Teachers - Set theory

Question

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xyztroy · Answer

I am not sure of the OA. I think answer should be D.

Set theory formula, when u have "atleast", is as follows:

P(A) +P(B)+P(C)-P(A)P(B)-P(A)P(C)-P(B)P(C)+P(A)P(B)P(C) = 100

Frm Stmt1 we can calculate total % of {P(A)P(B)+P(A)P(C)+P(B)P(C)} and add it with P(A)P(B)P(C).
Srom stmt2 we can calc P(A)P(B)P(C) and we already know P(A)P(B)+P(A)P(C), and P(B)P(C) is given in the stmt.

Note: % numbers may not be correct, since I do not remember them exactly.

msand · Answer

It is only talking about the %. Is it at all possible to reach to the exact number of teacher ?

vedprakashchauhan · Answer

Exactly!, it says percentage all over and asks for absolute number.
I opt for E

Cornelius · Answer

It should be D

Let T be the total number of teachers
Thus 0.64T teach Economics, 0.6T teach English and 0.7 T teach Science
Now, 40 % of the English teachers also teach either Science or Economics, but not both, that makes 0.4*0.6T=0.24T

Let the number of teachers who teach both Science and Economics be x
and the number of teachers who teach all 3 subjects be y

So, we have to find how MANY OF THE TEACHERS teach at least 2 or 3 subjects
i.e. (x+y+0.24T)/T*100. Note: I read the question asking a % and not how MANY TEACHERS

1. 50% of the teachers teach all 3 subjects i.e. y= 0.5T
By set theory formula, 
Science+Eco+English-(Science and English+English and Eco)-Science and Eco-All three = T
0.7T+0.64T+0.6T-0.24T-x-0.5T=T
x=1.2T-T=0.2T
i.e 20 %
So, we have x and y, thus (0.2T+0.5T+0.24T)/T*100= 96%
Suff

2. This statement gives us x. We can find y using the above formula.
So Sufficient
Hence D

I must confess that I solved it as C (did not use the set theory formula), but realized it is D only when I began typing the reply.
 
The question took 3 minutes and 48 seconds to solve....

targetMBA11 · Answer

Hi,

I have two questions to you

1 : statement two says atleast 20 % that means it could be equal to or even more than 20% , so we cant infer that we got the value of X .

2 : the Question says how many teachers ? ( it is basically asking the number and not the percentage ) so here i feel although we are able to find the % with option A as solved by you but that wont be of any help and we dont know T.

So i would say E.

Interesting question though ,,, looking forward for the official answer and explanation.

Thanks

Cornelius · Answer

Hi TargetMBA,
You are absolutely right. Statement 2 does say at least 20 %. Hence, Statement 2 is insufficient. I missed that. Very sorry.
However, I still feel that since the question says how many of the teachers, a factor or a percentage of total should suffice. Can't wait for the OA.
The answer should be A.

gurpreetsingh · Answer

IMO E

statement 2 is insufficient as it gives atleast.

statement 1 says 50% teaches all 3...but we also need those who teaches exactly 2...

whats the OA?

targetMBA11 · Answer

Even i feel its A ... lets wait buddy !!

xyztroy · Answer

This is a real question....

targetMBA11 · Answer

Buddy we never said its unreal .. it would be great if you could throw some light on the solution and the official answer.

xyztroy · Answer

I may not remember the exact verbiage and since it is "real", dont have the OA....

targetMBA11 · Answer

okie .... now i understand the literal meaning for the word REAL

... Ahuh what to do now ... then best bet is A .

Teachers - Set theory

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