NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 1: Real Numbers - Exercise 1.2 - Short Answer Questions with ReasoningQuestion 2
Class 10 - Mathematics - CHAPTER 1: Real Numbers - Exercise 1.2 - Short Answer Questions with Reasoning
Question. 2
“The product of two consecutive positive integers is divisible by 2”. Is this statement true or false? Give reasons.
Answer:
True. The product of two consecutive positive integers is always divisible by 2.
Detailed Answer with Explanation:
Step 1: Represent consecutive integers.
Let the first positive integer be \(n\).
Then the next consecutive integer is \(n + 1\).
Step 2: Write their product.
The product is:
\(n(n + 1)\).
Step 3: Reason about even and odd numbers.
Among any two consecutive integers, one is always even and the other is odd.
For example: \(2,3\) or \(5,6\) or \(10,11\).
Step 4: Conclude divisibility.
If one factor is even, the product is always even.
Therefore, \(n(n+1)\) is always divisible by 2.
Final Answer: The statement is True.