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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] New post 17 Oct 2009, 12:07
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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.
[Reveal] Spoiler: OA

Last edited by Bunuel on 31 Jan 2013, 02:59, edited 2 times in total.
Edited the question and added the OA
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Re: Japanese studetns [#permalink] New post 17 Oct 2009, 13:05
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amitgovin 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 schoool who study japanese also study french.


please explain. thanks.


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

Q: 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
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Re: word problem [#permalink] New post 05 Apr 2010, 08:02
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number of japanese students >= 100
number of students who study japanese and french = 4% of french students

st 1) 16 studens study both japanese and french = 4% of french studens
so number of french students = 16 * 100/4 = 400
but we dont know how many studetns study japanese. Not sufficient

st 2) number of students who study japanese and french = 10% of japanese = 4% of french
so french studens > japanese students
Sufficient

B
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Re: DS [#permalink] New post 10 May 2010, 19:36
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harikattamudi wrote:
Atleast 100 students at a certain high school study Japanes. If 4 Percent of the students at the school who study French also study Japanes, do more students at the school study French than Japanes

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


Please explain the way to solve these kind of probelms.

Thanks
-H

Is it B?
1. 16 students study both F and J, so there are 400 students studying F: insuff
2. 10% J study F while 4%F study J, so the number of students studying F is greater than that of studens studying J
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 [#permalink] New post 15 Jun 2010, 05:09
We have J >= 100, and 0.04F also study Japanese.

1. 16 students study both French and Japanese. This means 400 students study French, since 4% of 400 is 16, however we don't know how many students study Japanese. INSUFF

2. This tells us 0.1J also study French.
This number is actually identical to 0.04F because it represents the same quantity, which is the number of students who study both French and Japanese!

=> 0.1J = 0.04F
=> J = 0.4F
Thus more students study Japanese than French! Sufficient

Pick B
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Re: word problem [#permalink] New post 27 Jun 2010, 02:18
IMO, it cannot be B:

The 4% is for J&F not F alone (Thus it comprises students who study both Japanese and French). Hence, the statement 10% of J = 4 % of F is not correct. If we combine the two statements, we will get a definite answer:

From (1), we get F=400
From (2), we get 10% of J = 4% of J&F. From (1), J&F=16, therefore, if 10% of J = 16, J=160. Thus J<F. The two statements combined are sufficient.

Correct me if I am wrong...

Thus, my ans. is (C).
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Re: word problem [#permalink] New post 27 Jun 2010, 05:15
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dagmat wrote:
IMO, it cannot be B:

The 4% is for J&F not F alone (Thus it comprises students who study both Japanese and French). Hence, the statement 10% of J = 4 % of F is not correct. If we combine the two statements, we will get a definite answer:

From (1), we get F=400
From (2), we get 10% of J = 4% of J&F. From (1), J&F=16, therefore, if 10% of J = 16, J=160. Thus J<F. The two statements combined are sufficient.

Correct me if I am wrong...

Thus, my ans. is (C).


OA for this question is B.

Let # of students who study Japanese be J, the # of of students who study French be F and # of students who study Japanese and French be F&J.

From stem # of students who study Japanese and French is 4% of the # of students who study French --> F&J=4%F;

From (2) # of students who study Japanese and French is 10% of the # of students who study Japanese (so MORE share of the same group) --> F&J=10%J.

So, 10%J=4%F --> \frac{F}{J}=2.5 --> F>J.
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Re: word problem [#permalink] New post 28 Jun 2010, 04:38
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 schoool who study japanese also study french.
Let's put it this way...
From (1) --> 16 students study both F&J = 4% of F So F = 400, but we don't know how many students who study J coz they said "AT LEAST 100"

From (2) --> 10%J = 4%F --> we know that F is greater than J because only 4% of F is equal to 10% of J

So B is correct
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Re: overlap sets [#permalink] New post 15 Aug 2010, 20:56
Hi,

Statement 1:

16 students study F and J. There should be 400 students studying F. The number of J students could be any of 300 or 400 or 500 (lesser or greater? cannot tell).

Statement 2:

Let x be the number of students who study F and J.

x is 4% of F
x is 10% of J. This implies that J is definitely lesser than F.

Hence, sufficient.

Hope this helps. Thanks.
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Re: Atleast 100 students - DS - 700 level [#permalink] New post 15 Aug 2010, 23:28
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lalithajob 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.


Let J represent the set of students studying Japanese and F represent the set of students studying French
F^J is the set of students studying both Japanese and French
From the question J>=100 , .04F= F^J , is F>J ?

1) F^J=16 => .04F =16 => F=400 . We still don't have any information about J. It can >=100. If 100<= j<400 , F>J. Otherwise F<=J. So not sufficient
2) .1J = F^J => .1J=.04F => F = 2.5 J . Clearly F is bigger than J. So sufficient

Answer B
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Re: French & Japanese [#permalink] New post 19 Feb 2012, 19:15
Answer should be E. Here is how:

Question: 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?

Statement A: 16 students at the school study both French and Japanese.

We know that 4% of the students who study french also study Japanese, which means that of those who study french, 4% also study Japanese and there are 16 such people. So we can set up an equation as below:

Let x= no of people who study french. So:

\frac{4}{100}*(x)=16 so x=400 , so 400 people study French but we the number of Japanese students is greater than 100 and we do not know the exact number so japanese students could be less than 400 or greater than 400. Hence Insufficient.

Statement B: 10 percent of the students at the school who study Japanese also study French.

From Statement B we can see that:

4% of French Students = 10% of Japanese Students

So definitely the number of French Students is greater. Hence Sufficient.

Answer B.
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Re: At least 100 students at a certain high school study japanes [#permalink] New post 22 Jul 2013, 23:29
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Re: At least 100 students at a certain high school study japanes [#permalink] New post 13 Nov 2013, 01:05
"At least 100 studies Japanese". Is it trap? No one explains anything about it.
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Re: At least 100 students at a certain high school study japanes [#permalink] New post 13 Nov 2013, 01:16
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monirjewel wrote:
"At least 100 studies Japanese". Is it trap? No one explains anything about it.


This means that J\geq{100}. Check here: at-least-100-students-at-a-certain-high-school-study-japanes-92305.html#p640103
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Re: At least 100 students at a certain high school study japanes   [#permalink] 13 Nov 2013, 01:16
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