# Modern Math - Permutation & Combination - Previous Year CAT/MBA Questions

The best way to prepare for Modern Math - Permutation & Combination is by going through the previous year **Modern Math - Permutation & Combination XAT questions**.
Here we bring you all previous year Modern Math - Permutation & Combination XAT questions along with detailed solutions.

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**XAT 2019 QADI | Modern Math - Permutation & Combination XAT Question**

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"?

- (a)
Both statements taken together are suﬃcient to answer the question, but neither statement alone is suﬃcient.

- (b)
Each statement alone is suﬃcient to answer the question.

- (c)
Statements 1 and 2 together are not suﬃcient, and additional data is needed to answer the question.

- (d)
Statement 2 alone is suﬃcient, but statement 1 alone is not suﬃcient to answer the question.

- (e)
Statement 1 alone is suﬃcient, but statement 2 alone is not suﬃcient to answer the question.

Answer: Option D

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**Text Explanation** :

We know that in all there are 8 blue marbles.

Let us first look at statement I.

As per statement I if we are to pull out 17 marbles from the bag, we will ensure that there are at least 3 greeen marbles. Now out of 17 marbles removed, 8 are blue .So from the 9 marbles that are removed, if at least 3 are green, it would mean maximum possible no of red marbles removed are 9-3 or 6.Which means that the red marbles in the bag are 6.However, this statement alone gives us no information about the no of green marbles. Hence statement I alone is not sufficient to answer the question.

Let us next look at statement II.

As per this statement, if we are to pull out 19 marbles from the bag, we would have at least 2 red marbles. Out of the 19 marbles removed, suppose 8 are blue. Now out of the remaining 11 marbles removed, if we have at least 2 red marbles, it would mean that the maximum possible no of green marbles removed is 9.This means that in all there are 9 green marbles in the bag .

Hence statement 2 alone is sufficient to answer the question.

Hence, option (d).

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