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

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Math Expert
Joined: 02 Sep 2009
Posts: 51301
A certain marathon had 20,000 entrants, 52% of which were female and 3  [#permalink]

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26 Jan 2017, 09:28
00:00

Difficulty:

55% (hard)

Question Stats:

63% (02:42) correct 37% (02:35) wrong based on 158 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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Joined: 21 Mar 2016
Posts: 523
Re: A certain marathon had 20,000 entrants, 52% of which were female and 3  [#permalink]

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26 Jan 2017, 10:32
ans B 720

amatuer runners = 40% of 20000 = 8000
8000 minus the female amtuer runner will givve the answer
VP
Joined: 05 Mar 2015
Posts: 1003
Re: A certain marathon had 20,000 entrants, 52% of which were female and 3  [#permalink]

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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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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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Joined: 16 Feb 2017
Posts: 21
A certain marathon had 20,000 entrants, 52% of which were female and 3  [#permalink]

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25 Aug 2017, 22:53
2
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!

Attachments

solution.jpg [ 75.9 KiB | Viewed 928 times ]

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Joined: 25 Feb 2013
Posts: 1217
Location: India
GPA: 3.82
Re: A certain marathon had 20,000 entrants, 52% of which were female and 3  [#permalink]

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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 [ 42.65 KiB | Viewed 917 times ]

Manager
Joined: 03 May 2014
Posts: 160
Location: India
WE: Sales (Mutual Funds and Brokerage)
Re: A certain marathon had 20,000 entrants, 52% of which were female and 3  [#permalink]

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07 Sep 2017, 20:16
We can use 2X2 Matrix to solve questions of these types
Attachments

Screen Shot 2017-09-08 at 9.45.22 AM.png [ 26.96 KiB | Viewed 757 times ]

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

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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.

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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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