PS Problem Set 03

gdk800 wrote:1) 5 pieces of wood have an average length of 124cm and median length of 140cm. what is the maximum possible length of the shortest piece of wood?
a. 90
b. 100
c. 110
d. 130
e. 140

OA is B

In order to get the max value of the lowest we should get the min value of the highest.

If u know a median then make all values in the list those are right to the median in order to get the min value of the highest.

Let A B C D E be the 5 pieces of the wood respectively.
C = 140 (being Median)

Total = 124 * 5 = 620

So, C = D = E = 140 accumulating to 3 * 140 = 420

Sum of A and B = 620 - 420 = 200

Now we need to get the max value of the lowest. So we have to make A = B

Thus Length of wood piece A = 200/2 = 100cm

2) A city with population 132000 is to be divided into 11 voting districts, and no district is to have a population that is more than 10% greater than population of any other district. What is minimum possible population of the least populated district?
a. 10700
b. 10800
c. 10900
d. 11000
e. 11100

To find the min possible population of the least populated district, we should maximize the pop of all the other districts (each of which cant be more than 10% greater than the pop of the least populated district).

Assuming the pop of the least populated district = x
The max possible pop of each of the remaining 10 districts would = 110% of x = 1.1x

The total pop is 132,000. Hence the equation --> x + 10*(1.1x) = 132,000

Solve for x --> x + 11x = 132,000

Hence x = 132,000/12 = 11,000 - Answer