Question

2, 6, 10, x, 1, 9, 5?
the median of the seven given numbers is 6.
which of the following could be the value of x?
a) 3
b) 4
c) 5
d) 6

Explanation:

Step1: Arrange known numbers

First, we arrange the known numbers (excluding \( x \)) in ascending order: \( 1, 2, 5, 6, 9, 10 \).

Step2: Determine position of median

Since there are seven numbers (including \( x \)), the median will be the 4th number when all numbers are arranged in ascending order. We know the median is 6, so the 4th number in the ordered list must be 6.

Step3: Analyze possible values of \( x \)

Let's consider where \( x \) can be placed. If we insert \( x \) into the ordered list, we need the 4th element to be 6. Let's check each option:

• Option A: If \( x = 3 \), the ordered list is \( 1, 2, 3, 5, 6, 9, 10 \). The 4th number is 5, not 6.
• Option B: If \( x = 4 \), the ordered list is \( 1, 2, 4, 5, 6, 9, 10 \). The 4th number is 5, not 6.
• Option C: If \( x = 5 \), the ordered list is \( 1, 2, 5, 5, 6, 9, 10 \). The 4th number is 5, not 6.
• Option D: If \( x = 6 \), the ordered list is \( 1, 2, 5, 6, 6, 9, 10 \). The 4th number is 6, which matches the given median.

Answer:

D. 6