Three positive integers a, b, and c are such that their average is 12 and a ≤ b ≤ c. If the median is (a + 5), what is the least possible value of c?	Choose the correct choice:
A) 11	B) 13	C) 15	D) 17	E) 19
Solution   Given Data   3 positive integers   Average of a, b, and c = 12.   So, a+b+c3a+b+c3 = 36 or a + b + c = 36   a ≤ b ≤ c   Median = (a + 5)   Median of these 3 numbers a, b, and c is ‘b’ because a ≤ b ≤ c   Therefore, b = a + 5   Objective To find the least value of 'c'   Theoretically, the least value of c is when c = b.   Therefore, a + (a + 5) + (a + 5) = 36 (b and c are equal and b, the median, is a + 5)   Or 3a = 26 or a = 8.66   So, b = c = 8.66 + 5= 
<gadget id="calculator">8.66 + 5</gadget>
<output>13.66</output>
13.66   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 + 5) + (a + 6) = 36   Or 3a = 25. 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 + 5) + (a + 7) = 36   Or 3a = 24 or a = 8.   If a = 8, b = 13 and c = 15.   The least value for c that satisfies all these conditions is 15.   15orrect answer is choice 15.
<result>C</result>
Three positive integers a, b, and c are such that their average is 12 and a ≤ b ≤ c. If the median is (a + 5), what is the least possible value of c?