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
- The average of eleven consecutive positive integers is d. If the last two numbers are excluded, by how much will the average increase or decrease?
The numerator of fraction is 3 more than the denominator. When 5 is added to the numerator and 2 is subtracted from the denominator, the fraction becomes 8/3, When the original fraction is divided by \(5 \frac{1}{2}\) , the fraction so obtained is:
The sum of a non - zero number and twenty times its reciprocal is 9. What is the number?
If \(\frac{{45}}{{53}} = \frac{1}{{a + \frac{1}{{b + \frac{1}{{c - \frac{2}{5}}}}}}},\) where a, b and c are positive integers, then what is the value of (4a - b + 3c)
The denominator of a fraction is 4 more than the double of its numerator. When 3 is added to the numerator and 3 is subtracted from denominator the fraction becomes 2/3. Then find the difference between denominator and numerator of the original fration.
