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

[BTGmoderatorLU]

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 on the marathon amateur male runners?

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

The OA is B.

I solved this PS question as follows,

Number of females = 52% of 20,000 = 10,400
Professional females = 30% of 10,400 = 3,120
Total professional (M + F) = 60% of 20,000 = 12,000

Thus, male professional = total professional - female professional = 12,000 - 3,120 = 8,880.
Amateur males = Total runners - (total females + professional males) = 20,000 - (10,400 + 8,880) = 720.

Please, can someone explain another way to solving this question? Thanks!

[deloitte247]

Total entrants = 20,000
Female = 52% of 20,000 = 10,400
Professional female runners = 30% of 10,400
= 3,120
Total professional runners = 60% of 20,000
= 12,000
Male Entrants = 100 - 52% of 20,000
= 48% of 20,000 = 9,600
Out of 12,000 professional runner, 3,120 are female, male = 12,000 - 3,120 = 8,880
Professional male runners = 8,880
Amateur male runners = 9,600 - 8,880
= 720 amateur male entrants.
The correct answer is B

[Vincen]

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 on the marathon amateur male runners?

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

The OA is B.

I solved this PS question as follows,

Number of females = 52% of 20,000 = 10,400
Professional females = 30% of 10,400 = 3,120
Total professional (M + F) = 60% of 20,000 = 12,000

Thus, male professional = total professional - female professional = 12,000 - 3,120 = 8,880.
Amateur males = Total runners - (total females + professional males) = 20,000 - (10,400 + 8,880) = 720.

Please, can someone explain another way to solving this question? Thanks!

Hello BTGmoderatorLU.

That is the right way to solve it.

Number of women on the marathon: $$52\%\cdot20,000=10,400.$$ Number of men on the marathon: $$20,000-10,400=9600.$$ Number of professional runners on the marathon: $$60\%\cdot20,000=12,000.$$ Number of professional women on the marathon: $$30\%\cdot10,400=3,120.$$ Number of professional men on the marathon: $$12,000-3,120=8,880.$$ Number of amateur men on the marathon: $$9,600-8,880=720.$$ So, the correct answer is the option B.

I hope it helps you. <i class="em em-smiley"></i>

[Shahrukh@mbabreakspace]

Total male= 20000*0.48= 9600
Total professional male= 20000*(0.6-0.52*0.3)= 8880
So, Amateur male = 9600-8880=720

[Scott@TargetTestPrep]

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 on the marathon 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