What percent of the students at University X are enrolled in a science

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)

Some of us may argue that why should we take Biology as a part of science, when we are not given that.

Two reasons why we should, although most of the time we do not carry the knowledge of outside world
1) It is a fact that biology is a part of science, the same way as white is a color, as pizza is a type of food, and as horse is an animal.
2) If it is an official question, we may take it that GMAT considers it to be so.

We can draw Venn diagram where the smaller circle represents the biology courses, encompassed by the bigger circle representing science courses.

Let us take the total number of students be 100, and we are asked to find the non shaded portion, as the shaded portion is common to the two.

(1) 28 percent of the students at University X are enrolled in a biology course.
So, 28 students are enrolled in Biology courses. Just the shaded portion.
Insufficient

(2) 70 percent of the students at University X who are enrolled in a science course are enrolled in a biology course.
This tells us that 0.7x is the shaded portion, where x is the total number of students enrolled in science course.


Combined
\(0.7x=28....x=40\)
Non shaded portion = 0.3x=0.3*40=12

C

Solution:

The problem in this question is that one writes a very general Venn diagram with an intersection region here.

Since Biology is a science already, it will be fully inside the Science circle.

Biology is a Science is a fact and not an assumption.

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

This means that the 28% would also include Science and Biology and not only Biology as Biology is also a Science(fact not assumption).

However, we do not know the percentage of students enrolled in a science course.

If all the students ,that is 100% are in a Science course then 100-28=72% would be enrolled in Science without Biology and

If 50% of the students are in the Science course, then 50-28=22% would be enrolled in Science without Biology.

Hence no definite answer is possible unless we know the percentage of students in Science.(Insufficient)

​

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

​On similar lines like St(1),

Lets say all the students that is 100% are enrolled for a Science Course

=> 100- 70 = 30% are enrolled in a Science without Biology and

If 50% of the students are in the Science Course,​then
50-70%of 50

=50-35

=15% are enrolled in a Science without Biology.

Hence no definite answer is possible

(Insufficient)
​

Combining them,

Let x be the percentage of students enrolled for a Science Course

=>28 percent of the students at University X are enrolled in a biology course

(This will be a percentage belonging to Science enrollments)

and

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

=>0.7x are enrolled in Biology

=>0.7x =0.28

=> x =0.4 =40%

=>Percentage of students enrolled in Science =40%

=>Percentage of students enrolled in Science but not in Biology

= 40 - 28

= 12%
(Sufficient)

(option c)

Devmitra Sen
GMAT SME

Asked: 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.

NOT SUFFICIENT

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

NOT SUFFICIENT

(1) + (2)
(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.

There is no way to derive .3x%
NOT SUFFICIENT

IMO E

Bunuel
Please check whether OA is correct.

Official Explanation

Under the assumption that a biology course is a type of science course, determine the percent of University X students who are enrolled in a science course, but not in a biology course.

(1) Given that 28% of the students at University X are enrolled in a biology course, if 100% of the students are enrolled in a science course, then (100 − 28)% = 72% are enrolled in a science course, but not in a biology course. On the other hand if 50% of the students at University X are enrolled in a science course, then (50 − 28)% = 22% are enrolled in a science course, but not in a biology course; NOT sufficient.

(2) Given that 70% of the students at University X who are enrolled in a science course are enrolled in a biology course, if 100% of the students at University X are enrolled in a science course, then (100 − 70)% = 30% are enrolled in a science course, but not in a biology course. On the other hand if 50% of the students at University X are enrolled in a science course, then 70% of 50% = 35% are enrolled in a biology course, (50 − 35)% = 15% are enrolled in a science course, but not in a biology course; NOT sufficient.

Taking (1) and (2) together, 0.28 = 0.7x where x is the percent of the students at University X who are enrolled in a science course. It follows that x = 0.4 or 40%. Thus, (40 − 28)% = 12% of the students at University X are enrolled in a science course, but not in a biology course.

Both statements together are sufficient.

Hi,
According to the overall answer 28% = 0.7x which means all biologists are scientists which is not given in the passage.
Kindly elaborate.

Thanks in advance

sanjaysuryan pragya007 SairamRamo Abhimanyu201992 davidbeckham LipsaTripathy Kinshook
Guys, we are majorly flawing in the logic here. Statement 1 says. 28% are biology student and we are statistically filling that in total column. But if we put logic. Those students who are not studying science can't study biology too. That's the trick here.
The 28% belong to students who are studying science and biology not total biology. That's why the answer is turning out flawed.

So we have science and biology = 28 from statement 1.
But we need science but not biology
Hence statement 1 is insufficient.

Statement 2 says. Out of Students studying science, 70% are biology student.
But what no. Of students let say X are studying science? Not given. (Insufficient)

Combining both; 70% of X = 28 (given in statement 1)
So X = 28*100/70 = 40.
So forty students are studying science. And 40-28 = 12 students are studying science but not biology (SUFFICIENT)

I hope this resolves all of yours query.

Posted from my mobile device

Hi yashikaaggarwal
Assuming Biology as a branch of Science may not work here, since it is not mentioned explicitly. Assuming something from real world to be applicable in GMAT questions may not be necessary.
But if we assume that OA may be C.

Key takeaway is to realize that Biology is a subsection of Science. So if you going to set up a double matrix, it should look like this (First Figure), we are trying to solve for the square section:

Statement 1:
Using the information from statement 1, we should get a double matrix like this: (Second Figure).
We don't know the value of people taking science classes, so Statement 1 is insufficient.
Note; we can use any number values as long its a 28/72 split. I used 100 because it's easy to use 100 for percents

Statement 2: We only know the percentage splits of people taking science classes, but we don't know the total of all students.
So statement 2 is insufficient

Both Statements:
We get that .7x = 28, so we can find the value of x.
Plug that value into .3(x) and we can figure out the percent of the students who are enrolled in a science course but are not enrolled in a biology course

Yes, normally we cannot assume anything in GMAT. Which is why it took me a while to get the answer for this. But Biology is a Science. That is not an assumption. Like Earth is a planet. It's a fact. Explanation below.

total Students at the University = 100
Biology is a Science. So Biology will be a subset of the Science Group.
Let number of Students taking
Science = X
Biology = Y
Answer X-Y

Statement 1:
Y = 28
Insufficient

Statement 2:
(7/10) * X = Y
Insufficient

Statements 1 & 2 Together:
(7/10) * X = 28
X = (28 * 10)/7
X = 40
Answer X-Y = 40 - 28 = 12
Sufficient

Hi Members / Experts,

Why aren't we considering "Neither" Science or Biology?

Bunuel chetan2u

Hi,

There is no requirement of that anywhere. There must be some who are not doing science course.

Neither 'science or biology' would be same as Not science, as science encompasses biology.

I simply don't understand the logic of this question, why would you demarcate science and biology in the first place if one must consider biology as a field of science. and simply saying: "oh yes, but that's why this is a trick question" does not make a sound logic.

Let total number of students = 100

28 are enrolled in biology.

This amounts to 70 % of all students enrolled in a science course.

28 = 0,7x --> x = 40

12 students are enrolled in a science course but not in a biology course.

Statement 2 should mean , If Science is X - then B is 0.7X.
But it conveys
S&B ( Cases where science and biology taken by students) is 0.7

chetan2u

after studying for gmat for 2+years, i can't accept this assumption, on a test day i wont know the level of the question and i would straight away go for E as the answer, if any one tells me that i have to assume biology is part of science in this question i would not take that as answer as on test day , gmat should be testing my assumption skills in CR section , the exam is already very daunting as is. this is unacceptable