PS Problem Set 03

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gdk800: Senior | Next Rank: 100 Posts; Posts: 54; Joined: Tue Feb 02, 2010 5:17 am; Thanked: 2 times

by gdk800 » Fri Dec 10, 2010 12:56 pm

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

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

[spoiler]OA is D
[/spoiler]

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Source: Beat The GMAT — Problem Solving | Fri Dec 10, 2010 12:56 pm

shovan85: Community Manager; Posts: 991; Joined: Thu Sep 23, 2010 6:19 amFollowed by: 24 members; Location: Bangalore, India; Thanked: 146 times

by shovan85 » Fri Dec 10, 2010 1:25 pm

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

If the problem is Easy Respect it, if the problem is tough Attack it

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Salman Ghaffar: Senior | Next Rank: 100 Posts; Posts: 55; Joined: Tue Nov 16, 2010 1:21 pm; Location: Karachi, Pakistan; Thanked: 7 times

by Salman Ghaffar » Fri Dec 10, 2010 2:08 pm

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

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