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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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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

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 3349 times ]

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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

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
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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 3118 times ]

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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

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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