Three positive integers a, b, and c are such that their average is 22 and a ≤ b ≤ c. If the median is (a + 13), what is the least possible value of c?	Options
A) 22
B) 25
C) 26
D) 27
E) 29
Solution   Given Data   3 positive integers   Average of a, b, and c = 22   So, a+b+c3a+b+c3 = 66 or a + b + c = 66   a ≤ b ≤ c   Median = (a + 13)   Median of these 3 numbers a, b, and c is ‘b’ because a ≤ b ≤ c   Therefore, b = a + 13   Objective To find the least value of 'c'   Theoretically, the least value of c is when c = b.   Therefore, a + (a + 13) + (a + 13) = 66 (b and c are equal and b, the median, is a + 13)   Or 3a = 40 or a = 13.33   So, b = c = 10+ 13.33= 
<gadget id="calculator">10+ 13.33</gadget>
<output>23.33</output>
23.33   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 + 13) + (a + 14) = 66   Or 3a = 39 or a=13 The value of the numbers is an integer   If a = 13, b = 26 and c = 27   The least value for c that satisfies all these conditions is 27.   Correct answer is choice 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 + 13), what is the least possible value of c?