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A certain marathon had 20,000 entrants, 52% of which were female and 3

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A certain marathon had 20,000 entrants, 52% of which were female and 3  [#permalink]

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New post 26 Jan 2017, 09:28
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A certain marathon had 20,000 entrants, 52% of which were female and 30% of these female entrants were professional runners. If 60% of the entrants were professional, how many of the runners in the marathon were amateur male runners?

A. 72
B. 720
C. 3,120
D. 8,000
E. 8,880

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Re: A certain marathon had 20,000 entrants, 52% of which were female and 3  [#permalink]

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New post 26 Jan 2017, 10:32
ans B 720

amatuer runners = 40% of 20000 = 8000
8000 minus the female amtuer runner will givve the answer
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Re: A certain marathon had 20,000 entrants, 52% of which were female and 3  [#permalink]

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New post 26 Jan 2017, 11:06
Bunuel wrote:
A certain marathon had 20,000 entrants, 52% of which were female and 30% of these female entrants were professional runners. If 60% of the entrants were professional, how many of the runners in the marathon were amateur male runners?

A. 72
B. 720
C. 3,120
D. 8,000
E. 8,880



No. of females = 52% of 20000 = 10400
Professional females = 30% of 10400 = 3120
Total professional(M+F) = 60% of 20000 =12000
thus male professional = total professional - female professional = 12000-3120 = 8880
amateur males = Total runners -(total females + professional male) = 20000- (10400+8880) =720

Ans B
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Re: A certain marathon had 20,000 entrants, 52% of which were female and 3  [#permalink]

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New post 14 Aug 2017, 11:16
Amateur Professional Total
Male 720(9600-8880) 8880(12000-3120) 9600(20000-10400)

Female 3120(30%*10400) 10400(52%*20000)

Total 12000(60%20000) 20000(given)

First calculate 52%
then calculate 30%
then calculate 60%
then subtract 20000 -10400 and also 12000-3120
then finally subtract 9600-720
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A certain marathon had 20,000 entrants, 52% of which were female and 3  [#permalink]

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New post 25 Aug 2017, 22:53
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Bunuel wrote:
A certain marathon had 20,000 entrants, 52% of which were female and 30% of these female entrants were professional runners. If 60% of the entrants were professional, how many of the runners in the marathon were amateur male runners?

A. 72
B. 720
C. 3,120
D. 8,000
E. 8,880


the answer is in attached image.
calculated through the easiest possible method!
hope it helps! :)

Also, lemme know if any explanation is required! 8-)

Attachments

solution.jpg
solution.jpg [ 75.9 KiB | Viewed 928 times ]

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Re: A certain marathon had 20,000 entrants, 52% of which were female and 3  [#permalink]

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New post 25 Aug 2017, 23:16
Bunuel wrote:
A certain marathon had 20,000 entrants, 52% of which were female and 30% of these female entrants were professional runners. If 60% of the entrants were professional, how many of the runners in the marathon were amateur male runners?

A. 72
B. 720
C. 3,120
D. 8,000
E. 8,880


Another approach - Draw a Tree Structure for these kind of questions

As is clear from the tree structure below -
No of amateur males \(= 0.036*20000 = 720\)

Option B
Attachments

File comment: Tree Structure
Tree structure.jpg
Tree structure.jpg [ 42.65 KiB | Viewed 917 times ]

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Re: A certain marathon had 20,000 entrants, 52% of which were female and 3  [#permalink]

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New post 07 Sep 2017, 20:16
We can use 2X2 Matrix to solve questions of these types
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Screen Shot 2017-09-08 at 9.45.22 AM.png
Screen Shot 2017-09-08 at 9.45.22 AM.png [ 26.96 KiB | Viewed 757 times ]

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Re: A certain marathon had 20,000 entrants, 52% of which were female and 3  [#permalink]

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New post 19 Jul 2018, 11:44
Bunuel wrote:
A certain marathon had 20,000 entrants, 52% of which were female and 30% of these female entrants were professional runners. If 60% of the entrants were professional, how many of the runners in the marathon were amateur male runners?

A. 72
B. 720
C. 3,120
D. 8,000
E. 8,880


Since 52% of the 20,000 entrants were female, 0.52 x 20,000 = 10,400 were female and hence 20,000 - 10,400 = 9,600 were male. Since 30% of the female entrants were professional runners, 0.3 x 10,400 = 3,120 females were professional runners and hence 10,400 - 3,120 = 7,280 females were amateur runners.

Since 60% of the entrants were professional runners, 0.6 x 20,000 = 12,000 were professional runners and hence 20,000 - 12,000 = 8,000 were amateur runners. Since there are 7,280 female amateur runners, there are 8,000 - 7,280 = 720 male amateur runners.

Answer: B
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Re: A certain marathon had 20,000 entrants, 52% of which were female and 3 &nbs [#permalink] 19 Jul 2018, 11:44
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