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Confused with Sets! Help with problem, please?

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72% of the graduates from Harvard Law took the Bar exams while 23% took the CPA exams. 25% of the graduates didn't take either Bar or CPA exams.

(A) If there are 2000 graduates in total, how many took the Bar and CPA exams?

(B) If 80% of the graduates that took the Bar exams passed, how many graduates passed the Bar?

EDIT: To the person elected "Best Answer", thank you very much! I love you! Thank you for breaking the solutions into chunks! I now understand it a LOT better!

Guest Jun 14, 2017
edited by Guest  Jun 15, 2017

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Hi,

I use the cross multiplication method to calculate with percentages. ;)

(A) 2000 graduates will be 100%. if 72% took a BAR exam it equals 2000*72/100= 1440 graduates took the bar exam. Only 23% took the CPA exam. Which equals 460 graduates (2000*23/100). 25% took neither, which are 500 graduates. 1440+460=1900 exams were conducted by 2000-500=1500 graduates. Which means a surplus of 400 exams, thus 400 students took both the BAR and CPA exams.

(B) 1440 graduates took the BAR exam (see A). 1440 is the new 100%. Of the 1440 only 80% passed the exam. Which equals 1440*80/100= 1152 graduates passed the BAR exam.

I hope this helps.

Guest Jun 14, 2017
Sort:

#1
0

Hi,

I use the cross multiplication method to calculate with percentages. ;)

(A) 2000 graduates will be 100%. if 72% took a BAR exam it equals 2000*72/100= 1440 graduates took the bar exam. Only 23% took the CPA exam. Which equals 460 graduates (2000*23/100). 25% took neither, which are 500 graduates. 1440+460=1900 exams were conducted by 2000-500=1500 graduates. Which means a surplus of 400 exams, thus 400 students took both the BAR and CPA exams.

(B) 1440 graduates took the BAR exam (see A). 1440 is the new 100%. Of the 1440 only 80% passed the exam. Which equals 1440*80/100= 1152 graduates passed the BAR exam.

I hope this helps.

Guest Jun 14, 2017

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