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A certain marathon had 20,000 entrants, 52% of which were female and 3 26 Jan 2017, 10:28
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73% (02:42) correct 27% (02:35) wrong based on 273 sessions

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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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B
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A certain marathon had 20,000 entrants, 52% of which were female and 3 26 Jan 2017, 11:32
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ans B 720

amatuer runners = 40% of 20000 = 8000
8000 minus the female amtuer runner will givve the answer
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A certain marathon had 20,000 entrants, 52% of which were female and 3 26 Jan 2017, 12:06
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Bunuel
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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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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A certain marathon had 20,000 entrants, 52% of which were female and 3 14 Aug 2017, 12:16
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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 25 Aug 2017, 23:53
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Bunuel
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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the answer is in attached image.
calculated through the easiest possible method!
hope it helps! :)

Also, lemme know if any explanation is required! 8-)
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solution.jpg
solution.jpg [ 75.9 KiB | Viewed 3351 times ]

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A certain marathon had 20,000 entrants, 52% of which were female and 3 26 Aug 2017, 00:16
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Bunuel
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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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
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File comment: Tree Structure
Tree structure.jpg
Tree structure.jpg [ 42.65 KiB | Viewed 3290 times ]

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A certain marathon had 20,000 entrants, 52% of which were female and 3 07 Sep 2017, 21:16
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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 3120 times ]

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A certain marathon had 20,000 entrants, 52% of which were female and 3 19 Jul 2018, 12:44
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Bunuel
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
Show more

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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A certain marathon had 20,000 entrants, 52% of which were female and 3 10 Nov 2025, 06:55
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