Of the 40 researchers at a certain company, 60 percent work on project

Question

Of the 40 researchers at a certain company, 60 percent work on project P and 30 percent work on project Q. How many of the researchers at the company work on project P but not on project Q ?

(1) 4 of the researchers at the company work on project Q but not on project P.

(2) 12 of the researchers at the company do not work on either project P or project Q.

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Official Answer

D

Subliminal · Accepted Answer

Here's my solution for this question: 29th Jan _ Post 1_QD.jpeg 29th Jan _ Post 1_St1.jpeg 29th Jan _ Post 1_St2.jpeg Hope this helps!

sayan640 · Answer

gmatphobia   KarishmaB ,
Can you please solve this using box diagrams..
I am finding 2nd statement trickier to analyze..Request your help..

gmatophobia · Answer

Check if this helps sayan640 Screenshot 2024-03-13 015813.png Also, you have been tagging another user with a similar user name as mine

. I don't mind, unless we are not spamming them.

sayan640 · Answer

Oh yes...Thank you buddy !!
Can you please check this one too ?  gmatophobia 
 Is the median of the a + b quiz scores greater than the mean of the  : Data Sufficiency (DS) (gmatclub.com)

a_b_p · Answer

How can we be sure that there are only two projects, for all we know there can be more projects. The question doesn't mention that the two projects P and Q are the only two in the company. If that is the case, then statements give a different meaning.

CapnSal · Answer

gmatophobia , solved the same way as you did using a matrix approach. I do have a question, from the question stem P = 24 workers and Q = 12 workers for a total of 36 workers. But the question has 40 workers. What about the other 4 workers?

Since we were not given any information about them, I did not assume they belonged to neither P nor Q, is that the right approach? If not, what can we say/infer about the 4 workers?

Also, since we are not given that P and Q are the ONLY projects at the company, can we infer that there might be more than 2 projects and those 4 workers possibly belong to those projects?

psgmat0899 · Answer

can someone help with this? even i have the same doubt. 10% of 40 = 4 i assumed as neither, but statement two tells that 12 is neither. that got me confused.  Bunuel   gmatophobia   KarishmaB

KarishmaB · Answer

60% work on P and 30% work on Q. Does this mean that 10% work on neither? No, not until and unless we are given that nobody works on both. If the overlap is 0%, then Neither = 10%.
But if overlap is there, then neither will be greater. As 'Both' increases, 'Neither' will increase too. 
Say if 10% people work on both projects, then 20% work on Neither. 
If 20% people work on both projects, then 30% work on Neither.