Data Sufficiency

Set A, B and C have some elements in common. If 16 elements are in both A and B, 17 elements are in both A and C, and 18 elements are in both B and C, how many elements do all these three of the sets A, B and C have in common?

1. Of the 16 elements that are both in A and B, 9 elements are also in C.
2. A has 25 elements, B has 30 elements and C has 35 elements.

IMO A.

1. right away gives A & B & C = 7 - sufficient

2. For this one we need the total no of elements in A,B,C (A U B U C) to calculate A&B&C. - not sufficient

I am not too sure - Can we rule out B for the following reasons:

1. It doesn't give the total number of elements
2. It doesn't give the elements that do not belong to A, B and C.

@ punitkaur

You mean 9 elements in common ?

I think IMO is E .

the solution by punitkar is on the right lines

this is from gmatprep and OA is A.

Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three) + Neither

opt 1:
all 3 is 9. Sufficient.

opt 2:
Gives us Group1 Group2 & Group3. Unless we know 'Total' and 'neither' this info is useless. Insuff

I do not agree at all that A is right ans....

Even if u consider 9 are common among A, B and C

still we dont have any clue that

whether

elements which are common b/w B and C also common with A also.... ?

and

whether

elements which are common b/w C and A also common with B too... ?

without these inf... nothing can be said....


IMO Ans is E

What's the OA ?

OA is A

i agree with girish.

can you please explain why you chose A ?

IMO the information about how many elements of AC belong to ABC / how many elements of BC belong to ABC is necessary

can u use a venn diagram for this one? or is that too complicated? with these i am tryig to figure the most efficient way venn diagram vs. AuB formula. what is the formula for example?

set A = A - AUB - AUC ?

Neerj.. can you please ppost solution of this quistion