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# At least 100 students at a certain high school study

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SVP
Joined: 04 May 2006
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Schools: CBS, Kellogg
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At least 100 students at a certain high school study [#permalink]  02 May 2008, 22:53
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 school study 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

Detail explaination will be appreciated!
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Manager
Joined: 06 Feb 2008
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Re: Set [#permalink]  03 May 2008, 00:54
Answer is C i.e. both statements are necessary.

Japenese learning students = 100.
Let French learning student = x
then we can say student learning Jap along with French = 0.04x

so as per statement 1 and 2

16 = 0.04x + 10
x = 150

So,number of student learning Jap are more then learning French as per data given.

Hope this helps..!!!
Director
Joined: 01 Jan 2008
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Re: Set [#permalink]  03 May 2008, 00:55
The question says atleast 100 study Japanese.. It doesnt say 100 study Japanese .
Fact 1 : Also we are given that 4% of french students also study Japenese.

Now statement 1 says: 16 students at the school study both French and japanese . This will give us no of French students. (Using Fact1) But gives us no input on Japanese students . Hence A not applicable. Therefore BCE

Now statement 2 tells us 10% of the students at the school who study Japanese also study French.

10% of the students at the school who study Japanese also study French = 4% of french students who study Japenese.

This means that No of French students is more than Japanese , as smaller percentage of a larger value is equated to larger percentage of a smaller value . For eq. ( 10% of 100 = 10 , 4 % of 250 = 10 )

Hope it helps
Director
Joined: 14 Jan 2007
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Re: Set [#permalink]  03 May 2008, 07:55
Should be 'B'.

Common students i.e. J intersection F = 4% of French = 10% of Japanese
Hence French > Japanese
Manager
Joined: 22 Dec 2007
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Re: Set [#permalink]  03 May 2008, 11:32
I agree with B as well.

1st condition fixes the common students to 16 but this means that the # of french students can be less than or greater than the # of japanese students. So not sufficient.

2nd condition. By plugging in values for the japanese students ( 150 , 300 , etc ) and by using the relation : 10% of japanese = 4% of french
you find that the french students are always more in #.

So its B.
SVP
Joined: 04 May 2006
Posts: 1936
Schools: CBS, Kellogg
Followers: 19

Kudos [?]: 441 [0], given: 1

Re: Set [#permalink]  03 May 2008, 18:35
Thanks, OA is B

I found what I am confused!
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Re: Set   [#permalink] 03 May 2008, 18:35
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