SETS

[Zizou4]

I dont understand y its E.
Is it because it is not clearly stated that all 60 students took at least 1 test?
Is this the correct formula?
Group1 + Group2 + Neither - Both = total

Thanx in advance.

Z

[DanaJ]

Well, without further info, you can't say how many students took both tests. Each stmt taken separately is obviously insufficient. Take the two together and you get that you had 52 Science test-takers and 24 Math test-takers, but there is no way of knowing how many took both tests. Let me give you some examples:
a. say you have 24 students who took both tests. Then there are no students who took only the Math test, 28 students took only the Science test and 8 students who didn't take any tests.
b. say you've got 22 students who took both tests. Then you get that 2 other students only took the Math test, 30 students only took the Science test and 6 students who didn't take any tests.

There is no way of distinguishing between these two cases without further info. In both cases you get total number of students = 60, Math = 24, Science = 52.

[gaggleofgirls]

So DanaJ, you are saying that the reason we can't know how many took both is because we don't know how many didn't take any. In both of your examples, you are able the adjust the number of students who took both tests because you can adjust the number of students who took neither test.

The formula Zizou4 is using is correct
Group A + GroupB + Neither - Both = Total

Stem tells us only that total= 60 and that GroupA is took math test and Group B is took science test.

Cearly 1 and 2 are each insufficient since they only talk about one group each.

Together, we get:
60 = 52 + 24 + Neither - Both

So without knowing Neither, we can't get Both.

It is easy to assume from the question that all students took at least one test, but assume is not appropriate.

I guess this can be expanded also becuase it doesn't say that only math and science tests were offered. There could have been other tests too.

-Carrie

[Stuart@KaplanGMAT]

First, let me say that this is a HORRIBLY worded question. "How many of the 60 students..." isn't even gramatically correct ("the" doesn't make any sense without another reference, e.g. "how many of the 60 students in a class"). What's your source?

That issue aside, we can quickly solve using our old friend "# of equations vs # of unknowns".

As cited, here's our master formula:

Total # of objects = G1 + G2 + neither - both

From the original, we know that the total is 60. So, we have 1 equation and 4 unknowns. Therefore, barring special equations that eliminate multiple variables, we need 3 more equations.

1) gives us the value of G1. Just 1 more equation, insufficient.
2) gives us the value of G2. Just 1 more equation, insufficient.

Combined: We now have 3 equations and 4 unknowns. None of our equations get rid of multiple variables, therefore insufficient: choose (E) not enough information.

* * *

As an aside, an example of a "special" equation that eliminates more than one variable all in one shot is:

"A total of 30 students either wrote the math test or didn't write any test at all."

Translated, that would be:

G1 + Neither = 30

and would eliminate both of those variables from our master equation.

* * *

Remember, we should NEVER make assumptions in data sufficiency, so unless the question specifically tells us that everyone in the class writes at least one of the two tests, we don't know that to be the case.

[gaggleofgirls]

First, let me say that this is a HORRIBLY worded question. "How many of the 60 students..." isn't even gramatically correct ("the" doesn't make any sense without another reference, e.g. "how many of the 60 students in a class"). What's your source?

Thanks for confirming that this wording is ambiguous. I assume we can expect that the actual test questions will be better worded (although I won't make assumptions during the test, I promise)?

I am in final countdown (test on Tuesday).

-Carrie

[Stuart@KaplanGMAT]

First, let me say that this is a HORRIBLY worded question. "How many of the 60 students..." isn't even gramatically correct ("the" doesn't make any sense without another reference, e.g. "how many of the 60 students in a class"). What's your source?

Thanks for confirming that this wording is ambiguous. I assume we can expect that the actual test questions will be better worded (although I won't make assumptions during the test, I promise)?

I am in final countdown (test on Tuesday).

-Carrie

Yes, questions on the actual GMAT will never be worded as poorly as this one is.

Good luck on Tuesday!

[gaggleofgirls]

Thanks. This forum (and a lot of hours of studying) has really helped me to re-learn (and in some cases really learn for the fist time) this math that I knew in High School/College (which was over 22 years ago, yikes). But it has been a fun challenge to get this stuff again and good prep as my oldest daughter heads into Middle School next year and is just starting with algebra and geometry.

-Carrie