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# At least 100 students at a certain high school study Japanes

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At least 100 students at a certain high school study Japanes [#permalink]

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31 Aug 2007, 10:25
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46% (02:20) correct 54% (01:30) wrong based on 105 sessions

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At least 100 students at a certain high school study Japanese. If 4 percent of the studetns 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 percent of the students at the school who study Japanese also study French.

OPEN DISCUSSION OF THIS QUESTION IS HERE: at-least-100-students-at-a-certain-high-school-study-japanes-92305.html
[Reveal] Spoiler: OA
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Re: At least 100 students at a certain high school study Japanes [#permalink]

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31 Aug 2007, 13:46
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jp888 wrote:
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 percent of the students at the school who study Japanese also study French

B.

You are trying to find if F/J > 1?
(1) 16 students study both Japanese and French, that's 4% of the total number of students given from the question. So you have
16 = (4/100) * Total
Total = 400 students
You know that at least 100 students study Japanese and 16 studied both. So it could be that 101 students studied Japanese 299 studied French, or vice versa. INSUFFICIENT

(2) (10/100)*J = (4/100)*Total = (4/100)*(J+F)
=> F/J > 3/2
SUFFICIENT
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Re: At least 100 students at a certain high school study Japanes [#permalink]

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31 Aug 2007, 18:02
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jp888 wrote:
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 percent of the students at the school who study Japanese also study French

I got B

used a little different approach for 2nd statement

You are trying to find if F/J > 1?

1 st- copied from bbk post

(1) 16 students study both Japanese and French, that's 4% of the total number of students given from the question. So you have
16 = (4/100) * Total
Total = 400 students
You know that at least 100 students study Japanese and 16 studied both. So it could be that 101 students studied Japanese 299 studied French, or vice versa. INSUFFICIENT

(2) since # of students studying both is the same, I mean it is one.
we have 0.04(French)=0.1(Japanese)----->ratio of French to Japanese is more than 1

Sufficient
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Re: At least 100 students at a certain high school study Japanes [#permalink]

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31 Aug 2007, 18:07
bkk145 wrote:
jp888 wrote:
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 percent of the students at the school who study Japanese also study French

B.

You are trying to find if F/J > 1?
(1) 16 students study both Japanese and French, that's 4% of the total number of students given from the question. So you have
16 = (4/100) * Total
Total = 400 students
You know that at least 100 students study Japanese and 16 studied both. So it could be that 101 students studied Japanese 299 studied French, or vice versa. INSUFFICIENT

(2) (10/100)*J = (4/100)*Total = (4/100)*(J+F)
=> F/J > 3/2
SUFFICIENT

Please explain part in bold...?

Is not

total=F+J-both(F&J)...?

though ultimate result does not change.
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Re: At least 100 students at a certain high school study Japanes [#permalink]

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19 Jun 2014, 05:47
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Re: At least 100 students at a certain high school study Japanes [#permalink]

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19 Jun 2014, 06:06
Expert's post
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jp888 wrote:
At least 100 students at a certain high school study Japanese. If 4 percent of the studetns 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 percent of the students at the school who study Japanese also study French.

Given: $$J\geq{100}$$ and $$0.04*F=Both$$

Question: is $$F>J$$?

(1) $$Both=16=0.04*F$$ --> $$F=400$$. We don't know $$J$$. Not sufficient

(2) $$0.1*J=Both=0.04*F$$ (given) --> $$0.1*J=0.04*F$$ --> $$\frac{F}{J}=\frac{10}{4}$$ --> $$F>J$$. Sufficient.

Answer: B.

OPEN DISCUSSION OF THIS QUESTION IS HERE: at-least-100-students-at-a-certain-high-school-study-japanes-92305.html
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Re: At least 100 students at a certain high school study Japanes   [#permalink] 19 Jun 2014, 06:06
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