A is a set of even integers, while B is a set of integers...

[NileshG679]

Hi All,

This is a question from the MGMAT Guide 3, Problem set 5, #1.
A is a set of even integers, while B is a set of integers that are multiples of 3. There are 16 integers in set A, 22 integers in set B, and 7 integers in both sets. How many integers are in exactly one of the two sets?

I drew my double set matrix and had the setup correct just like the solution but I'm confused about exactly what the question is asking. How would someone know that when a question asks "How many integers are in exactly one of the two sets?" that we are supposed to add the value of the combination of [Set B and not in Set A] + [Set A and not in set B] = 9 + 15 = 24.

When I read a question like that, I think I should be getting two answers that are the same or something like that.

Thanks!

edit: changed & to 7, thanks for the catch and explanation!

[RonPurewal]

can't tell how many integers are in both sets, because you accidentally put an "and" sign there instead of a number.

in any case--just remember that words mean whatever they would mean in the real world (or, at least, in any real-world situation in which precision is desirable).

let's say that a scholarship form asks whether the applicant is female. let's say it also asks whether the applicant is hispanic.
what does it mean to be exactly one of these two things?

you know the answer-- it means either (a) male hispanic, or (b) female non-hispanic.

you also know that, if you wanted to find the total number of people who meet exactly one of these two criteria, you'd have to count groups (a) and (b) above, and then add the numbers together.

finally, you also know that there's no reason to expect the two numbers to be the same.

just take that knowledge from the real world, and transfer it to the problems.

[RonPurewal]

more generally-- and more importantly-- don't ever forget: there is no such thing as "tricky GMAT wording".

in fact, it's quite the opposite:
• words that are unexplained mean whatever they would mean in everyday life (as is the case here);
• if there is ANY chance of ambiguity, the definition(s) in question willl be explained meticulously.

[RonPurewal]

ironically, if you do have issues with a wording on this exam, the problem is probably that the writers are trying TOO hard to make the statement unambiguous.
for instance, look at this problem:
https://www.manhattanprep.com/gmat/foru ... t4110.html

in that problem, there's actually a definition of the word "different" (really, no kidding).
all they're saying is what everyone already knows-- i.e., that a group consisting of A, B, and C is "different" from a group consisting of A, B, and D.
the point, though, is that they're trying so hard NOT to be tricky that, sometimes, the result is a bit pedantic/annoying/obtuse. (but that's certainly better than erring on the side of less precision!)

[KakakkdeK400]

I think that this information is the best.

[RonPurewal]

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