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# In a country the total population is 50 million and they are distribut

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Intern
Joined: 04 Sep 2009
Posts: 37
In a country the total population is 50 million and they are distribut  [#permalink]

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28 May 2011, 07:54
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Difficulty:

55% (hard)

Question Stats:

63% (02:16) correct 38% (02:29) wrong based on 71 sessions

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In a country the total population is 50 million and they are distributed among 6 territories in descending order as follows, J,K,L,M,N,P where some territories can have the same amount of people. If M has 21% of the total population and P has 2 million people, what is the maximum amount of people (in millions) in territory N?

a) 4
b) 6
c) 8.5
d) 9
e) 10.5

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Aeros
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Re: In a country the total population is 50 million and they are distribut  [#permalink]

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28 May 2011, 08:02
$$J\ge K\ge L\ge M\ge N\ge P$$

N is maximum when J, K and L are minimum. It's possible when:

$$J= K= L=M\ge N\ge P$$

So,

4*21%*50 + N + 2 = 50

42 + N + 2 = 50

N = 6
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Re: In a country the total population is 50 million and they are distribut  [#permalink]

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30 May 2011, 04:00
4* (21/100) * 50 * 10^6 = 42 * 10^6

42* 10^6 + 2 * 10^6 = 44 * 10^6

thus 6 million.
Intern
Joined: 25 Mar 2017
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Re: In a country the total population is 50 million and they are distribut  [#permalink]

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30 Jun 2017, 05:31
What is the source of this question?My friend got this question in his GMAT today.
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Re: In a country the total population is 50 million and they are distribut  [#permalink]

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04 Jul 2017, 07:47
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aeros232 wrote:
In a country the total population is 50 million and they are distributed among 6 territories in descending order as follows, J,K,L,M,N,P where some territories can have the same amount of people. If M has 21% of the total population and P has 2 million people, what is the maximum amount of people (in millions) in territory N?

a) 4
b) 6
c) 8.5
d) 9
e) 10.5

Since there are 50 million people and M has 21% of them, M has:

0.21 x 50 million = 10.5 million people

Since the number of people in N is between the number of people in M and P, N has between 2 million and 10.5 million people. Since we want to maximize the number of people in N, we want to minimize the number of people in J, K, and L such that each has at least the number of people in M, or 10.5 million. Thus, we can say that J, K, and L have 10.5 million people each; if we add to that the 10.5 million and 2 million people in M and P, respectively, we have 10.5 x 4 + 2 = 44 million people in J, K, L, M, and P combined. Thus, the maximum number of people in N is:

50 - 44 = 6 million

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Re: In a country the total population is 50 million and they are distribut   [#permalink] 04 Jul 2017, 07:47
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