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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]  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]  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]  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]  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]  15 Jun 2010, 05:09
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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]  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]  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]  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]  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]  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]  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]  22 Jul 2013, 23:29
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From 100 hardest questions.

Bumping for review and further discussion.
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Re: At least 100 students at a certain high school study japanes [#permalink]  13 Nov 2013, 01:05
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"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]  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]  14 Nov 2014, 02:06
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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At least 100 students at High school study Japanese. [#permalink]  22 Jan 2015, 22:33
Hey All,

Need to know...How to solve this DS Problem.

At least 100 students at High school study Japanese.
If 4% of the students at the school who study French also study Japanese,
Do more students 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.

Answer given was B.
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Re: At least 100 students at a certain high school study japanes [#permalink]  23 Jan 2015, 02:21
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sharadnc wrote:
Hey All,

Need to know...How to solve this DS Problem.

At least 100 students at High school study Japanese.
If 4% of the students at the school who study French also study Japanese,
Do more students 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.

Answer given was B.

Merging topics.

Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html pay attention to rules, 1, 3, and 7. Thank you!
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At least 100 students at a certain high school study japanes [#permalink]  24 May 2015, 17:27
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 school who study Japanese also study French.

Simply put:

Students who study both languages represent 4% of all French students (given in the Q) but 10% of all Japanese students (Statement 2). The number of French students then has to be higher than Japanese students.

Only 2 is sufficient.
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Re: At least 100 students at a certain high school study japanes [#permalink]  26 May 2015, 23:44
Expert's post
This question can also be solved by using venn diagram.

Interpreting the Given Info
The question tells us about students in a school studying Japanese and French. Let's represent them using a venn diagram.

a - Number of students who study only Japanese
b - Students who study both Japanese and French
c- Students who study only French
d- Students who study neither Japanese nor French

We are given that atleast 100 students study Japanese i.e. a + b => 100

Also we are told that 4% of the students who study French also study Japanese i.e. 4%(b + c) = b. It can be simplified to c = 24b

We are asked to find if there are more students at the school who study French than Japanese i.e. if b + c > b + a, which simplifies to c > a?

We can either
i. find the values of c and a to answer the question or
ii. express a in terms of b and then compare it with c to answer the question.

Let's see if the statements provide us with the required information.

Statement-I
St-I tells us that 16 students study both French and Japanese i.e. b = 16. This would give us a => 84 and c = 384. As a => 84, a > 384 or a < 384. Since we do not have a definite value of a we can't say for sure if c > a.

Hence st-I is insufficient to answer the question.

Statement-II
St-II tells us that 10% of the students who study French also study Japanese i.e. 10%(a + b) = b i.e. a = 9b.
Now, we have a and c both in terms of b. We see that c =24b and a = 9b i.e. c > a .

Hence st-II is sufficient to answer the question.

Hope this helps

Regards
Harsh
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Re: At least 100 students at a certain high school study japanes [#permalink]  12 Oct 2015, 04:26
Bunuel wrote:
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

Hi Bunuel,

How should one interpret "If 4 percent of the students at the school who study French also study Japanese"

I took it in this way

Suppose total num of students who know F =100
So 4% of this know both J and F , this doesn't mean that the entire number of students who know both F & J is 4

Its just telling out of 100 french 4 know both J and F
and further if it is stated that out of 200 J students 20 know both

Then total no of students who know J & F is 24.

After viewing your explanation ,came to know that "If 4 percent of the students at the school who study French also study Japanese" talks about the entire num of students who know J & F not just subset.

Can you let us know how to avoid such blunders.
Re: At least 100 students at a certain high school study japanes   [#permalink] 12 Oct 2015, 04:26
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