Three positive integers a, b, and c are such that their average is 18 and a ≤ b ≤ c. If the median is (a + 11), what is the least possible value of c? Select:
A) 21  B) 23  C) 25  D) 27  E) 29
Solution:   We know that the average value is 18 therefore (a+b+c)/3 = 18   so a+b+c = 54   and b = a + 11   therefore a + (a + 11) + c = 54   The least value of c is when c = b   so take c = a + 11   hence, a + (a + 11) + (a + 11) = 54   i.e., a = 32/3 a non integer therefore c is not equal to b   so take c = b+1 therefore c = a+12   a + (a + 11) + (a + 12) = 54   i.e., a= 31/3 again a non integer therefore c is not equal to b+1   next take c= b+2 therefore c = a+13   a + (a + 11) + (a + 13) = 54   i.e., a=30/3= 
<gadget id="calculator">30/3</gadget>
<output>10</output>
10   hence, a= 10, b = 21, and c = 23   Answer: 23
<result>B</result>
Three positive integers a, b, and c are such that their average is 18 and a ≤ b ≤ c. If the median is (a + 11), what is the least possible value of c?