In a college, 300 graduates sit for the recruitment drive of three com

Question

In a college, 300 graduates sit for the recruitment drive of three companies-A, B, and C. 120 graduates are placed in A, 180 are placed in B and 80 are placed in C. 5 students are placed in all the three companies. How many of them are not placed in any of the three companies?

(1) Out of the graduates who got placed in A, 75 and 45 are also placed in B and C respectively.
(2) Out of the graduates who got placed in C, 35 are also placed in B.

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nick1816 · Answer

Total graduates - None = A + B +C -(A ⋂ B) - (B ⋂ C) - (A ⋂ C) + (A ⋂ B ⋂ C)

Total graduates = 300

A= 120; B= 180; and C=80

(A ⋂ B ⋂ C) = 5

If we know (A ⋂ B) + (B ⋂ C) + (A ⋂ C), we can find none.

Statement 1-

It gives the value of (A ⋂ B) and (A ⋂ C), but (B ⋂ C) is unknown

Insufficient

Statement 2-

It gives the value of (B ⋂ C)

Insufficient

Combining both equation , we can find (A ⋂ B) + (B ⋂ C) + (A ⋂ C).

Sufficient

Loop123 · Answer

Looks good,thank ou

allan89 · Answer

No. of students who pass in only exactly subject = a
No. of students who pass in exactly 2 subjects = b
No. of students who pass in exactly 3 subjects = c = 5
No. of students who do not pass any subject = x
Given, 
a+2b+3c = 380 
or, a + 2b = 365 .................(1)

also, a + b + c + x =300 
or a + b + x = 295 --------------(2)

Now, we have 2 eqns and 3 unknowns hence we need to atleast know 1 of a or b or x to to be able to solve this.

Statement 1 essentially gives us the full breakdown of A, including A and B and A and C but it doesnt tell us intersection of B and C so we cant find out either a or b
Similarly Statement 2 again doesnt tell us anything about a or b but only gives us the intersection of B and C

when combined, we get the intersections of AB, BC, CA, essentially we get value of b

hence we can find out the rest of the values. Sufficient

In a college, 300 graduates sit for the recruitment drive of three com

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GMAT Data Sufficiency (DS) Questions

In a college, 300 graduates sit for the recruitment drive of three com

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