A and B are the sets shown above. Another set C also has a total of 4

Question

A = {2, 4, 7, 8} 
 B = {3, 6, 7, 8}

A and B are the sets shown above. Another set C also has a total of 4 elements. Exactly two elements are shared by sets A and C. Exactly two elements are shared by sets B and C, and these could be the elements shared by A and C. If none of the elements in the sets appears more than once in the same set, how many elements do the three sets share?

(1) 6 is not in set C.

(2) 3 is in set C.

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Jezza · Answer

Imagine C includes (7,2,3,x), in which x is a number not in either A or B. The 3 sets share 1 element: 7
now if C includes (7,8,3,x). The 3 sets now share 2 elements: 7 and 8.
Both suffices (1)and (2).
So the answer is E imo.

Rahul257 · Answer

IMO Answer is C

A=2,4,7,8A=2,4,7,8 
B=3,6,7,8B=3,6,7,8

A and B are the sets shown above. Another set C also has a total of 4 elements. Exactly two elements are shared by sets A and C. Exactly two elements are shared by sets B and C, and these could be the elements shared by A and C. If none of the elements in the sets appears more than once in the same set, how many elements do the three sets share?
So basically asking is it 7&8 or just 7or8 or nothing

(1) 6 is not in set C.
Not sufficient
Set C can have 7,8 are common and also have only 7or 8 as elements

(2) 3 is in set C.
Not Sufficient
if 3 is an element if C, then as only 2 elements can be shared between B and C, the other element can only be 7or 8 or 6
if it is 7 or 8 it shares 1 element and if it is 6 then no elements

combining B&C

it can share only either 7 or 8, as statement 1 gives 6 not an element of C

So Sufficient

Hence C is the answer

Jezza · Answer

What about (7,2,3,100) and (7,8,3,100)?
each set suffices both conditions, but the first yields only 1 common element: 7, the second yields 2: 7,8

av1901 · Answer

A={2,4,7,8} B={3,6,7,8}
C shares exactly 2 elements with A as well as with B, and they could be the same too.

1. 6 is not in set C

C={7,8,10,11} or C={2,4,3,8}
In first case: 2 elements shared 
In second case: 1 element shared
Not sufficient

2. 3 is in set C

C={3,6,2,4} or C={3,10,8,4}
First case: None shared
Second case: 1 element shared
Not sufficient

Together 1 and 2 combined

A={2,4,7,8} B={3,6,7,8}
6 is NOT in set C and 3 IS IN Set C

Set C contains 3 but cannot have 6, so it has to have either 7 or 8 so as to meet the condition that 2 elements have to be common between B and C
So considering it now:

If 2nd element in C is 7/8: C = {3,7,n1,n2}, now for it to also match with 2 elements common with Set A condition, it needs to have either 2 or 4 in it because it already has 8 in common with Set A and it cannot have 7 because then Set C will have 3 in common with Set B which cannot happen.

So C = {3,7,2,100}/{3,7,4,100}/{3,8,2,100}/{3,8,4,100} and in all these cases there is only 1 element common between all 3 sets

SUFFICIENT

Answer - C

Rahul257 · Answer

(7,2,3,100) in this the answer is what i said earlier, the 3 sets share only 1 element, which is 7.
(7,8,3,100)... This is not possible because the question condition says B and C shares only 2 elements. As 7,8 and 3 are all elements of B, thats 3 elements which is not possible.

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A and B are the sets shown above. Another set C also has a total of 4

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GMAT Data Sufficiency (DS) Questions

A and B are the sets shown above. Another set C also has a total of 4

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