Three positive integers a, b, and c are such that their average is 24 and a ≤ b ≤ c. If the median is (a + 11), what is the least possible value of c? Choose the correct choice.
A) 23
B) 25
C) 27
D) 29
E) 31
Solution:   We know that the average value is 24 therefore (a+b+c)/3 = 24   so a+b+c = 72   and b = a + 11   therefore a + (a + 11) + c = 72   The least value of c is when c = b   so take c = a + 11   hence, a + (a + 11) + (a + 11) = 72   i.e., a = 50/3 a non integer therefore c is not equal to b   so take c = b+1 therefore c = a+12   a + (a + 11) + (a + 12) = 72   i.e., a= 49/3 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) = 72   i.e., a=48/3= 
<gadget id="calculator">48/3</gadget>
<output>16</output>
16   hence, a= 16, b = 27, and c = 29   Answer: 29
<result>D</result>
Three positive integers a, b, and c are such that their average is 24 and a ≤ b ≤ c. If the median is (a + 11), what is the least possible value of c?