Question

The range, median and mode of 21, 4, 27, 9, 29, 12, 8, 10, x, y, z are 26, x and y respectively. If x, y and z are prime numbers and x $\ne$ y, then (x + y + z) equals

• A. 41
• B. 39
• C. 43
• D. 47

Answer 1

The correct option is C 43

Given: Range = 26
Median = x
Mode = y
and, x, y, z are prime numbers and x $\ne$ y
Number of observations (n) = 11 (odd)
$\therefore$ Median = $(\frac{n+1}{2}{)}^{th}$ observation
$\Rightarrow$ Median = 6th term of the data
Therefore, x is the 6th term.
Now, the minimum value of the data is 4 and the maximum value is 29. Since range is 26, z can be 3 or 30.
Since, z has to be a prime number.
$\Rightarrow$ z = 3
Arranging the data roughly in increasing order,
3, 4, 8, 9, 10, x, 12, 21, 27, 29, y (Not fixed)
Again, x is a prime number and the only prime number between 10 and 12 is 11.
$\Rightarrow$ x = 11
Now, y lies somewhere to the right of the median x = 11 and it must be a prime number.
Therefore, y can be 11 or 29.
Since, y $\ne$ x, we can say that y = 29.
$\Rightarrow$ x + y + z = 11 + 29 + 3
= 43
Hence, the correct answer is option (c).