Here’s the English translation of your math problem: If the ascending data set is \[ 27,\ 31,\ 46,\ 52,\ x,\ y + 2,\ 71,\ 79,\ 85,\ 90 \] and the median of the set is \(64\), then what is the value of \(x + y\)?

Q.Here’s the English translation of your math problem: If the ascending data set is \[ 27,\ 31,\ 46,\ 52,\ x,\ y + 2,\ 71,\ 79,\ 85,\ 90 \] and the median of the set is \(64\), then what is the value of \(x + y\)? (a) 125 (b) 126 (c) 127 (d) 128

Answer: B

Total number of terms \(n = 10\) ∴ Median = \(\frac{1}{2}\) × (5th term + 6th term) \[ = \frac{1}{2}(x + y + 2) = \frac{x + y + 2}{2} \] According to the condition: \[ \frac{x + y + 2}{2} = 64 \Rightarrow x + y + 2 = 128 \Rightarrow x + y = 128 - 2 \Rightarrow x + y = 126 \]