Data Sufficiency

What is the method to solve such questions?

IMO C.
1st Statement can be used to find out the number of students taking french but not clear if that number is greater than no of students taking japaneese..
2nd statement can be used to find out no of students taking Japaneese..

Using both we may answer the questions.

Please correct me if i sound wrong.

According to me answer should be E. Can someone explain this question

I think the answer is C.

Atleast 100 Japanese students. 4%French = Japanese+French

Statement I
16 students study Japanese and French

4%French = 16
French=400
At least 100 Japanese - 16 = At least 84 only study Japanese.

Insufficient, because we dont know the exact number of Japanese, We know the lower limit i.e. 84 but we dont know the upper limit.

Statement II

10% of Japanese also study french
At least 100*10% = at least 10
4%F= atleast 10
French=250 atleast

Therefore only study Japanese = 90 atleast, Only study French=240 at least
Not sufficient. (reasoning same as above)


Combining Statement I & II

10%Japanese =16

Japanese=160, Only Japanese = 160-16 = 144

4%French =16
French=400, Only French = 400-16 = 384.

Hence C is the answer.


If they would have taken out "AT LEAST" from the question stem then the answer would be D.

Let me know what you guys think.

Whats the OA?

whats the OA?

IMO C.

n represents intersection in the explanation given below
From Question:

Atlesat 100 = Japanese and
(4%(french) = (French n Japanese)

Statement 1.

French n Japanese = 16. ----------------------->eq1

Substituting this value in question , we can only find out the value of French.This is not sufficient since we need the number of japanese to say who is greater.(excuse me for the miserabler english )

Statement 2.

10% (Japanese) = ( Japanese n French) ------------------>eq2
This info does not help much .

Combining 1 and 2.



From eq1 and question we can find the no of French

Substitute eq 1 in eq 2 we can find out the value of Japanese.

The question does not ask us to solve for any values.
The knowledge that the values and French and Japanese can be found will suffice

Note : Japanese n French = French n Japanese (VENN DIAGRAM)

Please correct me if am wrong.

Regards,
Vignesh

Statement (2) is sufficient by itself.

From the original, we know that 4% of French speakers also speak Japanese. So, we can derive the equation:

4%(f) = (f&j)

From (2), we know that 10% of Japanese speakers also speak French. So, we can derive the equation:

10%(j) = (f&j)

Now, since the right side of each equation is the same, that means the left sides must also be equal.

In other words:

4%(f) = (f&j) = 10%(j)

or simply:

4%(f) = 10%(j)
f = (10%/4%)j
f = (5/2)j

and, since we know that there's a positive number of japanese speaking students (if we didn't know that, it would be possible that f=j=0), we can definitely conclude that f > j.

Choose (b)!

Yes Answer is (B). Thanks Stuart.