Question

A list of numbers is 5.1, 17.2, 12.2, 7.2, 22.2. What is the value of \(l\) in the list above?
(1) \(l>7.2\)
(2) The median of the numbers in the list is 14.7.
Note: The question implies that \(l\) is one of the numbers in the list, or a number to be added. Based on the phrasing and the statements, it's most likely that the list is composed of \(l\) and four other given numbers: \{l, 17.2, 12.2, 7.2, 22.2\. The "5.1" in the OCR is likely a typo for the question number "5.".}

• A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• D. EACH statement ALONE is sufficient.
• E. Statements (1) and (2) TOGETHER are NOT sufficient.

Hint:

When a data sufficiency question involves a median and an unknown value, sort the known values first. Then, consider the different cases for where the unknown value could fall in the sorted list. This systematic approach helps you check all possibilities and determine if a unique solution exists.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The question asks for the value of an unknown number \(l\) in a list. The concept being tested is the definition of a median. The median is the middle value of a dataset when it is sorted in ascending order. For a list with an odd number of elements, the median is the single middle element.
Step 2: Detailed Explanation:
Let's assume the list has 5 numbers: \{l, 7.2, 12.2, 17.2, 22.2\}. To find the median, we first need to sort the list. The sorted order of the known numbers is 7.2, 12.2, 17.2, 22.2. The position of \(l\) is unknown. Since there are 5 numbers, the median is the 3rd number in the sorted list.
Analyzing Statement (1):
This statement says \(l>7.2\). This is an inequality and does not give a unique value for \(l\). For example, \(l\) could be 8, 10, 15, etc. Therefore, statement (1) alone is not sufficient.
Analyzing Statement (2):
This statement says the median of the list is 14.7. Let's analyze the possible positions of \(l\) in the sorted list.
Case A: If \(l\) is less than or equal to 12.2. The sorted list would begin with {7.2, ...} and the third element would be 12.2. For example, if \(l=10\), the sorted list is \{7.2, 10, 12.2, 17.2, 22.2\}. The median is 12.2. This is not 14.7.
Case B: If \(l\) is between 12.2 and 17.2. The sorted list would be \{7.2, 12.2, \(l\), 17.2, 22.2\}. In this case, the median (the 3rd element) is \(l\). So, we must have \(l = 14.7\). This value is consistent with our assumption for this case (12.2<14.7<17.2).
Case C: If \(l\) is greater than or equal to 17.2. The sorted list would be \{7.2, 12.2, 17.2, ...\}. The median (the 3rd element) would be 17.2. This is not 14.7.
The only possibility that results in a median of 14.7 is that \(l=14.7\). Therefore, statement (2) alone is sufficient to find a unique value for \(l\).
Step 3: Final Answer:
Statement (2) alone provides enough information to uniquely determine the value of \(l\), while statement (1) does not. Therefore, the correct option is (B).