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# At least 100 students at a certain high school study

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Senior Manager
Joined: 23 May 2005
Posts: 266
Location: Sing/ HK
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At least 100 students at a certain high school study [#permalink]

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11 Dec 2006, 02:58
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At least 100 students at a certain high school study Japanese. If 4 percent of the students at the school who study French also study Japanese, do more students at the schoool stude French than Japanese?

(1) 16 students at the school study both French and Japanese
(2) 10% of the students at the school who study Japanese also study French

Looking for the most logical and fastest way to solve this...
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Impossible is nothing

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Joined: 25 Sep 2006
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11 Dec 2006, 04:47
B

Njf + Nj > 100 .................(1)
0.04(Njf + Nf) = Njf which means
24Njf = Nf........................(2)

Question: Nf > Nj ? Finding the ratio of Nf and Nj will do.

I) Njf = 16
We can work out Njf = 384 from (2)
Not sufficient to tell the ratio of Nf/Nj

II) 0.1(Nj + Njf) = Njf which means
Nj = 9Njf
plug this into (2) and you got the ratio of Nj and Nf

Sufficient
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11 Dec 2006, 18:02
Viperace wrote:
B

Njf + Nj > 100 .................(1)
0.04(Njf + Nf) = Njf which means
24Njf = Nf........................(2)

Question: Nf > Nj ? Finding the ratio of Nf and Nj will do.

I) Njf = 16
We can work out Njf = 384 from (2)
Not sufficient to tell the ratio of Nf/Nj

II) 0.1(Nj + Njf) = Njf which means
Nj = 9Njf
plug this into (2) and you got the ratio of Nj and Nf

Sufficient

Viperace,
Can you please explain how did you constructed the part in blue. To me it is not clear how did you get 24Njf = Nf
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Joined: 25 Sep 2006
Posts: 151
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12 Dec 2006, 02:15
dr_sabr wrote:
Viperace wrote:
B

Njf + Nj > 100 .................(1)
0.04(Njf + Nf) = Njf which means
24Njf = Nf........................(2)

Question: Nf > Nj ? Finding the ratio of Nf and Nj will do.

I) Njf = 16
We can work out Njf = 384 from (2)
Not sufficient to tell the ratio of Nf/Nj

II) 0.1(Nj + Njf) = Njf which means
Nj = 9Njf
plug this into (2) and you got the ratio of Nj and Nf

Sufficient

Viperace,
Can you please explain how did you constructed the part in blue. To me it is not clear how did you get 24Njf = Nf

The terminology I used is
Njf = Number of ppl who study Jap AND French
Nf = Number of ppl who study French ONLY
Nj = Number of ppl who study Jap ONLY

It is given 4% of ppl who study french also study japanese, this means
0.04(Njf + Nf) = Njf
simplifying..
0.04Njf + 0.04Nf = Njf
0.04Nf = 0.96Njf
Nf = 24Njf
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livin in a prison island...

12 Dec 2006, 02:15
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