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# Every student of a certain school must take one and only one

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Every student of a certain school must take one and only one [#permalink]

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19 Feb 2012, 06:30
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Difficulty:

35% (medium)

Question Stats:

78% (09:57) correct 22% (03:40) wrong based on 192 sessions

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Every student of a certain school must take one and only one elective course. In last year, 1/2 of the students took biology as an elective, 1/3 of the students took chemistry as an elective, and all of the other students took physics. In this year, 1/3 of the students who took biology and 1/4 of the students who took chemistry left school, other students did not leave, and no fresh student come in. What fraction of all students took biology and took chemistry?

A. 7/9
B. 6/7
C. 5/7
D. 4/9
E. 2/5
[Reveal] Spoiler: OA

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-Aravind Chembeti

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Re: Every student of a certain school must take one and only one [#permalink]

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19 Feb 2012, 06:37
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Lets pick smart numbers. Total number of students: 12

Biology (1/2): 6
Chemistry (1/3): 4
Physics (1/6): 2

After leaving school
Biology: 4
Chemistry: 3
Physics: 2

New Total number of students: 9
Biology and Chemistry: 7

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Re: Every student of a certain school must take one and only one [#permalink]

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05 Mar 2013, 20:11
2
KUDOS
I did in this way (was wrong earlier)

Biology = 1/2
Chemistry = 1/3
So, physics = 1 - (1/2+1/3) = 1/6

Biology students left = (1/2)/3 = 1/6. So remaining = 1/2 - 1/6 = 1/3 ------------- (i)
Chemistry students left = (1/3)/4 = 1/12. So remaining = 1/3 - 1/12 = 1/4 --------------- (ii)

Total Biology & Chemistry students left = (i) + (ii) = 7/12
Total all students left = 7/12 + 1/6 = 9/12 = 3/4

So the fraction comes up as (7/12) / (3/4) = 7/9

the
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Re: Every student of a certain school must take one and only one [#permalink]

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03 Jan 2014, 07:28
MSoS wrote:
Lets pick smart numbers. Total number of students: 12

Biology (1/2): 6
Chemistry (1/3): 4
Physics (1/6): 2

After leaving school
Biology: 4
Chemistry: 3
Physics: 2

New Total number of students: 9
Biology and Chemistry: 7

Agree with MSOS , as soon as I see fractions on answer choices you know what's the first thing that comes to my mind? Yup, you got it!

'Smart Numbers'

Those two beautiful words can do miracles in questions such as this one

Good job

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Re: Every student of a certain school must take one and only one [#permalink]

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31 Jan 2014, 06:08
1
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Chembeti wrote:
Every student of a certain school must take one and only one elective course. In last year, 1/2 of the students took biology as an elective, 1/3 of the students took chemistry as an elective, and all of the other students took physics. In this year, 1/3 of the students who took biology and 1/4 of the students who took chemistry left school, other students did not leave, and no fresh student come in. What fraction of all students took biology and took chemistry?

A. 7/9
B. 6/7
C. 5/7
D. 4/9
E. 2/5

The answer is A but the wording is quite poor. The question should ask what fraction of the remaining students took biology or chemistry

That will make the question more clear

Anyways if you pick 120 as a Smart Numbers you get 70/90 = 7/9 (A)

Just my 2c

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Re: Every student of a certain school must take one and only one [#permalink]

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31 Jan 2014, 12:15
Chembeti wrote:
Every student of a certain school must take one and only one elective course. In last year, 1/2 of the students took biology as an elective, 1/3 of the students took chemistry as an elective, and all of the other students took physics. In this year, 1/3 of the students who took biology and 1/4 of the students who took chemistry left school, other students did not leave, and no fresh student come in. What fraction of all students took biology and took chemistry?

A. 7/9
B. 6/7
C. 5/7
D. 4/9
E. 2/5

This is kind of confusing. Shouldn't the question be asking what fraction of students took either biology or chemistry?
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Every student of a certain school must take one and only one [#permalink]

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24 Dec 2014, 10:14
What fraction of all students took biology and took chemistry? OR
What fraction of the remaining students took biology and took chemistry?

For the former correct answer will be 5/6 [(1/2+1/3)/(1)] and for the later correct answer will be 7/9[(1/2*2/3+1/3*3/4)/(1/3+1/4+1/6)].

It took me 7 minutes to understand that too after matching the answers that what exactly the question is ??

Chembeti wrote:
Every student of a certain school must take one and only one elective course. In last year, 1/2 of the students took biology as an elective, 1/3 of the students took chemistry as an elective, and all of the other students took physics. In this year, 1/3 of the students who took biology and 1/4 of the students who took chemistry left school, other students did not leave, and no fresh student come in. What fraction of all students took biology and took chemistry?

A. 7/9
B. 6/7
C. 5/7
D. 4/9
E. 2/5

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Re: Every student of a certain school must take one and only one [#permalink]

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20 Feb 2016, 10:31
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Re: Every student of a certain school must take one and only one [#permalink]

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20 Feb 2016, 22:56
Let's use 120 as the total number of students. (Using 120 because the fractions 1/3 and 1/4 so a multiple of 12 will work)

1st year:
Biology: 1/2 *120 = 60
Chemistry: 1/3*120 = 40
Physics: 20 (remaining students)

2nd year:
Students who left from Biology(60) and Chemistry(40): 1/3*60 + 1/4*40 = 30
Students left in school taking Biology and Chemistry = 60 + 40 - 30 = 70
Students left in school = 120 - 30 = 90
Fraction of students taking Biology and Chemistry = 70/90 = 7/9

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Re: Every student of a certain school must take one and only one   [#permalink] 20 Feb 2016, 22:56
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