Bunuel wrote:
In the jar there are white and black marbles (W>0 and B>0). How many black marbles are there?
(1) There are total 101 marbles in the jar.
(2) From any two marbles from the jar at least one is white.
My take is B.
consider 1 alone) it tells us nothing about the number of white or black marbles in particular.
consider 2 alone) consider the total number of marbles to be 5 (for simplicity, it can be extended up to infinite number of marbles)
let the 5 marbles be --> A,B,C,D and E.
now option 2 says, if we pick any 2 marbles...at least 1 of them would be white.
if we form every possible group of 2 from these, we get - AB,AC,AD,AE,BC,BD,BE,CD,CE and DE. (10 groups, which is nothing but C(5,2))
since at least one of any two is white, we can safely say A,B,C and D are definitely white. E can be either black or white. but since our fact statement says W>0 and B>0; E has to be a black marble.
Hence, with statement 2 alone we can determine the number of black marbles...which would always be 1.
Good question.
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Illegitimi non carborundum.