A certain country with a total population of 50 million is divided in

Question

A certain country with a total population of 50 million is divided into six regions J, K, L, M, N and P, ranked from the most populated to the least populated, with some of the populations possibly equal. If 21 percent of the total population of the country is in region M and if the population of region P is 2 million, what is the greatest possible population of region N?

A. 5 million
B. 6 million
C. 7 million
D. 8 million
E. 9 million

Show Spoiler

A. 5 million
B. 6 million
C. 7 million
D. 8 million
E. 9 million

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chetan2u · Accepted Answer

21% of total population is in M, so M has a population = 21/100 * 50 = 10.5 million

So, J+K+L+M+N+P = 50......J+K+L+10.5+N+2 = 50

To maximize N, make J, K and L equal to M, that is each is 10.5. .......4*10.5+N+2 = 50.......N = 50-44 = 6 million

DanTheGMATMan · Answer

To maximize N, minimize everything else within the constraints:

https://www.youtube.com/watch?v=S_TCCwcLDO4

ashdank94 · Answer

This question is confusing, I thought they were ranked in order so N had to be a value between 10.5 and 2 so I took 9 million as maximum value.

Bunuel · Answer

A certain country with a total population of 50 million is divided into six regions J, K, L, M, N and P, ranked from the most populated to the least populated, with some of the populations possibly equal. If 21 percent of the total population of the country is in region M and if the population of region P is 2 million, what is the greatest possible population of region N?

A. 5 million
B. 6 million
C. 7 million
D. 8 million
E. 9 million

Show Spoiler

A. 5 million
B. 6 million
C. 7 million
D. 8 million
E. 9 million

We are given that  J \geq K \geq L \geq (M=10.5) \geq N \geq (P=2) .

To maximize N, we should minimize J, K, and L. The least values of them will be 10.5. Hence, we'd have

(J=10.5) \geq (K=10.5) \geq (L=10.5) \geq (M=10.5) \geq N \geq (P=2) .

Given that  J + K + L + M + N + P =50 , then:

4*10.5 +N + 2 =50

N = 6

Answer: B.

lovesuit · Answer

Bunuel  why can't we maximize "N"
M+P=12.4 
N+J+K+L=37.6 
maximum value of N = 37.6/4 = 9.4?

Bunuel · Answer

Becasue in this case J, K, or L would become less than M = 10.5, while we are given that   J \geq K \geq L \geq (M=10.5) \geq N \geq (P=2) .

MintTea · Answer

J, K, L, M,N, P

P=2 million, means 4%, and we know that M is 21%, so J+ K+ L+ N = 75%, N is highest when J, K,L are lowest, we know that M is 21%, so J=K=L=M =21% => N=12%. => population in N = 12% x 50 mil = 6mil

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