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

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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, 04:02
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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.
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Re: SETS A, B and C - Experts take a look at this! [#permalink]

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26 Sep 2009, 11:22
1
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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.

A
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Location: Turkey
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Kudos [?]: 130 [1] , given: 80

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

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26 Sep 2009, 11:26
1
KUDOS
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
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Kudos [?]: 69 [0], given: 32

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

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26 Sep 2009, 21:25
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?
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Re: SETS A, B and C - Experts take a look at this! [#permalink]

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27 Sep 2009, 00:22
I wud go with option A. Venn diagram is the best way to solve this q.

We need to find out the no.of elements common all 3 sets.This is given by statement A.

Statement 2:This doesn't say about the no.of non-distinct elements in each set.so insuff.

I wud go with option 1
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Re: SETS A, B and C - Experts take a look at this! [#permalink]

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27 Sep 2009, 07:00
deepakraam wrote:
I wud go with option A. Venn diagram is the best way to solve this q.

We need to find out the no.of elements common all 3 sets.This is given by statement A.

Statement 2:This doesn't say about the no.of non-distinct elements in each set.so insuff.

I wud go with option 1

What is the answer for the number of elements common in the three sets?
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Re: SETS A, B and C - Experts take a look at this! [#permalink]

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27 Sep 2009, 07:15
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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
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Senior Manager
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Kudos [?]: 69 [0], given: 32

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

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27 Sep 2009, 07:35
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".
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Kudos [?]: 17 [0], given: 9

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

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28 Sep 2009, 09:02
AUBUC=A+B+C-AnB-BnC-CnA+AnBnC

AnB=16, AnC=17, BnC=18 => AnBnC?

(1) Of the 16 elements in both A and B, 9 elements are also in C
=> AnBnC=9, suff => A,D

(2) A has 25 elements, B has 30 elements and C has 35 elements.
=>AUBUC=25+30+35+16+17+18+AnBnC, not enough info to find AnBnC, insuff

Re: SETS A, B and C - Experts take a look at this!   [#permalink] 28 Sep 2009, 09:02
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