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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 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.
Re: At least 100 students at a certain high school study japanes
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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
Re: At least 100 students at a certain high school study japanes
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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
Re: At least 100 students at a certain high school study japanes
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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
Re: At least 100 students at a certain high school study japanes
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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
Re: At least 100 students at a certain high school study japanes
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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.
Re: At least 100 students at a certain high school study japanes
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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, \(10%J=4%F\) --> \(\frac{F}{J}=2.5\) --> \(F>J\). _________________
Re: At least 100 students at a certain high school study japanes
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15 Aug 2010, 20:56
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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.
Re: At least 100 students at a certain high school study japanes
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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
Re: At least 100 students at a certain high school study japanes
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26 May 2015, 23:44
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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 .
Re: At least 100 students at a certain high school study japanes
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12 Sep 2017, 04:50
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
So, "4 percent of the students at the school who study french also study japanese" and "10 percent of the students at the school who study japanese also study french" - these 2 are the same group of people?
Re: At least 100 students at a certain high school study japanes
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12 Sep 2017, 04:58
Expert Reply
SinhaS wrote:
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
So, "4 percent of the students at the school who study french also study japanese" and "10 percent of the students at the school who study japanese also study french" - these 2 are the same group of people?
Yes. Students who study french and also study japanese are those who study both languages the same way students who study japanese and also study french are also those are those who study both languages. _________________
At least 100 students at a certain high school study japanes
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Updated on: 26 Mar 2021, 05:49
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Top Contributor
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.
A student asked me to provide a step-by-step solution using the Double Matrix method, so here goes.... This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions). Here, we have a population of students, and the two characteristics are: - studies Japanese or does NOT study Japanese - studies French or does NOT study French
Let's let J = the TOTAL number of students taking Japanese And let F = the TOTAL number of students taking French
When we sketch our diagram, we get:
Target question:Is F greater than J?
Given: 4 percent of the students at the school who study French also study Japanese Since we let F = the TOTAL number of students taking French, we can say that 4% of F = number of students taking BOTH French and Japanese. In other words, 0.04F = number of students taking BOTH French and Japanese We can also say that 96% of the students who study French do NOT study Japanese In other words, 0.96F = number of students taking French but NOT Japanese
So, our diagram now looks like this:
Statement 1: 16 students at the school study both French and Japanese Since 0.04F = number of students taking BOTH French and Japanese, we can write: 0.04F =16 When we solve this equation for F, we get F = 400 So, 0.96F = 384 So, our diagram now looks like this:
Is this enough information to determine whether or not F is greater than J? No.
For example, we COULD fill in the remaining boxes this way...
In this case, F = 400 and J = 116, which means F IS greater than J
However, we COULD also fill in the remaining boxes this way...
In this case, F = 400 and J = 1016, which means F is NOT greater than J
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 10 percent of the students at the school who study Japanese also study French. J = the TOTAL number of students taking Japanese So, 0.1J = number of students taking BOTH French and Japanese
Notice that we already determined that 0.04F = number of students taking BOTH French and Japanese So, we now have two ways to represent the SAME value.
So, it MUST be the case that 0.1J = 0.04F Let's see what this tells us. First, to make things easier, let's multiply both sides by 100 to get: 10J = 4F Divide both sides by 10 to get: J = 4F/10 Divide both sides by F to get: J/F = 4/10 From this, we can conclude that F IS greater than J Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Re: At least 100 students at a certain high school study japanes
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14 Oct 2017, 17:38
Expert Reply
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.
We are asked whether we can find if more students study French than Japanese. The concept used here is , we can compare similar expressions of measuring in finding out which one of the measured is greater, say we can compare percentages or compare absolute numbers .
In statement 1 absolute number is given, and in the stem percentage is given. Also the first is about percentage of French studying Japanese and the second is the number who study both. We can intuitively understand there is insufficient information in this.
In statement 2 , percentage is given and we can now compare the percentage who study French and the percentage who study Japanese in the school. So sufficient.
Re: At least 100 students at a certain high school study japanes
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01 May 2019, 16:13
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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 school who study Japanese also study French.
We can let f = the number of students who study French and j = number of who study Japanese, and we need to determine whether f is greater than j. Furthermore, we are given that j ≥ 100 and 4 percent of the students at the school who study French also study Japanese; in other words, 4 percent of the students at the school who study French study both languages.
Statement One Alone:
16 students at the school study both French and Japanese.
We can create the equation:
0.04f = 16
4f = 1600
f = 400
However, since we don’t know the value of j (except that it’s at least 100), statement one alone is not sufficient.
Statement Two Alone:
10 percent of the students at the school who study Japanese also study French.
In other words, 10 percent of the students at the school who study Japanese study both languages. Even though we don’t know the exact number of students who study both languages, we know that it’s 0.04f. Therefore,
0.1j = 0.04f
10j = 4f
2.5j = f
We see that the number of students who study French is 2.5 times those who study Japanese. So f is indeed greater than j. Statement two alone is sufficient.
Re: At least 100 students at a certain high school study japanes
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07 Jul 2019, 14:20
This question made me chuckle. While we spend days and months memorizing formulas and rules, it is actually questions as simple as this one that decide the fate of GMAT takers. 4% of X = 10% Y. A primary school kid can tell you that X > Y. But as the statistics suggest, 49% of us over thought it.
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