In a class, 20 students speak Spanish, 15 speak French, and 15 speak

Question

In a class, 20 students speak Spanish, 15 speak French, and 15 speak Chinese. How many students are in the class?

(1) Exactly 30 percent of the students in the class speak French.

(2) All of the students speak English and none speaks more than two languages.

testtester293 · Answer

Hi Bunuel.

The answer for this is (A) as only the first statement is sufficient.

If 15 students speak French and exactly 30% of the students speak French, then the total number of students in the class=15x100/30=50.

Statement 2 talks about the students who speak English, which is not mentioned in the main question, thus, it is not sufficient.

Hope this helps!

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adstudy · Answer

IMO, Answer should be   'A'

From prompt we know - In a class,
Students speaking Spanish = 20
Students speaking French = 15
Students speaking Chinese = 15
We need to find total number of students in the class = ?

Statement 1 -  Exactly 30 percent of the students in the class speak French.

So here we have, students who speak French = 30% of the total class strength.
So if we know the number of students who speak french we can find the answer to our question of what is the total number of students in the class.

As from the prompt we know that  Students speaking French = 15 . 
Hence we can find the total number of students in the class.

Hence Statement 1 is Sufficient

Statement 2 -  All of the students speak English and none speaks more than two languages.

So here we have that all class students speak English and no one in the class speaks more than two languages.

So all students mentioned above able to speak French, Spanish and Chinese will also be speaking English.

And as students do not know more than 2 languages, can we say Class Strength = 'French' + 'Spanish' + 'Chinese' = 20 + 15 + 15 = 50 ???
 NO, WE CANNOT SAY THIS.

We did not consider students who can speak ONLY ENGLISH as it is given in statement all speak English and none speaks more than two languages. 
But we can have some students who only speak English which satisfies the above statement.
That number can likely be zero or can likely be any other value. We cannot say for sure.

Hence Statement 2 is Insufficient

sampad · Answer

how we are considering, 15 students speak only french? in that 15 students may be some speak another language also. in that case the answer should not be correct.

catinabox · Answer

It doesn't matter if the students who speak French also speak some other language. Statement 1 mentions that students who speak french comprise 30% of the class. Therefore the total no. of students must be 50.

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In a class, 20 students speak Spanish, 15 speak French, and 15 speak

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