Three positive integers a, b, and c are such that their average is 28 and a ≤ b ≤ c. If the median is (a + 13), what is the least possible value of c?	Choose the correct option:
A) 31
B) 32
C) 33
D) 34
E) 35
Solution   Given Data   3 positive integers   Average of a, b, and c = 28.   So, a+b+c3a+b+c3 = 84 or a + b + c = 84   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) = 84 (b and c are equal and b, the median, is a + 13)   Or 3a = 58 or a = 19.33   So, b = c = 19.33+ 13= 
<gadget id="calculator">19.33+ 13</gadget>
<output>32.33</output>
32.33   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) = 84   Or 3a = 57or a=19 The value of the numbers is an integer.   If a = 19, b = 32 and c = 33.   The least value for c that satisfies all these conditions is 33   33orrect answer is choice 33.
<result>C</result>
Three positive integers a, b, and c are such that their average is 28 and a ≤ b ≤ c. If the median is (a + 13), what is the least possible value of c?