Bunuel wrote:
A class has 4 sections P, Q, R and S and the average weights of the students in the sections are 45lb, 50lb, 55lb and 65lb respectively. What is the maximum possible number of students in section R if there are 40 students in all sections combined and the average weight of the all students across all the sections is 55lb? It is known that each section has at least one student.
(A) 18
(B) 20
(C) 25
(D) 35
(E) 37
What to look in an average problem is distance of a object from its average... so here average is 55lb which is section R
distance of P from section R= -10lb (negative as I consider R as centre since average lies at R)
distance of Q from R = - 5lb (negative as I consider R as centre since average lies at R)
distance of S from R = 10lb
Given: Each section has at least one student ..
So 37 is ruled out since if we take 1 from P, 1 from Q, 1 from S and 37 from R....average will not be 55lb....Lets see how?
1 from P = -10 distance from R.....1 from S = +10 distance from R...so both negate each other but we have additional -5 from P...so average will be slightly below 55lb now
Lets take another case 1 from P = -10lb
2 from Q = 2*-5lb = -10lb
and 2 from S= 2*+10lb= 20lb
So overall 1 from P + 2from Q = 2 from S...and average still remains at 55lb in section R
So total students taken= 1from P + 2 from Q + 2 from S = 5
Remaning students in R = 40-5= 35, which is the answer
Please give kudos if it is useful for you to understand..