All attendees at a university gathering are faculty or alumni of the u

VERITAS PREP OFFICIAL SOLUTION:

Now, many test takers (about half in the Veritas Prep Question Bank, as well as a couple of admittedly-distracted VP staffers seeing this question for the first time) will go through the following progression:

(1) 3/5 = 60%, so I see what’s going on here…statement 1 says 60% and statement 2 says 40%
(2) (and this is incorrect…more on that in a second) Well if 60% are faculty and 40% are “something else”, and there are only faculty and alumni and no one at this event is “neither”, then it looks like it’s 60% faculty and 40% alumni with no overlap, so the answer must be C, both statements together.

Which isn’t horrible logic, even though it’s incorrect. It’s a relatively understandable progression – but here’s where “No News is Good News” can help. If you really think about it, statements 1 and 2 basically say the same thing. If someone were to ask “what percent of people are not faculty” after statement 1, you’d have to say “well if 60% are, then 40% are not”. So if you think about it, statement 2 doesn’t tell you anything new. So how could the answer be C?

This is your clue to go back and re-investigate and save yourself. Statement 2 doesn’t mean “exactly 40% are alumni”, it only means “40% are not faculty”. So those 40% have to be alumni, but alumni isn’t limited to 40%. That 40% is just “alumni who are not faculty”. Consider the hypothetical that, out of 100 attendees, 60 are faculty, 50 are alumni, and 10 are therefore “both”. That’s perfectly consistent with the statements but doesn’t give you the same number for “both” that you would have had had you picked C.

So the answer is E, but the lesson is probably more important – the fact that the two statements gave you the exact same information was your clue that had you initially thought “C” you had to go back and do some work. When the two statements each tell you the same thing, the answer has to be D or E, and usually that means you have to put in a little due diligence to make sure you choose wisely

In the Venn diagram shown below I present a (1+2) BIFURCATION, that is, two possible viable scenarios for (1+2).



The correct answer is therefore (E).


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

All attendees at a university gathering are faculty or alumni of the university. Are any of the attendees both faculty and alumni?

(1) 3/5 of the attendees are members of the university faculty

(2) 40% of the attendees are not members of the university faculty

drawing 2*2 matrix

1) statement 1. 3/5 F so 2/5 NF. Nothing about Alumn. NOT SUFFICIENT

F Nf Tot
A
NA
Tot 3/5T 2/5T T

2) 40% not faculty. so, 60% faculty. essentially same info in %. 40%*T is 2/5T. NOT SUFFICIENT

F Nf Tot
A
NA
Tot (60%*T) (40%*T) T

Together NS. Answer E

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