Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Of the 200 students at College T majoring in one or more of [#permalink]

Show Tags

29 Dec 2012, 05:57

3

This post received KUDOS

48

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

55% (hard)

Question Stats:

70% (01:45) correct 30% (01:43) wrong based on 1610 sessions

HideShow timer Statistics

Of the 200 students at College T majoring in one or more of the sciences, 130 are majoring in chemistry and 150 are majoring in biology. If at least 30 of the students are not majoring in either chemistry or biology, then the number of students majoring in both chemistry and biology could be any number from

(A) 20 to 50 (B) 40 to 70 (C) 50 to 130 (D) 110 to 130 (E) 110 to 150

Of the 200 students at College T majoring in one or more of the sciences, 130 are majoring in chemistry and 150 are majoring in biology. If at least 30 of the students are not majoring in either chemistry or biology, then the number of students majoring in both chemistry and biology could be any number from

(A) 20 to 50 (B) 40 to 70 (C) 50 to 130 (D) 110 to 130 (E) 110 to 150

Since given that {Neither}>=30, then {Both} - 80>=30 --> {Both}>=110.

Now, as the number of students majoring in both chemistry and biology cannot possibly be more than the number of students majoring in either of sciences, then 110<={Both}<=130.

Re: Of the 200 students at College T majoring in one or more of [#permalink]

Show Tags

18 Aug 2013, 04:22

1

This post received KUDOS

1

This post was BOOKMARKED

Let X be the number majoring in Both Chemistry and Biology .

Then

130-X+X+150-X+GT30 = 200

X= GT110 ( Here GT=Greater than )

X>= 110

And as one of the set consists of only 130 , the maximum value cannot exceed 130.

110<=X<=130
_________________

Rgds, TGC! _____________________________________________________________________ I Assisted You => KUDOS Please _____________________________________________________________________________

Re: Of the 200 students at College T majoring in one or more of [#permalink]

Show Tags

18 Sep 2014, 08:05

1

This post received KUDOS

Bunuel wrote:

Walkabout wrote:

Of the 200 students at College T majoring in one or more of the sciences, 130 are majoring in chemistry and 150 are majoring in biology. If at least 30 of the students are not majoring in either chemistry or biology, then the number of students majoring in both chemistry and biology could be any number from

(A) 20 to 50 (B) 40 to 70 (C) 50 to 130 (D) 110 to 130 (E) 110 to 150

Since given that {Neither}>=30, then {Both} - 80>=30 --> {Both}>=110.

Now, as the number of students majoring in both chemistry and biology cannot possibly be more than the number of students majoring in either of sciences, then 110<={Both}<=130.

Answer: D.

Bunuel, I have a question. I'm a bit confused about the wording:

to me the current stem (....at least 30 of the students are not majoring in either chemistry or biology.....) sounds like "at least 30 students are majoring in only one subject, chem or bio". However, the only way to solve the problem is to apply that at least 30 students relate to the section "neither".

Additionally, at the beginning of the stem it is provided that "Of the 200 students at College T majoring in one or more of the sciences.....". To me it sound like each of the students is majoring in at least one subject, bio or che.

Am I wrong? Apologies if the question is stupid - I'm not a native speaker

Of the 200 students at College T majoring in one or more of the sciences, 130 are majoring in chemistry and 150 are majoring in biology. If at least 30 of the students are not majoring in either chemistry or biology, then the number of students majoring in both chemistry and biology could be any number from

(A) 20 to 50 (B) 40 to 70 (C) 50 to 130 (D) 110 to 130 (E) 110 to 150

Since given that {Neither}>=30, then {Both} - 80>=30 --> {Both}>=110.

Now, as the number of students majoring in both chemistry and biology cannot possibly be more than the number of students majoring in either of sciences, then 110<={Both}<=130.

Answer: D.

Bunuel, I have a question. I'm a bit confused about the wording:

to me the current stem (....at least 30 of the students are not majoring in either chemistry or biology.....) sounds like "at least 30 students are majoring in only one subject, chem or bio". However, the only way to solve the problem is to apply that at least 30 students relate to the section "neither".

Additionally, at the beginning of the stem it is provided that "Of the 200 students at College T majoring in one or more of the sciences.....". To me it sound like each of the students is majoring in at least one subject, bio or che.

Am I wrong? Apologies if the question is stupid - I'm not a native speaker

1. At least 30 of the students are not majoring in either chemistry or biology, means that there are at least 30 of the students who are majoring in something else, maybe in math (so neither chemistry nor biology).

2. Of the 200 students at College T majoring in one or more of the sciences, means that all of them are majoring in at least one of the sciences BUT this does not mean that they are majoring only in chemistry or in biology. There might be some other sciences, so there might be some students who are not majoring in either chemistry or biology.

C= Chemistry NC= not Chemistry B= Biology NB= not Biology

We start by adding the values we know:200, 30 the least, 130, 150. 200-150= 50, so we add 50 under NB for ALL. 50-30= 20. Since 30 was the least possible, 20 is the most possible. 130-20=110. Since 20 was the most, 110 is the most. Otherwise, if BC is 111, C-ALL would be 131.

So, the first row gives us the answer: 110 to 130. ANS D

Of the 200 students at College T majoring in one or more of the sciences, 130 are majoring in chemistry and 150 are majoring in biology. If at least 30 of the students are not majoring in either chemistry or biology, then the number of students majoring in both chemistry and biology could be any number from

(A) 20 to 50 (B) 40 to 70 (C) 50 to 130 (D) 110 to 130 (E) 110 to 150

This is how I would do this question: Total 200 students, Chemistry (130), Biology(150), Neither (30)

So let's ignore 30 of the 200 and we only have to worry about the 170 students who do take Chemistry or Biology. So our relevant total is 170.

Out of these 170, 130 take Chemistry. Let's say that the rest 40 take Biology but then, the leftover 110 of Biology must overlap with Chemistry. So the overlap must be at least 110. The other side of the situation is that all 130 of Chemistry take Biology too so the overlap in that case will be 130.

This gives us that the range of students majoring in both could be anywhere from 110 to 130.

Re: Of the 200 students at College T majoring in one or more of [#permalink]

Show Tags

06 Nov 2015, 13:20

Walkabout wrote:

Of the 200 students at College T majoring in one or more of the sciences, 130 are majoring in chemistry and 150 are majoring in biology. If at least 30 of the students are not majoring in either chemistry or biology, then the number of students majoring in both chemistry and biology could be any number from

(A) 20 to 50 (B) 40 to 70 (C) 50 to 130 (D) 110 to 130 (E) 110 to 150

Re: Of the 200 students at College T majoring in one or more of [#permalink]

Show Tags

28 Apr 2016, 18:47

So I did this one with a grid set up Given: ..............Bio...................Not . . Chem......BC..................CN...........................130 . . Not.........BN..............NN 30<=x<=50............70=(200-130) . . .............150..................50= (200-150)..........T = 200

^^This will hold true throughout the problem

Since we know that the minimum in NN has to be 30, we also know the max has to be 50 With NN at minimum 30, we know that BN must equal 40, CN must equal 20, and BC is minimum 110 With NN at maximum 50, we know that BN must equal 20, CN must equal 0, and BC is maximum 130

Of the 200 students at College T majoring in one or more of the sciences, 130 are majoring in chemistry and 150 are majoring in biology. If at least 30 of the students are not majoring in either chemistry or biology, then the number of students majoring in both chemistry and biology could be any number from

(A) 20 to 50 (B) 40 to 70 (C) 50 to 130 (D) 110 to 130 (E) 110 to 150

Solution:

This is an overlapping set question that is testing our ability to solve for maximum and minimum values. We know this because the answer choices each provide a range of values. The best way to solve this problem would be to set up a table with two categories: chemistry and biology. More specifically, our table will be labeled as follows:

1) Majored in chemistry (Chemistry)

2) Did not major in chemistry (No Chemistry)

3) Majored in biology (Biology)

4) Did not major in biology (No Biology)

We are given:

Total = 200

Chemistry = 130

Biology = 150

No Chemistry and No Biology = at least 30

We can fill all this into our table. Remember, all the columns and rows sum together.

Now that we have our chart initially filled in, we can determine the greatest and least number of students who majored in biology and chemistry.

Because we are given that at least 30 students majored in neither biology or chemistry, let’s assume that this number is exactly 30 students. Using the value 30 as the "No Chemistry-No Bio" entry, we can solve for the remaining entries in the table by subtraction.

We see that there are 110 students who majored in both biology and chemistry. Even though at this point we don’t know whether this is the maximum or the minimum number of students who could major in both sciences, we can guess it’s a minimum by looking at the answer choices given. Furthermore, if that is the case, the answer must be either choice D or E.

Now, if 110 is indeed the minimum, how can we find the maximum? Recall that we used 30 as the number of students who majored in neither science, and 30 is the smallest number we can use for the “No Chemistry-No Bio” entry. So, now let’s find the largest number we can use for that entry. Recall that there are a total of 50 students who did not major in Bio, so the “No Chemistry-No Bio” entry can be at most 50. That is, the largest number we can use for that entry is 50. Now let’s fill in the rest of the table.

We see that there are now 130 students who majored in both biology and chemistry, which is also the maximum number of students who could major in both sciences.

The answer is D.
_________________

Scott Woodbury-Stewart Founder and CEO

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

Re: Of the 200 students at College T majoring in one or more of [#permalink]

Show Tags

23 Nov 2017, 21:36

Walkabout wrote:

Of the 200 students at College T majoring in one or more of the sciences, 130 are majoring in chemistry and 150 are majoring in biology. If at least 30 of the students are not majoring in either chemistry or biology, then the number of students majoring in both chemistry and biology could be any number from

(A) 20 to 50 (B) 40 to 70 (C) 50 to 130 (D) 110 to 130 (E) 110 to 150

hi

when "none" is at least 30, the total value is 170 so overlapping is ( 130 + 150 - 170) = 110

however, as 150 students are majoring biology, "none" can also be 50 in this case overlapping will be (130 + 150 - 150) = 130