Question 68

A bag contains marbles of three colours-red, blue and green. There are 8 blue marbles in the bag.

There are two additional statement of facts available:
If we pull out marbles from the bag at random, to guarantee that we have at least 3 green marbles, we need to extract 17 marbles.
If we pull out marbles from the bag at random, to guarantee that we have at least 2 red marbles, we need to extract 19 marbles.

Which of the two statements above, alone or in combination shall be sufficient to answer the question "how many green marbles are there in the bag"?

Solution

From statement 1:

Red +Ā Blue + Green = 17

Since, this ensures that there are at least 3 green marbles, so, remaining marbles must be red and blue.Ā 

$$\therefore $$Ā Red + Blue = 17 - 3 = 14

Blue = 14 - Red = 14 - 8 = 6

But, this doesn't give us the total number of green marbles. So, statement 1 alone is not sufficient.

From statement 2:

Red +Ā Blue + Green = 19

Since, this ensures that there are at least 2 red marbles, so, remaining marbles must be blue and greenĀ 

$$\therefore $$Ā Blue + Green = 19 - 2 = 17

Again, Green = 17 - Blue = 17 - 8 = 9.

Hence, statement 2 alone is sufficient to answer the question.

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