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

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Senior Manager
Joined: 26 Jul 2009
Posts: 359
Followers: 2

Kudos [?]: 35 [0], given: 32

Sets A, B and C have some elements in common. If 16 elements [#permalink]  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.
Senior Manager
Joined: 23 Jun 2009
Posts: 354
Location: Turkey
Schools: UPenn, UMich, HKS, UCB, Chicago
Followers: 5

Kudos [?]: 98 [1] , given: 63

Re: SETS A, B and C - Experts take a look at this! [#permalink]  26 Sep 2009, 11:22
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
Senior Manager
Joined: 23 Jun 2009
Posts: 354
Location: Turkey
Schools: UPenn, UMich, HKS, UCB, Chicago
Followers: 5

Kudos [?]: 98 [1] , given: 63

Re: SETS A, B and C - Experts take a look at this! [#permalink]  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
Senior Manager
Joined: 26 Jul 2009
Posts: 359
Followers: 2

Kudos [?]: 35 [0], given: 32

Re: SETS A, B and C - Experts take a look at this! [#permalink]  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?
Manager
Joined: 15 Sep 2009
Posts: 138
Followers: 1

Kudos [?]: 18 [0], given: 2

Re: SETS A, B and C - Experts take a look at this! [#permalink]  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
Senior Manager
Joined: 26 Jul 2009
Posts: 359
Followers: 2

Kudos [?]: 35 [0], given: 32

Re: SETS A, B and C - Experts take a look at this! [#permalink]  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?
Verbal Forum Moderator
Joined: 02 Aug 2009
Posts: 1075
Followers: 24

Kudos [?]: 433 [1] , given: 16

Re: SETS A, B and C - Experts take a look at this! [#permalink]  27 Sep 2009, 07:15
1
KUDOS
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
Senior Manager
Joined: 26 Jul 2009
Posts: 359
Followers: 2

Kudos [?]: 35 [0], given: 32

Re: SETS A, B and C - Experts take a look at this! [#permalink]  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".
Manager
Joined: 25 Mar 2009
Posts: 56
Followers: 1

Kudos [?]: 11 [0], given: 9

Re: SETS A, B and C - Experts take a look at this! [#permalink]  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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# Sets A, B and C have some elements in common. If 16 elements

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