Mr. NARESH KUMAR K · Answer

A number divisible by 2 and 3 is divisible by 6

Mr. NARESH KUMAR K · Answer

The correct Option is "A number divisible by 2 and 4 is divisible by 8"

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