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Sets A, B and C have some elements in common. If 16 elements [#permalink]

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26 Sep 2009, 05:02

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A

B

C

D

E

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Sets 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 three of the sets A, B and C have in common?

(1) Of the 16 elements in both A and B, 9 elements are also in C.

(2) A has 25 elements, B has 30 elements and C has 35 elements.

Re: SETS A, B and C - Experts take a look at this! [#permalink]

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26 Sep 2009, 12:22

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1) A is sufficient. No need to explain. 2)insuff. Elements of A = only in A + both in A and B + both in A and C - in all the sets. same is for B and C. We will find the answer if we know the number of elements in only A or in only B or in only C.

Re: SETS A, B and C - Experts take a look at this! [#permalink]

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26 Sep 2009, 12:26

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1) A is sufficient. No need to explain. 2)insuff. Elements of A = only in A + both in A and B + both in A and C - in all the sets. same is for B and C. We will find the answer if we know the number of elements in only A or in only B or in only C.

Re: SETS A, B and C - Experts take a look at this! [#permalink]

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26 Sep 2009, 22:25

maliyeci wrote:

1) A is sufficient. No need to explain. 2)insuff. Elements of A = only in A + both in A and B + both in A and C - in all the sets. same is for B and C. We will find the answer if we know the number of elements in only A or in only B or in only C.

A

Think i'm missing something... can anyone plot on a venn diagram to show A is sufficient?

Re: SETS A, B and C - Experts take a look at this! [#permalink]

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27 Sep 2009, 08:15

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Expert's post

HI , we dont even require any venn diag as the statement I itself gives the ans.... boeinz, sI 'Of the 16 elements in both A and B, 9 elements are also in C.' .... so it tells us that there are 9 elements in common to all three _________________

Re: SETS A, B and C - Experts take a look at this! [#permalink]

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27 Sep 2009, 08:35

chetan2u wrote:

HI , we dont even require any venn diag as the statement I itself gives the ans.... boeinz, sI 'Of the 16 elements in both A and B, 9 elements are also in C.' .... so it tells us that there are 9 elements in common to all three

Thanks chetan2u! I mistook "16 elements are in both A and B" for "A U B".