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805+ (Hard)|   Overlapping Sets|            
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What percent of the students at University X are enrolled in a science 13 Jul 2025, 04:25
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GMAT keeps finding new ways to completely astonish me! Assuming that Biology is a subset of science in a DS question is a game changer. I wonder what other things GMAT expects us to assume.
randommbaguy
What percent of the students at University X are enrolled in a science course but are not enrolled in a biology course?

(1) 28 percent of the students at University X are enrolled in a biology course.
(2) 70 percent of the students at University X who are enrolled in a science course are enrolled in a biology course.


ID: 700297
DS60130.02
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agrasan
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What percent of the students at University X are enrolled in a science 01 Aug 2025, 08:00
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Hi KarishmaB

I am a bit confused here.
I understand that it is a well-known real world general knowledge that biology is in Science but I am just not sure why it was required for us to assume that. Due to this only, I had marked (E) and realised that we had to make that assumption using outside knowledge upon seeing the solution. Is this question a bit vague from that perspective?

KarishmaB
randommbaguy
What percent of the students at University X are enrolled in a science course but are not enrolled in a biology course?

(1) 28 percent of the students at University X are enrolled in a biology course.
(2) 70 percent of the students at University X who are enrolled in a science course are enrolled in a biology course.


DS60130.02
Quantitative Review 2021


The question is based on knowing that Biology is one of the sciences. So Biology circle lies inside the Science circle.
We need to know what % lies inside the Science circle but not inside the Biology circle (so they may have taken Physics or Chemistry etc)

(1) 28 percent of the students at University X are enrolled in a biology course.

B = 28% of Total
Not sufficient alone.

(2) 70 percent of the students at University X who are enrolled in a science course are enrolled in a biology course.

Note here that the statement does not say that 70% enrolled in science course are enrolled in a biology course too. It says 70% enrolled in science are enrolled in biology. It makes sense. Biology is a science.

70% of Science = B
Not sufficient alone.

Using both statements, 70% of Science = B = 28% of Total
Science = 28/70 of Total = 40% of Total

% of students enrolled in Science but not in Biology = 40% of Total - 28% of Total = 12% of Total
Sufficient.

Answer (C)
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KarishmaB
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What percent of the students at University X are enrolled in a science 02 Aug 2025, 03:10
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agrasan
Hi KarishmaB

I am a bit confused here.
I understand that it is a well-known real world general knowledge that biology is in Science but I am just not sure why it was required for us to assume that. Due to this only, I had marked (E) and realised that we had to make that assumption using outside knowledge upon seeing the solution. Is this question a bit vague from that perspective?

KarishmaB
randommbaguy
What percent of the students at University X are enrolled in a science course but are not enrolled in a biology course?

(1) 28 percent of the students at University X are enrolled in a biology course.
(2) 70 percent of the students at University X who are enrolled in a science course are enrolled in a biology course.


DS60130.02
Quantitative Review 2021


The question is based on knowing that Biology is one of the sciences. So Biology circle lies inside the Science circle.
We need to know what % lies inside the Science circle but not inside the Biology circle (so they may have taken Physics or Chemistry etc)

(1) 28 percent of the students at University X are enrolled in a biology course.

B = 28% of Total
Not sufficient alone.

(2) 70 percent of the students at University X who are enrolled in a science course are enrolled in a biology course.

Note here that the statement does not say that 70% enrolled in science course are enrolled in a biology course too. It says 70% enrolled in science are enrolled in biology. It makes sense. Biology is a science.

70% of Science = B
Not sufficient alone.

Using both statements, 70% of Science = B = 28% of Total
Science = 28/70 of Total = 40% of Total

% of students enrolled in Science but not in Biology = 40% of Total - 28% of Total = 12% of Total
Sufficient.

Answer (C)
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It is tricky because we tend to think in terms of sets A, B and C when working on overlapping sets problems and we tend to ignore what A, B and C are. Here we are required to identify that Biology is a Science. Anyone preparing for MBA needs to know this just like they need to know that red is a color and Asia is a continent. Will we call it outside knowledge?
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What percent of the students at University X are enrolled in a science 02 Aug 2025, 03:12
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Thanks KarishmaB
I am clear now.
KarishmaB
agrasan
Hi KarishmaB

I am a bit confused here.
I understand that it is a well-known real world general knowledge that biology is in Science but I am just not sure why it was required for us to assume that. Due to this only, I had marked (E) and realised that we had to make that assumption using outside knowledge upon seeing the solution. Is this question a bit vague from that perspective?


It is tricky because we tend to think in terms of sets A, B and C when working on overlapping sets problems and we tend to ignore what A, B and C are. Here we are required to identify that Biology is a Science. Anyone preparing for MBA needs to know this just like they need to know that red is a color and Asia is a continent. Will we call it outside knowledge?
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What percent of the students at University X are enrolled in a science 10 Oct 2025, 01:54
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Answer is C.

We need →
% of total students at University X who are enrolled in a science course but not in biology.

Let’s define variables:

  • T = total students (100%).
  • S = % enrolled in science courses.
  • B = % enrolled in biology (a subset of science).
  • S \text{ and not } B = S - B.


We need S - B as a % of total students.

[hr]


Statement (1):


Quote:
28% of the students are enrolled in a biology course.
Show more
Quote:
That means B = 28\%.
Show more

We don’t know S.
Without S, we cannot find S - B.
→ INSUFFICIENT.

[hr]


Statement (2):


Quote:
70% of the students who are enrolled in a science course are enrolled in a biology course.
Show more
Quote:
That means:
Show more
Quote:
B = 0.70S
Show more
Quote:
We still don’t know S.
Show more
Quote:
So S - B = S - 0.70S = 0.30S.
Show more
Quote:
Without knowing S, we can’t get a numerical % of total students.
Show more
Quote:
→ INSUFFICIENT.
Show more

[hr]


Combine (1) and (2):


From (2): B = 0.70S.
From (1): B = 28\%.
→ 28 = 0.70S
→ S = 40\%.

Now,
S - B = 40 - 28 = 12\%.

✅ Answer: 12% of the students are enrolled in a science course but not biology.
randommbaguy
What percent of the students at University X are enrolled in a science course but are not enrolled in a biology course?

(1) 28 percent of the students at University X are enrolled in a biology course.
(2) 70 percent of the students at University X who are enrolled in a science course are enrolled in a biology course.


ID: 700297
DS60130.02
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Ethan39
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What percent of the students at University X are enrolled in a science 10 Oct 2025, 01:54
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Answer is C.

We need →
% of total students at University X who are enrolled in a science course but not in biology.

Let’s define variables:

  • T = total students (100%).
  • S = % enrolled in science courses.
  • B = % enrolled in biology (a subset of science).
  • S \text{ and not } B = S - B.


We need S - B as a % of total students.

[hr]


Statement (1):


Quote:
28% of the students are enrolled in a biology course.
Show more
Quote:
That means B = 28\%.
Show more

We don’t know S.
Without S, we cannot find S - B.
→ INSUFFICIENT.

[hr]


Statement (2):


Quote:
70% of the students who are enrolled in a science course are enrolled in a biology course.
Show more
Quote:
That means:
Show more
Quote:
B = 0.70S
Show more
Quote:
We still don’t know S.
Show more
Quote:
So S - B = S - 0.70S = 0.30S.
Show more
Quote:
Without knowing S, we can’t get a numerical % of total students.
Show more
Quote:
→ INSUFFICIENT.
Show more

[hr]


Combine (1) and (2):


From (2): B = 0.70S.
From (1): B = 28\%.
→ 28 = 0.70S
→ S = 40\%.

Now,
S - B = 40 - 28 = 12\%.

✅ Answer: 12% of the students are enrolled in a science course but not biology.
randommbaguy
What percent of the students at University X are enrolled in a science course but are not enrolled in a biology course?

(1) 28 percent of the students at University X are enrolled in a biology course.
(2) 70 percent of the students at University X who are enrolled in a science course are enrolled in a biology course.


ID: 700297
DS60130.02
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What percent of the students at University X are enrolled in a science 02 Aug 2026, 05:33
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Why is it that in this question we are assuming that students are not enrolled in any other course , other than Biology or Science?
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What percent of the students at University X are enrolled in a science 02 Aug 2026, 05:45
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ANUP17062000
Why is it that in this question we are assuming that students are not enrolled in any other course , other than Biology or Science?
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Because students' being enrolled in another course doesn't change the answer to the question.

After all, the percentage of students enrolled in a science course but not a biology course wouldn't be changed by student enrolment in other courses.

To confirm, you could try having some enrolled or not enrolled in another course. Does the percentage enrolled in a biology course change? Does the percentage enrolled in a science course change? No, right?
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What percent of the students at University X are enrolled in a science 02 Aug 2026, 21:49
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ANUP17062000
Why is it that in this question we are assuming that students are not enrolled in any other course , other than Biology or Science?
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We are not assuming this. It is just irrelevant to us. Say 30% students are enrolled in English, 20% in Spanish, 55% in Philosophy etc. Since your question focuses only on the Science and Bio enrollments, these other enrollments of students are irrelevant.
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What percent of the students at University X are enrolled in a science 08 Aug 2026, 07:22
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Natural Science is Science
Social Science is also Science

Biology is part of Natural Science but not part of Social Science

How do you decipher intentions of GMAC?

randommbaguy
What percent of the students at University X are enrolled in a science course but are not enrolled in a biology course?

(1) 28 percent of the students at University X are enrolled in a biology course.
(2) 70 percent of the students at University X who are enrolled in a science course are enrolled in a biology course.


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KarishmaB
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What percent of the students at University X are enrolled in a science 08 Aug 2026, 22:02
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Social science is not a part of this discussion. Don't worry about hypotheticals. GMAC puts in a lot of effort to ensure that there is no ambiguity in the actual test questions.

SteelBranch
Natural Science is Science
Social Science is also Science

Biology is part of Natural Science but not part of Social Science

How do you decipher intentions of GMAC?


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What percent of the students at University X are enrolled in a science 10 Aug 2026, 14:47
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Hi SteelBranch,

You're actually raising a fair point about how wide the word "science" is, so let me meet you right there. You're worried that "science" might be a big umbrella (natural + social science), and that biology sits under only one part of it. But here's the thing: the size of the umbrella doesn't matter - only that biology sits somewhere under it.

Think about what the question actually needs. The entire solution rests on one relationship: every biology course is a science course, so the biology group lives inside the science group. That's all. It does not need science to be only natural science, and it does not need biology to cover any particular slice.

Now test your own worry against that:

- If "science" = natural science only - biology is still inside it. ✓
- If "science" = natural plus social science - the science circle just got bigger, and biology is still inside it. ✓

Widening the category can only make the science circle larger; it can never push biology out of it. So no matter how GMAC intends the scope, the subset relationship - biology ⊆ science - holds. And that subset relationship is the only assumption the combined statements use to get 40% - 28% = 12%.

A quick parallel to lock it in: "A robin is a bird." That stays true whether you define "bird" narrowly (songbirds, like the robin) or broadly (every feathered animal). Broadening "bird" never kicks the robin out.

So you don't have to decipher GMAC's exact taxonomy here. You only have to confirm the containment - is biology a kind of science? Yes - and that single fact is enough to keep the answer at C.

Answer: C

SteelBranch
Natural Science is Science
Social Science is also Science

Biology is part of Natural Science but not part of Social Science

How do you decipher intentions of GMAC?


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