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msignatius
19 Dec 2025, 02:12
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Okay, this isn't really as much of a math question as a logic / one might even say Critical Reasoning question, which I mostly enjoy, but this one tickled my brain like there's no tomorrow. Anyway, here's my faithful attempt at explaining it.
There's a university. That university may or may not have courses other than Biology and Chemistry, but it definitely has Biology and Chemistry, with each having 25+ students enrolled. Is there is at least one student enrolled in both courses - AKA, out of the 25+-ers in each of the two, is there at least 1 who is enrolled in both? Let's see.
STATEMENT I: Every student who is not enrolled in Biology is also not enrolled in Chemistry.
Um, now here's the thing. As I sit writing this explanation - something dawns upon me which definitely didn't last night while I was solving this. If every student who is not enrolled in Biology is also not enrolled in Chemistry, this means, say, there are 10 students in the university outside of the 25+ each we're talking about for Chem and Bio, who are not enrolled in Biology, and thus also in Chemistry and vice versa. And then, say, there are 26 students who are enrolled in Biology, hypothetically, 36 students, who are enrolled in Chemistry. Now, this creates a really cool oxymoron: if all of those 36 Bio students are not studying Chemistry - as the statement states - then they cannot study Bio either. It says right - that "Every student who isn't enrolled in Bio, isn't enrolled in Chemistry", and these 36 Bio students are not enrolled in Chemistry, and thus, cannot be in Bio.
Wait so how do we solve this oxymoron? Well, first, by not taking a different value for the number of Biology and Chemistry students - 26 and 36. Imagine both have 26 students. Now, all those who aren't enrolled in Biology and thus also not enrolled in Chemistry as those outside of the equation, and since both have more than more than 25 students, all of them studying both the courses, which is directly what the answer seeks.
Hence, STATEMENT I is sufficient.
(I must add, I completely missed this logic last evening. And honestly, I sit with awe seeing how intelligent this question is. Also, this really shows how explaining these questions can help improve the logic / understanding behind GMAT so effectively. I wouldn't have arrived at the right answer if I hadn't done this)
Not so fast: STATEMENT II is there too: Every Student enrolled in Chemistry is also enrolled in Biology
We don't even need to give this a second thought. This shows 25+ students are enrolled in both courses, which is more than one, hence STATEMENT II is also sufficient.
We get the answer, D: Both Statements are sufficient.
There's a university. That university may or may not have courses other than Biology and Chemistry, but it definitely has Biology and Chemistry, with each having 25+ students enrolled. Is there is at least one student enrolled in both courses - AKA, out of the 25+-ers in each of the two, is there at least 1 who is enrolled in both? Let's see.
STATEMENT I: Every student who is not enrolled in Biology is also not enrolled in Chemistry.
Um, now here's the thing. As I sit writing this explanation - something dawns upon me which definitely didn't last night while I was solving this. If every student who is not enrolled in Biology is also not enrolled in Chemistry, this means, say, there are 10 students in the university outside of the 25+ each we're talking about for Chem and Bio, who are not enrolled in Biology, and thus also in Chemistry and vice versa. And then, say, there are 26 students who are enrolled in Biology, hypothetically, 36 students, who are enrolled in Chemistry. Now, this creates a really cool oxymoron: if all of those 36 Bio students are not studying Chemistry - as the statement states - then they cannot study Bio either. It says right - that "Every student who isn't enrolled in Bio, isn't enrolled in Chemistry", and these 36 Bio students are not enrolled in Chemistry, and thus, cannot be in Bio.
Wait so how do we solve this oxymoron? Well, first, by not taking a different value for the number of Biology and Chemistry students - 26 and 36. Imagine both have 26 students. Now, all those who aren't enrolled in Biology and thus also not enrolled in Chemistry as those outside of the equation, and since both have more than more than 25 students, all of them studying both the courses, which is directly what the answer seeks.
Hence, STATEMENT I is sufficient.
(I must add, I completely missed this logic last evening. And honestly, I sit with awe seeing how intelligent this question is. Also, this really shows how explaining these questions can help improve the logic / understanding behind GMAT so effectively. I wouldn't have arrived at the right answer if I hadn't done this)
Not so fast: STATEMENT II is there too: Every Student enrolled in Chemistry is also enrolled in Biology
We don't even need to give this a second thought. This shows 25+ students are enrolled in both courses, which is more than one, hence STATEMENT II is also sufficient.
We get the answer, D: Both Statements are sufficient.
Bunuel
19 Dec 2025, 02:40
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1. gives information of outside the venn diagram. Does not tell what the intersection could be
2. Says that chemistry overlaps with biology. Hence Sufficient.
B
2. Says that chemistry overlaps with biology. Hence Sufficient.
B
19 Dec 2025, 03:06
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S1 Logically this means all the students enrolled in Biology are also enrolled in Chemistry hence sufficient
S2 This is outright sufficient
Ans D
S2 This is outright sufficient
Ans D
Bunuel
