CMAT Exam 2023 Shift 1 Solved Paper

Question : 9 of 100

Marks: +1, -0

Given below are two statements:
Statement I : A bag captains 10 white and 10 red face masks which are all mixed up. The fewest number of face masks you can take from a bag without looking and be sure to get a pair of the same color is 3. Statement II: The minimum number of students needed in a class to guarantee that there are at least 6 students whose birthdays fall in the same month, is 61.
In the light of the above statements, choose the most appropriate answer from the option given below:

Both Statement I and Statement II are correct
Both Statement I and Statement II are incorrect
Statement I is correct but Statement II is incorrect
Statement I is incorrect but Statement II is correct

Validate

Solution:

Statement 1
After drawing 3 masks, there can be 2 combinations possible -All three are of same color or two are of same color and 1 is of different color. Hence we can ensure that we can get two masks of same color after drawing 3 masks, randomly.
If we draw less than 3 masks i.e. 2 masks, there is a possibility of both the masks being of different color hence we can't ensure that these masks can be of different color, hence the minimum number of masks we need to draw is 3.
Statement 2
To calculate the minimum number of students required, we need to consider the worst case scenario i.e. the birthdays of students are evenly spread across all the 12 months. We'll have to assume that there are atleast 5 birthday is each month, so the total number of students required

=5^* 12=60

. To assure that there is 1 month in which we have 6 birthdays, we'll have to add 1 to this number, hence the minimum number of students required

=60+1=61

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