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

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Joined: 02 Dec 2012
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Of the 200 students at College T majoring in one or more of the [#permalink]

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29 Dec 2012, 06:57
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70% (01:45) correct 30% (01:40) wrong based on 1900 sessions

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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
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Posts: 46283
Re: Of the 200 students at College T majoring in one or more of the [#permalink]

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29 Dec 2012, 07:03
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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

$${Total} = {Chemistry } + {Biology} - {Both} + {Neither}$$;

$$200 = 130 + 150 - {Both} + {Neither}$$;

$${Neither} = {Both} - 80$$.

Since given that $${Neither} \geq 30$$, then $${Both} - 80 \geq 30$$ --> $${Both} \geq 110$$.

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 $$110 \leq {Both} \leq 130$$.

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

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18 Aug 2013, 05:22
1
1
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
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Re: Of the 200 students at College T majoring in one or more of the [#permalink]

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18 Sep 2014, 09:05
1
Bunuel 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

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

200 = 130 + 150 - {Both} + {Neither} --> {Neither} = {Both} - 80.

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.

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
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Joined: 02 Sep 2009
Posts: 46283
Re: Of the 200 students at College T majoring in one or more of the [#permalink]

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18 Sep 2014, 11:19
1
Maksym wrote:
Bunuel 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

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

200 = 130 + 150 - {Both} + {Neither} --> {Neither} = {Both} - 80.

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.

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.

Hope it's clear.
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Re: Of the 200 students at College T majoring in one or more of the [#permalink]

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18 Sep 2014, 20:49
I realized that students in both subjects are >=110, so stuck between D and E. Thanks Bunuel for explanation
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Re: Of the 200 students at College T majoring in one or more of the [#permalink]

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02 Oct 2014, 03:22
10
1
Refer diagram below:

Attachment:

sqa.png [ 4.78 KiB | Viewed 22300 times ]

130 + 150-x + 30 = 200

x = 110

Least of Chemistry(130) & Biology(150) is Chemistry = 130

Range = 110 to 130

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

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10 Jan 2015, 19:59
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Re: Of the 200 students at College T majoring in one or more of the [#permalink]

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20 Jan 2015, 12:12
I created a table like this:

__________B_________NB_________ALL
C.........110most........20most............130
NC.........40least........30least..................
ALL............150..............50...............200

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

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26 Feb 2015, 23:57
2
1
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.

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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Director Joined: 10 Mar 2013 Posts: 562 Location: Germany Concentration: Finance, Entrepreneurship GMAT 1: 580 Q46 V24 GPA: 3.88 WE: Information Technology (Consulting) Re: Of the 200 students at College T majoring in one or more of the [#permalink] ### Show Tags 04 Sep 2015, 01:18 3 1 We can use here a double matrix (see MGMAT - Word Problems) Attachments PS 222.JPG [ 19.13 KiB | Viewed 18691 times ] _________________ When you’re up, your friends know who you are. When you’re down, you know who your friends are. Share some Kudos, if my posts help you. Thank you ! 800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50 GMAT PREP 670 MGMAT CAT 630 KAPLAN CAT 660 Intern Joined: 17 Feb 2013 Posts: 11 Re: Of the 200 students at College T majoring in one or more of the [#permalink] ### Show Tags 06 Nov 2015, 14:20 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 [from;to] inclusive or [min;max] denotes a range 1. [30;50] 2. [50-50;50-30]=[0;20] 3. [130-20;130-0]=[110;130] Attachments IMG_20151106_211502.jpg [ 838.48 KiB | Viewed 17705 times ] Current Student Joined: 23 Mar 2016 Posts: 33 Schools: Tulane '18 (M) Re: Of the 200 students at College T majoring in one or more of the [#permalink] ### Show Tags 28 Apr 2016, 19:47 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 Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 2772 Location: United States (CA) Re: Of the 200 students at College T majoring in one or more of the [#permalink] ### Show Tags 02 May 2016, 09:13 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 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 Manager Joined: 23 Jun 2009 Posts: 196 Location: Brazil GMAT 1: 470 Q30 V20 GMAT 2: 620 Q42 V33 Re: Of the 200 students at College T majoring in one or more of the [#permalink] ### Show Tags 12 Sep 2016, 09:44 My 2 cents with credi to Magoosh Attachments Screenshot_20160912-140617.jpg [ 676.14 KiB | Viewed 12713 times ] Senior Manager Status: love the club... Joined: 24 Mar 2015 Posts: 275 Re: Of the 200 students at College T majoring in one or more of the [#permalink] ### Show Tags 23 Nov 2017, 22:36 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 so, 110 <= both <= 130 cheers through the kudos button if this helps EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 11814 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Re: Of the 200 students at College T majoring in one or more of the [#permalink] ### Show Tags 30 Jan 2018, 14:50 Hi All, This question can be solved rather handily with the Tic-Tac-Toe board, but you can also use the Overlapping Sets Formula here (although it won't be applicable on every Overlapping Sets question that you might see on Test Day). This prompt comes with a couple of 'twists' to it: 1) The number of students who study 'neither' is NOT a fixed value - it's a range. 2) The question asks for the RANGE of students who could study both Chemistry and Biology. Here's how you can use the Formula though... Total = Gp.1 + Gp.2 - Both + Neither 200 = 130 + 150 - B + (>=30) 200 = 280 - B + (>=30) 200 = (>=310) - B B = >=110 This gives you the 'lower end' of the range, but does not immediately give you the 'upper end.' To find that, you have to think about the numbers involved. Since 130 students study Chemistry and 150 study Biology, the MAXIMUM number who could study both would be 130 (and that's if EVERY Chemistry student also studied Biology). Thus, the range is 110 to 130, inclusive. Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: Of the 200 students at College T majoring in one or more of the [#permalink]

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25 Mar 2018, 04:20
VeritasPrepKarishma 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

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.

VeritasPrepKarishma i am bit confised with you solution cause we could have second option as well - see below the remake can you advise whats wrong with it ?

Out of these 170, 150 take Biology. Let's say that the rest 20 take Chemistry but then, the leftover 110 of Chemistry must overlap with Biology. So the overlap must be at least 110.
The other side of the situation is that all 150 of Biology take take Chemistry too so the overlap in that case will be 150
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Re: Of the 200 students at College T majoring in one or more of the [#permalink]

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25 Mar 2018, 04:30
1
dave13 wrote:
VeritasPrepKarishma 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

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.

VeritasPrepKarishma i am bit confised with you solution cause we could have second option as well - see below the remake can you advise whats wrong with it ?

Out of these 170, 150 take Biology. Let's say that the rest 20 take Chemistry but then, the leftover 110 of Chemistry must overlap with Biology. So the overlap must be at least 110.
The other side of the situation is that all 150 of Biology take take Chemistry too so the overlap in that case will be 150

Note the constraint that only 130 are majoring in Chemistry. Then the overlap cannot be 150.
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Re: Of the 200 students at College T majoring in one or more of the   [#permalink] 25 Mar 2018, 04:30
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