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At a certain high school, the junior class is twice the size of the se

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kashishh
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At a certain high school, the junior class is twice the size of the se [#permalink] New post   21 May 2012, 05:29
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At a certain high school, the junior class is twice the size of the senior class. If 1/3 of the seniors & 1/4 of the juniors study Japanese, what fraction of the students in both classes do not study Japanese?

A. 1/6
B. 5/18
C. 5/12
D. 7/12
E. 13/18

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Is it possible to do as follows?
1/3*s+1/4*2s = study japanese
then 5/6 * s = study japanese and 1/6 do not
why is this wrong?
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E
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Bunuel
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Re: At a certain high school, the junior class is twice the size of the se [#permalink] New post   21 May 2012, 06:25
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kashishh wrote:
At a certain high school, the junior class is twice the size of the senior class. If 1/3 of the seniors & 1/4 of the juniors study Japanese, what fraction of the students in both classes do not study Japanese?

A. 1/6
B. 5/18
C. 5/12
D. 7/12
E. 13/18

Is it possible to do as follows?
1/3*s+1/4*2s = study japanese
then 5/6 * s = study japanese and 1/6 do not
why is this wrong?


If we do the way you proposed then the # of the students that study Japanese is 1/3*s+1/4*2s=5s/6. Since the total # of the students is s+2s=3s then the # of the students that does not study Japanese is 3s-5s/6=13s/6, so fraction of the students that do not study Japanese is (13s/6)/3s=13/18.

Answer: E.

Else you can do as follows: say there are 6 seniors and 2*6=12 juniors, so total of 6+12=18 students.

2/3 of the seniors do not study Japanese, so 2/3*6=4 seniors do not study Japanese;
3/4 of the juniors do not study Japanese, so 3/4*12=9 juniors do not study Japanese;

Total of 4+9=13 students do not study Japanese, which is 13/18 of all students.


Answer: E.

Hope it helps.
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Re: At a certain high school, the junior class is twice the size of the se [#permalink] New post   02 Sep 2014, 23:11
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Let strength of senior class = x

Strength of junior class = 2x

Total = 3x

Japanese Speaking\(= \frac{x}{2} + \frac{x}{3} = \frac{5x}{6}\)

Not Japanese speaking \(= 3x - \frac{5x}{6} = \frac{13x}{6}\)

Fraction \(= \frac{\frac{13x}{6}}{3x} = \frac{13}{18}\)

Answer = E
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Re: At a certain high school, the junior class is twice the size of the se [#permalink] New post   06 Dec 2016, 10:55
kashishh wrote:
At a certain high school, the junior class is twice the size of the senior class. If 1/3 of the seniors & 1/4 of the juniors study Japanese, what fraction of the students in both classes do not study Japanese?

A. 1/6
B. 5/18
C. 5/12
D. 7/12
E. 13/18

Is it possible to do as follows?
1/3*s+1/4*2s = study japanese
then 5/6 * s = study japanese and 1/6 do not
why is this wrong?




J = junior class size
S = senior class size
Total class size = J+S = 3S ( because J= 2S)

2/3 S and 3/4J don't study Japanese.
Total number not studying Japanese = (2/3)S + (3/4)J= (2/3)S + (3/4) * 2S
= (13/6)S

So required fraction = [(13/6)S]/3S = 13/18

Hope this helps.
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Re: At a certain high school, the junior class is twice the size of the se [#permalink] New post   06 Dec 2016, 11:05
kashishh wrote:
At a certain high school, the junior class is twice the size of the senior class. If 1/3 of the seniors & 1/4 of the juniors study Japanese, what fraction of the students in both classes do not study Japanese?

A. 1/6
B. 5/18
C. 5/12
D. 7/12
E. 13/18


Let the no of students in Senior Class be 6
So, the no of students in Junior Class be 12

Total No of Students is 18

So, 2 students of Senior Class study Japanese
And, 3 students of Junior Class study Japanese

Students who study Japanese is 5

Hence, 13 students do not study Japanese.

Thus, fraction of the students in both classes do not study Japanese is 13/18

Hence, answer will be (E) 13/18
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At a certain high school, the junior class is twice the size of the se [#permalink] New post   06 Oct 2018, 07:31
kashishh wrote:
At a certain high school, the junior class is twice the size of the senior class. If 1/3 of the seniors & 1/4 of the juniors study Japanese, what fraction of the students in both classes do not study Japanese?

A. 1/6
B. 5/18
C. 5/12
D. 7/12
E. 13/18

Show Spoiler
Is it possible to do as follows?
1/3*s+1/4*2s = study japanese
then 5/6 * s = study japanese and 1/6 do not
why is this wrong?


Let there be 60 junior and 30 senior students

hence 1/3*3 = 10 and 1/4*60 = 15

so 25 students study Japenese

90-25 =65 students who dont study japanese

65/90 i.e 13/18 is fraction of the students in both classes do not study Japanese
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Re: At a certain high school, the junior class is twice the size of the se [#permalink] New post   03 Apr 2019, 18:04
Expert Reply
kashishh wrote:
At a certain high school, the junior class is twice the size of the senior class. If 1/3 of the seniors & 1/4 of the juniors study Japanese, what fraction of the students in both classes do not study Japanese?

A. 1/6
B. 5/18
C. 5/12
D. 7/12
E. 13/18


We can let the number of juniors = 240 and the number of seniors = 120.

Thus, 1/3 x 120 = 40 seniors study Japanese and 1/4 x 240 = 60 juniors study Japanese.

In other words, 80 seniors and 180 juniors do not study Japanese. Therefore, the fraction of the students in both classes not studying Japanese is:

(80 + 180)/360 = 260/360 = 26/36 = 13/18

Answer: E
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Re: At a certain high school, the junior class is twice the size of the se [#permalink] New post   31 Aug 2021, 23:39
Expert Reply
Hey guys,

When you have unknowns, it's useful to use variables

Let's say that:

x = # of juniors

and

y = # of seniors

x = 2y

Lets use theoretical numbers that are easy to work with

Let's say x = 120 and y = 60

A third of seniors study Japanese or:

\(\frac{1}{3 }\)(60) = 20

A quarter of juniors study Japanese or:

\(\\
\frac{1}{4}\) (120) = 30

The total number of students in question is x + y = 180

20 + 30 = 50 study Japanese

That means that 130 do not study Japanese

In fraction form:

\(\frac{130}{180}\) do not study Japanese = \(\frac{13}{18}\) of all students

The answer is E
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Re: At a certain high school, the junior class is twice the size of the se [#permalink] New post   19 Feb 2024, 12:20
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