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

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Of the 200 students at College T majoring in one or more of [#permalink] New post 29 Dec 2012, 05:57
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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
[Reveal] Spoiler: OA
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Re: Of the 200 students at College T majoring in one or more of [#permalink] New post 29 Dec 2012, 06:03
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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


{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.

Answer: D.
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Re: Of the 200 students at College T majoring in one or more of [#permalink] New post 18 Aug 2013, 04:22
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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 [#permalink] New post 18 Sep 2014, 08:05
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


{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.

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 :)
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Re: Of the 200 students at College T majoring in one or more of [#permalink] New post 18 Sep 2014, 10:19
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Maksym wrote:
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


{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.

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.

Hope it's clear.
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Re: Of the 200 students at College T majoring in one or more of [#permalink] New post 18 Sep 2014, 19:49
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 [#permalink] New post 02 Oct 2014, 02:22
Refer diagram below:

Attachment:
sqa.png
sqa.png [ 4.78 KiB | Viewed 280 times ]


130 + 150-x + 30 = 200

x = 110

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

Range = 110 to 130

Answer = D
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Re: Of the 200 students at College T majoring in one or more of   [#permalink] 02 Oct 2014, 02:22
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