BTGmoderatorLU wrote:Source: Princeton Review
For the set of positive, distinct integers \(v, w, x, y, z,\) the median is 10. What is the minimum value of \(v+w+x+y+z\)?
A. 25
B. 32
C. 36
D. 40
E. 50
The OA is C
Since there are five (Odd numbers of) integers, one of \(v, w, x, y, z,\) is the median. Say \(v, w, x, y, z,\) are arranged in ascending order; thus, x = median = 10. Since we want the minimum value of \(v+w+x+y+z\), the minimum possible value of v = 1 and w = 2. Again, since x < y < z, the minimum possible values of y = 11 and z = 12.
Thus, the minimum value of \(v+w+x+y+z\) = 1 + 2 + 10 + 11 + 12 = 36.
The correct answer:
C
Hope this helps!
-Jay
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