Problem Solving

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!

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

BTGmoderatorLU 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 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>

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