Question

A set contains six odd numbers. What is its median?
Statement 1: Sum of 6 odd numbers is 300 and they are consecutive
Statement 2: The mean of six numbers is 20
Directions: This question has a problem and two statements numbered (1) and (2) giving certain information. You have to decide if the information given in the statements is sufficient for answering the problem. Indicate your answer :

• A. statement (1) alone is sufficient to answer the question
• B. statement (2) alone is sufficient to answer the question
• C. both the statements together are needed to answer the question
• D. either statement (1) alone or statement (2) alone is sufficient to answer the question
• E. neither statement (1) nor statement (2) suffices to answer the question

Answer 1

The Correct Option is A

To find the median of a set containing six odd numbers, we need to determine the correct sequence or values of these numbers. Let's analyze the provided statements:

1. Statement 1: Sum of 6 odd numbers is 300 and they are consecutive.
   • Let the six consecutive odd numbers be \(x, x+2, x+4, x+6, x+8,\) and \(x+10\).
   • According to the statement, their sum is 300. Thus, the equation is \(x + (x+2) + (x+4) + (x+6) + (x+8) + (x+10) = 300\).
   • This simplifies to \(6x + 30 = 300\).
   • Solving for \(x\), we get \(6x = 270\) or \(x = 45\).
   • Therefore, the numbers are 45, 47, 49, 51, 53, and 55.
   • In a sorted list of an even number of values, the median is the average of the two middle numbers.
   • Here, the middle numbers are 49 and 51. Thus, the median is \(\frac{49 + 51}{2} = 50\).

   This statement alone is sufficient to determine the median.

2. Statement 2: The mean of six numbers is 20.
   • Given that the mean is the average, we have \(\frac{\text{Sum of the numbers}}{6} = 20\), which implies \(\text{Sum} = 120\).
   • However, this statement provides no information about the numbers being consecutive or any other characteristics that would help in determining individual numbers.
   • Therefore, it is not possible to determine the exact sequence or find the median using only this statement.

   Thus, statement 2 alone is not sufficient.

In conclusion, statement (1) alone is sufficient to answer the question as it allows us to find the exact numbers and calculate the median. Hence, the correct answer is: statement (1) alone is sufficient to answer the question.