A set of 16 different integers has median of 25 and a range of 25. What is greatest possible integer that could be in this set?  Pick: A) 32 B) 37 C) 40 D) 44 E) 50
The correct answer is D.   A set of 16 different integers has median of 25 and a range of 25. What is greatest possible integer that could be in this set?   Given 15 different integers, lets say   n1, n2, n3, n4, n5, n6, n7, n8, n9, n10, n11, n12, n13, n14, n15   Also given median is 25 i.e. n8 = 26   n1, n2, n3, n4, n5, n6, n7, 25, n9, n10, n11, n12, n13, n14, n15   As each integer is different we need to find the maximum values for all those numbers before the median.   the maximum value n7 can have is one less then the median i.e. 24, similarly n6 will be one less than 24 i.e. 23 ... using this process the values for all number before the median would be..   18, 19, 20, 21, 22, 23, 24, 25, n9, n10, n11, n12, n13, n14, n15   Also given the range is 25 i.e. n15 - n1 (18) = 26   The maximum value n15 can have is 26 + n1 (18) = 44   44
<result>D</result>
A set of 16 different integers has median of 25 and a range of 25. What is greatest possible integer that could be in this set?