Three positive integers a, b, and c are such that their average is 80 and a ≤ b ≤ c. If the median is (a + 20), what is the least possible value of c?
Select the correct option: A) 88 B) 89 C) 90 D) 92 E) 94
Solution   Given Data   3 positive integers   Average of a, b, and c = 80   So, a+b+c3a+b+c3 = 240 or a + b + c = 240   a ≤ b ≤ c   Median = (a + 20)   Median of these 3 numbers a, b, and c is ‘b’ because a ≤ b ≤ c   Therefore, b = a + 20   Objective To find the least value of 'c'   Theoretically, the least value of c is when c = b.   Therefore, a + (a + 20) + (a + 20) = 240 (b and c are equal and b, the median, is a + 20)   Or 3a = 200 or a = 66.66   So, b = c = 66.66+ 20= 
<gadget id="calculator">66.66+ 20</gadget>
<output>86.66</output>
86.66   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 + 20) + (a + 21) = 240   Or 3a = 199. 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 + 20) + (a + 22) = 240   Or 3a = 198 or a = 66   If a = 66, b = 86 and c = 88.   The least value for c that satisfies all these conditions is 88.   Correct answer is choice 88.
<result>A</result>
Three positive integers a, b, and c are such that their average is 80 and a ≤ b ≤ c. If the median is (a + 20), what is the least possible value of c?