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 Post subject: GMAT Percentage
PostPosted: Sat May 04, 2013 5:35 am 
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30% of all fishermen in Piscataquis County are also hunters while only 20% of all hunters are fishermen. If there are 1500 hunters in Piscataquis County then how many fishermen are there?

A. 800
B. 1000
C. 1200
D. 1500
E. 1800

(B) People who do both hunting and fishing make 30% of fishermen and 20% of hunters. There are 1500 hunters so 1500 × 20% = 300 pers. do both hunting and fishing. Same people make 30% of all fishermen.30% of fishermen = 300 pers.

Fishermen = (300 / 30) × 100 pers. = 1000 pers.

The correct answer is choice (B).
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I don't understand this question or #29 on this practice test. They both seem to involve the same reasoning. Are these overlapping problems? Can you set up a grid to figure it out? I'm really confused.


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 Post subject: Re: GMAT Percentage
PostPosted: Sat May 04, 2013 5:36 am 
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Yes, this is an "overlapping sets" question. The intersection of the set of fishermen and the set of hunters is the set of people, who both hunt and fish. The key for solving this question is to understand what the given percentages mean.

Let's use a Venn diagram for the analysis:
Image

The intersection is 20% of the set of hunters:
Image

On the other hand, the intersection is 30% of the set of fishermen:
Image

The resulting Venn diagram is:
Image
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 Post subject: Re: GMAT Percentage
PostPosted: Sat May 04, 2013 5:37 am 
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Please, explain how you solved this problem step by step.


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 Post subject: Re: GMAT Percentage
PostPosted: Sat May 04, 2013 5:37 am 
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1. There are 1500 hunters. 20% of them do both: hunting and fishing.
1500 × 20% = 1500 × 0.2 = 1500 × 1/5 = 1500/5 = 300 pers.
So 300 pers. both hunting and fishing.

2. Same people make 30% of all fishermen.
30% of fishermen = 300 pers.
(30/100) × fishermen = 300 pers.
Fishermen = (300 / 30) × 100 pers. = 1000 pers.

The correct answer is B.


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 Post subject: Re: GMAT Percentage
PostPosted: Sat May 04, 2013 5:38 am 
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Hi! Could you please kindly explain to me why it's × 100 ? Thanks!


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 Post subject: Re: GMAT Percentage
PostPosted: Sat May 04, 2013 5:38 am 
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questioner wrote:
Hi! Could you please kindly explain to me why it's × 100 ? Thanks!
Let's look at the whole step 2:
2. Same people make 30% of all fishermen.
30% of fishermen = 300 pers.
(30/100) × fishermen = 300 pers.
fishermen = (300 / 30) × 100 pers. = 1000 pers.

So "× 100" came from the initial "(30/100) ×".
30/100 is just one of many ways to write down a percentage value:
30/100 = 0.30 = 0.3 = 30%. All these notations define the same value.


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