Three positive integers a, b, and c are such that their average is 20 and a ≤ b ≤ c. If the median is (a + 11), what is the least possible value of c?  Choose the correct choice from the following options.
A) 23	B) 21	C) 25	D) 26	E) 24
Solution   Given Data   3 positive integers   Average of a, b, and c = 20.   So, a+b+c3a+b+c3 = 20 or a + b + c = 60   a ≤ b ≤ c   Median = (a + 11)   Median of these 3 numbers a, b, and c is ‘b’ because a ≤ b ≤ c   Therefore, b = a + 11   Objective To find the least value of 'c'   Theoretically, the least value of c is when c = b.   Therefore, a + (a + 11) + (a + 11) = 60 (b and c are equal and b, the median, is a + 11)   Or 3a = 38 or a = 12.66   So, b = c = 12.66 + 11= 
<gadget id="calculator">12.66 + 11</gadget>
<output>23.66</output>
23.66   However, we know that these numbers are all integers.   Therefore, a, b, and c cannot take these values.   So, the least value for c with this constraint is NOT likely to be when c= b   Let us increment c by 1. Let c = (b + 1)   In this scenario, a + (a + 11) + (a + 12) = 60   Or 3a = 37. The value of the numbers is not an integer in this scenario as well.   Let us increment c again by 1. i.e., c = b + 2   Now, a + (a + 11) + (a + 13) = 60   Or 3a = 36 or a = 12.   If a = 12, b = 23 and c = 25.   The least value for c that satisfies all these conditions is 25.   25orrect answer is choice 25.
<result>C</result>
Three positive integers a, b, and c are such that their average is 20 and a ≤ b ≤ c. If the median is (a + 11), what is the least possible value of c?