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805+ Level|   Overlapping Sets|         
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yazlal25
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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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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
Show more
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