OG - PS - #197

[mww7786]

I have solved this the Vendiagram way. I thought that MGMAT would have another approach. Is this so?
I hope things are going your way. Thanks for your help. :cool: Will you please throw some light on this one.

If 75% of a class answered the first question on certain test correctly, 55% answered the second question on the test correctly, and 20%
answered neither of the questions correctly, what percent answered both correctly?



a 10%
b 20%
c 30%
d 50%
e 65%

[GMAT 5/18]

mww7786,

Overlapping sets would be the quickest way to solve this problem. It took me approx. 45s.

I used a table with the column headings = 1st Correct, 1st Not Correct, Total and the row headings 2nd Correct, 2nd Not Correct, Total. This gave me a table with 9 "boxes" to fill. Simply fill in the boxes with the given data:

Total/Total = 100, 1st Correct/Total = 75, Total/2nd Correct = 45 and 1st Not Correct/2nd Not Correct = 20.

From here you can fill in every remaining combination, using addition and subtraction.

Hope this helps!

By the way, the answer is D, 50%.

[dbernst]

Overlapping sets is a great approach. I also have an even quicker formula should you really feel the need for speed. In one group that is broken down into two overlapping sets, the following formula applies.

Total = Group 1 + Group 2 + Neither - Both

In this problem, let's make the total 100. Thus,

100 = 75 + 55 + 20 - B.

B = 50!

[GMAT 5/18]

Wow, I stand corrected!

Overlapping sets certainly is not the quickest way to solve this problem. Thanks Dan, for enlightening us!

Total = Group 1 + Group 2 + Neither - Both.

Got it!