Mega Quiz 33 & Weekly Revision || Quantitative Aptitude || CAT 2021 || 31 October for CAT & MBA Exams

Question 1

In how many ways is it possible to choose two black squares on an 8 × 8 chessboard so that they neither lie in the same row nor in the same column?

Question 2

Five gates labelled A, B, C, D & E, all having different décor outside are kept for VIP entries. Three different country delegates were invited and were taken inside through three different gates and while leaving it was made sure that they do not go out through the same gate from which they entered and also NOT from the same gate from which the other delegate is leaving. How many ways can the entry and exit arrangements be made?

Question 3

The probability of hitting a target by Pawan, Qasim and Ratna is 75%, 50% and 80% respectively. Find the probability that exactly two of them hit the target.

Question 4

A box contains 3 black and 7 red balls. Two balls are drawn from the bag in succession without replacement. What is the probability that both the balls are red?

Question 5

4 girls and 2 boys stand in a row. The probability that the number of girls ahead of every boy is at least one more than the number of boys ahead of him is ‘p’ then 5p equals:

Question 6

Which of the following can be the range of the values of the median for the series 36, 8, 12, 42, 16, 21, 32, 23, 33, x, 9,6,25,40,37,45 and 19

Question 7

A list of 9 natural numbers, in which 2 is the smallest number, has two modes. The range of the data of the list is 9. The mean, the median and the largest mode of the list are equal. If 2, 3 and 10 appear once in the list, then how many such list(s) is/are possible?

Question 8

We have two unknown positive integers m and n, whose product is less than 100. There are two additional statement of facts available:

1) mn is divisible by six consecutive integers { j, j + 1,...,j + 5 }

2) m + n is a perfect suare.

Which of the two statements above, alone or in combination shall be sufficient to determine the numbers m and n?

Question 9

Direction: The question below is followed by two statements marked I and II. Mark as your answer.

A group of six friends noticed that the sum of their ages is the square of a prime number. What is the average age of the group?

Statement I: All members are between 50 and 85 years of age.

Statement II: The standard deviation of their ages is 4.6

Question 10

In a society, 90% of boys play at least one of the three games among Cricket, Football and Hockey. The number of boys who play Hockey and Football but not Cricket is the average of the number of boys who play Hockey and Cricket but not Football and Football and Cricket but not Hockey. The number of boys who play all the three games is one-third of the numbers of boys who play exactly two games. The number of boys who play only Cricket, only Hockey and only Football is 10 each. The number of boys who play Hockey but not Football is 6 more than the number of boys who play Football but not Hockey. If the number of boys who do not play any of the three games is 10, then how many boys play Football?