In College X the number of students enrolled in both a

Question

In College X the number of students enrolled in both a chemistry course and a biology course is how much less than the number of students enrolled in neither?

(1) In College X there are 60 students enrolled in a chemistry course.
(2) In College X there are 85 students enrolled in a biology course.

Bunuel · Accepted Answer

SOLUTION

In College X the number of students enrolled in both a chemistry course and a biology course is how much less than the number of students enrolled in neither?

{Total} = {Chemistry} + {Biology} - {Both} + {Neither} .

The question asks to calculate  {Neither} - {Both} .

(1) In College X there are 60 students enrolled in a chemistry course.  {Chemistry} = 60 . Not sufficient.
(2) In College X there are 85 students enrolled in a biology course.  {Biology} = 85 . Not sufficient.

(1)+(2)  {Chemistry} = 60  and  {Biology} = 85 . Still not sufficient to get  {Neither} - {Both} .

Answer: E.

rajareena · Answer

Level: 600

Unless we know the total population and/or overlapping set, we will not be able to find the difference between neither and both.

Hence E.

Fanja91 · Answer

We're being asked how many the students are that enrolled in both Ch and Bio in comparison to the ones that did not enroll in any of the two classes.

In statement 1 we're given the amount of Ch students. We're still in need of Bio and the students that didn't enroll in any of the two classes.

Statement 2 gives us the amount of Bio students. We're still missing the last part with students that did not enroll in any.

Hence, E.

sandy2105 · Answer

BOTH the statements are inconclusive as they do not give any information about 1 . total no of students 2 overlapping set 3. null set kudos me if you can :twisted:

bimalr9 · Answer

What would be the answer if the total was given in the question?

Total= Set A + Set B - intersection. Isn't this sufficient to calculate total? Do we need neither. Neither can be zero, can't it?

I would have gone with C if total was given.

kamranko · Answer

x+y - both + neither

we just have x and y 
nothing else 
so we cannot solve this one
E

JeffTargetTestPrep · Answer

An easy way to solve this problem is to set up a double set matrix. In our matrix, we have two main categories: biology and chemistry. More specifically, our table will be labeled with:

1) Number of people who are enrolled in chemistry (Chem)

2) Number of people who are not enrolled in chemistry (No Chem)

3) Number of people who are enrolled in biology (Bio)

4) Number of people who are not enrolled in biology (No Bio)

(To save room on our table headings we will use the abbreviations for the categories.)

We need to determine the difference between the number of students who are enrolled in both chemistry and biology and the number of students who are enrolled in neither course.

Although we are not provided any given information, we can create our table.

https://i.imgur.com/tG395GM.png

Statement One Alone:

In College X there are 60 students enrolled in a chemistry course.

Let’s fill the information from statement one into our table.

https://i.imgur.com/nN1QXe0.png

The information in statement one is not enough to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

In College X there are 85 students enrolled in a biology course.

https://i.imgur.com/Hd7z969.png

The information in statement two is not enough to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

https://i.imgur.com/bbE4Bzm.png

Without more information, we cannot answer the question.

Answer: E

ProfX · Answer

E it is. I end up spending a lot of time in this kind of questions to figure out what the catch is (ultimately find that there is none)

Sent from my iPhone using  GMAT Club Forum mobile app

herbgatherer · Answer

It is clear that statements (a), (b) do not help in answering the question. (a) + (b) too, is insufficient.
Answer: E

Hope the representation helps.

Shiv2016 · Answer

In official guide, several values are being tested before eliminating an answer choice. When should we really test value? Or should we always test values ?

arvind910619 · Answer

Imo E
We can not arrive at the solution from both of these statements 
We need total number of students and number of students who went to both the classes.

Sent from my ONE E1003 using  GMAT Club Forum mobile app

TheKingInTheNorth · Answer

In College X the number of students enrolled in both a chemistry course and a biology course is how much less than the number of students enrolled in neither?

(1) In College X there are 60 students enrolled in a chemistry course.
(2) In College X there are 85 students enrolled in a biology course.

Refer the attached file .

Attachment:

og.png [ 22.33 KiB | Viewed 26116 times ]

EMPOWERgmatRichC · Answer

Hi All,

We're asked to determine how much LESS the number of students enrolled in BOTH a chemistry course and a biology course is relative to the number of students enrolled in NEITHER. The wording of this prompt implies that we're dealing with a standard Overlapping Sets question, so we can use the Overlapping Sets formula to solve it:

Total = (Group 1) + (Group 2) - Both + Neither

1) In College X there are 60 students enrolled in a chemistry course.

Fact 1 tells us one of the Groups, but nothing else. 
Fact 1 is INSUFFICIENT

2) In College X there are 85 students enrolled in a biology course.

Fact 2 tells us one of the Groups, but nothing else. 
Fact 2 is INSUFFICIENT

Combined, we can fill in 2 parts of the formula:

Total = (60) + (85) - Both + Neither

There's no way to determine any of the other values though. 
Combined, INSUFFICIENT

Final Answer:  E

GMAT assassins aren't born, they're made, 
Rich

CEdward · Answer

Answer is E.

We are only given two quantities, but we don't know:

-Total # 
-# who took C and B
-# who took C or B only
-# who took neither

Too many missing quantities.

GMATinsight · Answer

Answer: Option E

Video solution by  GMATinsight

https://www.youtube.com/watch?v=R-HcLiVk4XI

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In College X the number of students enrolled in both a

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