AAPL wrote:e-GMAT
A set of 51 different integers has a median of 30 and a range of 60. What is the value of the least possible integer in this set?
A. -10
B. -6
C. -5
D. 5
E. 10
Range = biggest - smallest
Smallest = biggest - range
Since the range = 60, we get:
Smallest = biggest - 60
To minimize the smallest integer, we must minimize the biggest integer.
Since the median of the 51 distinct integers = 30, there must be 25 integers above 30, with the other 25 integers below 30.
Implication:
The least possible value for the biggest integer = 30+25 = 55.
Substituting biggest = 55 into the blue equation above, we get:
Smalest = 55-60 = -5.
The correct answer is
C.
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