A military garrison in a wild frontier has 600 men : GMAT Problem Solving (PS)
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# A military garrison in a wild frontier has 600 men

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Intern
Joined: 25 Jan 2013
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A military garrison in a wild frontier has 600 men [#permalink]

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21 Feb 2013, 21:05
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35% (medium)

Question Stats:

76% (03:22) correct 24% (02:37) wrong based on 83 sessions

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A military garrison in a wild frontier has 600 men who have provisions to last 26 weeks. At the end of 6 weeks they are joined by another 300 men. How long will the provisions last?

A. 13 1/3
B. 12 1/3
C. 11 3/3
D. 12 1/2
E. 12 3/4
[Reveal] Spoiler: OA
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Re: A military garrison in a wild frontier has 600 men [#permalink]

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21 Feb 2013, 21:41
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KUDOS
Total provisions=600*26*7=109200

Provisions used for in 6 weeks=6*7*600=25200

remaining provisions=84000

remaining provisions need to be split between 900(600+300) people.

Number of provisions per person= 84000/900

we need to find the answer in terms of weeks=(84000/900)/7=131/3

Hope it helps!

antoxavier wrote:
A military garrison in a wild frontier has 600 men who have provisions to last 26 weeks. At the end of 6 weeks they are joined by another 300 men. How long will the provisions last?

A. 13 1/3
B. 12 1/3
C. 11 3/3
D. 12 1/2
E. 12 3/4
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Re: A military garrison in a wild frontier has 600 men [#permalink]

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21 Feb 2013, 21:50
antoxavier wrote:
A military garrison in a wild frontier has 600 men who have provisions to last 26 weeks. At the end of 6 weeks they are joined by another 300 men. How long will the provisions last?

A. 13 1/3
B. 12 1/3
C. 11 3/3
D. 12 1/2
E. 12 3/4

Assume 1 group = 300 men, And 1 group can eat one box

So.,
52 boxes will cover 2 groups for 26 weeks

In 6 weeks, 2 groups will have consumed 12 boxes.

Remaining = 40 boxes
New No. of groups = 3

No. of weeks = 40/3 = 13.33

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Re: A military garrison in a wild frontier has 600 men [#permalink]

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22 Feb 2013, 00:51
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So we know that the number of the weeks of provision left is inversely proportional to the number of people.

Thus, at the end of 6 weeks, the total provision left is for 20 weeks.

Thus, $$600*20 = 900*x$$

or $$x = \frac{40}{3} = 13.3333$$

A.
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Re: A military garrison in a wild frontier has 600 men [#permalink]

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27 Jul 2014, 09:45
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A military garrison in a wild frontier has 600 men   [#permalink] 27 Jul 2014, 09:45
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