Suppose $a, b, c, d$ and $e$ are five consecutive odd numbers in ascending order. Consider the following statements:
1. Their average is $(a + 4)$.
2. Their average is $(b+2)$.
3. Their average is $(e-4)$.
Which of the statements given above is/are correct?
To find the validity of the given statements about the consecutive odd numbers \(a, b, c, d, e\), let's analyze each statement:
Consecutive odd numbers can be represented as \(a, a+2, a+4, a+6, a+8\).
The average of these numbers is calculated as follows:
\[\text{Average} = \frac{a + (a+2) + (a+4) + (a+6) + (a+8)}{5} = \frac{5a + 20}{5} = a + 4\]Now, let's examine each statement:
- Statement 1: Their average is \((a + 4)\).
This statement is correct because we derived that the average is indeed \(a + 4\).
- Statement 2: Their average is \((b+2)\).
Since \(b = a + 2\), substituting in the average gives us:
This statement is also correct.
- Statement 3: Their average is \((e-4)\).
Since \(e = a + 8\), substituting in the average gives us:
This statement is also correct.
Since all the statements (1, 2, and 3) are correct, the correct answer is "1, 2 and 3".
Important Questions from Integers
How many three digit whole numbers are there between 75 and 405?
Find the number of integers between $1$ and $150$ (inclusive) having $7$ as one of the digits but which are not divisible by $7$.
Integers are listed from 700 to 1000. In how many integers is the sum of the digits 10 ?
Using 2, 2, 3, 3, 3 as digits, how many distinct numbers greater than 30000 can be formed ?
Consider the following statements :
1. The sum of 5 consecutive integers can be 100.
2 The product of three consecutive natural numbers can be equal to their sum.
Which of the above statements is/are correct ?
