An organization has 4 committees. Only 3 persons are members of all four committees, but every pair of committees has 4 members in common. What is the LEAST possible number of the members on any one committee?

• 6 least possible no. of members in any one committee.
  C1 C2 C3 C4
  x x x x
  y y y y
  z z z z
  w w v t
  r v t u
  s u s r
  
  now every two committee has 4 members in common.
  ans : 6
• 10 years agoHelpfull: Yes(26) No(7)
• 4 with help of set diagram
• 10 years agoHelpfull: Yes(10) No(1)
• let w,x,y,z are four committees....A,B,C are common in all committee...
  
  w x y z
  __________
  
  A A A A
  
  B B B B
  
  C C C C
  
  D D _ D
  
  E E E _
  
  F _ F F
  __________
  
  pairs of the commiittee -->AB,AC,AD,BC,BD,CD
  
  IN AB-->A,B,C,D are common
  IN AC-->A,B,C,E are common
  IN AD-->A,B,C,F are common
  IN BC-->A,B,C,E are common
  IN BD-->A,B,C,D are common
  IN CD-->A,B,C,F are common
  
  SO,the LEAST possible number of the members on any one committee is= 5 (ans.)
• 10 years agoHelpfull: Yes(9) No(1)
• 4 with the help of ven diagram
• 10 years agoHelpfull: Yes(5) No(2)
• the least possible no of member of members on any one committee = 4 .. option a)
  
  In all 4 committees, say W,X,Y,Z, 3 persons say A,B and c are common.
  D is common between W and X.
  E is common between X and Y.
  F is common between Y and Z.
  G is common between Z and W.
  
  so W committee has ABCDG. X committee has ABCDE. Y committee has ABCEF.
  Z committee has ABCFG.
  
  
  
• 10 years agoHelpfull: Yes(3) No(4)
• 1 2 3 4
  A A A A
  B B B B
  C C C C
  e e f d
  d f d
  Here,1 2 3 4 are the committees,and A B C are the members common to all the committees,A B C e is common to 1 2,A B C f is comm to 2 3,A B C d is comm to 3 4, A B C d is comm to 4 3 so ans is the 4th committee which has least mem 4
• 10 years agoHelpfull: Yes(2) No(1)
• (ABC)DGI
  (ABC)DFH
  (ABC)EGH
  (ABC)EFI
• 10 years agoHelpfull: Yes(2) No(0)
• 8 with help of set diagram
• 10 years agoHelpfull: Yes(1) No(8)
• 6 people using venn diagram
• 10 years agoHelpfull: Yes(1) No(1)
• let w,x,y,z are four committees....A,B,C are common in all committee...
  
  w x y z
  __________
  
  A A A A
  
  B B B B
  
  C C C C
  
  D D _ D
  
  E E E _
  
  F _ F F
  __________
  
  pairs of the commiittee -->AB,AC,AD,BC,BD,CD
  
  IN WX-->A,B,C,D are common
  IN WY-->A,B,C,E are common
  IN WZ-->A,B,C,F are common
  IN XY-->A,B,C,E are common
  IN XZ-->A,B,C,D are common
  IN YZ-->A,B,C,F are common
  
  SO,the LEAST possible number of the members on any one committee is= 5 (ans.)
• 10 years agoHelpfull: Yes(1) No(0)
• 0 is the answer cause here 3 members are there for all 4 committees
• 10 years agoHelpfull: Yes(0) No(6)
• Let the committies be 1,2,3 and 4 then,
  A,B,C are common to all the four commities(since given in the que that only 3 persons are the members of all the four committies)
  now, D is common to 1&2
  E is common to 2&3
  F is common to 3&1
  so, the least possible number are 4
  ANSWER: 4
  
• 10 years agoHelpfull: Yes(0) No(1)
• let the committees be 1234
  1 2 3 4
  a a a a
  b b b b
  c c c c (since 3 mem common in all four committee)
  d d
  e e
  f f
  g g
  i i
  h h (each pair of committee has 4 members in common)
  therefore least possible number of mem in any group is 6
  
• 10 years agoHelpfull: Yes(0) No(0)
• 6 is the answer.
  Lets us assume A,B,C,D are 4 committees.
  now using Venn diagram ,
  A ∩ B ∩ C ∩ D =3
  Now every pair must have 4 members in common
  possible pairs are(each containing +1 member since there're already 3 common members) :
  A ∩ B - 1
  A ∩ C - 1
  A ∩ D - 1
  B ∩ C - 1
  B ∩ D - 1
  C ∩ D - 1
  Now if we take A alone there are
  3+ 1 (in A ∩ B)+1 (in A ∩ C ) + 1 (in A ∩ D)= 6
  Similarly if u check for all , there will be 6 members in each.(minimum possibility)
  For even more clear understanding , apply this in a Venn diagram.
• 6 years agoHelpfull: Yes(0) No(0)