pratik2018 wrote:
In a class of 5 students, average weight of the 4 lightest students is 40 kgs, Average weight of the 4 heaviest students is 45 kgs. What is the difference between the the maximum and minimum possible average weight overall?
a. 2.8 kgs
b. 3.2 kgs
c. 3 kgs
d. 4 kgs
e. 4.2 kgs
Let a, b, c, d and e be the weights of the 5 students such that a ≤ b ≤ c ≤ d ≤ e. Since the total weight of the 4 lightest students is 4 x 40 = 160 kg, we have a + b + c + d = 160. Similarly, since the total weight of the 4 heaviest students is 4 x 45 = 180 kg, we have b + c + d + e = 180. We need to determine the maximum and minimum value of (a + b + c + d + e)/5.
The maximum average weight of all 5 students occurs when a is as large as possible. However, since the average weight of the 4 lightest students is 40 kg, a is at most 40, so the maximum average weight is:
(a + b + c + d + e)/5 = (a + 180)/5 = a/5 + 180/5 = 40/5 + 36 = 8 + 36 = 44 kg
The minimum average weight of all 5 students occurs when e is as small as possible. However, since the average weight of the 4 heaviest students is 45 kg, e is at least 45 kg, so the minimum average weight is:
(a + b + c + d + e)/5 = (160 + e)/5 = 160/5 + e/5 = 32 + 45/5 = 32 + 9 = 41 kg
Therefore, the difference between the maximum and minimum average weight is 44 - 41 = 3 kg.
Answer: C
_________________
5-star rated online GMAT quant
self study course
See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
If you find one of my posts helpful, please take a moment to click on the "Kudos" button.