Three positive integers a, b, and c are such that their average is 22 and a ≤ b ≤ c. If the median is (a + 11), what is the least possible value of c?	Choices.
A) 21 B) 23 C) 25 D) 27 E) 29
Solution:   We know that the average value is 22 therefore (a+b+c)/3 = 22   so a+b+c = 66   and b = a + 11   therefore a + (a + 11) + c = 66   The least value of c is when c = b   so take c = a + 11   hence, a + (a + 11) + (a + 11) = 66   i.e., a = 44/3 a non integer therefore c is not equal to b   so take c = b+1 therefore c = a+12   a + (a + 11) + (a + 12) = 66   i.e., a= 43/3 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) = 66   i.e., a=42/3= 
<gadget id="calculator">42/3</gadget>
<output>14</output>
14   hence, a= 14, b = 25, and c = 27   Answer: 27
<result>D</result>
Three positive integers a, b, and c are such that their average is 22 and a ≤ b ≤ c. If the median is (a + 11), what is the least possible value of c?