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CAT 2019 | Quantitative Aptitude || Super Quiz 9 || 20.11.2019

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Question 1

Consider the numbers f(n) = 22n – 1, where n is a positive integer. Which of the following statements is correct?

Question 2

How many factors are there of the number 720 (including both 1 and 720)?

Question 3

From the following conversation, can you tell how old is Ram’s oldest child?
Shyam: How old are your three children?
Ram: The product of their ages is 36.
Shyam: That’s not enough information.
Ram: The sum of their ages is the number of your house.
Shyam: I need to know more.
Ram: My oldest child is visiting his grandparents today.
Shyam: Now I know the ages of your children.

Question 4

Each page of a book is printed and numbered serially on both sides in the usual manner, that is, the front side of the first page is numbered 1, the back side of the first page is numbered 2, and so on. Of course, as usual, there is a possibility that the book ends at the front side of the last page in which case only the front side of this page is numbered and the back side of this page is left blank. The book has one of its pages missing. The total of the remaining page numbers is 15000. What is the last page number in the complete book?

Question 5

A triangle ABC with an obtuse angle B is inscribed in a circle. The altitude AD of the triangle is tangent to the circle. The side BC has length 12 cm. and the segment BD has length 4 cm. What is the area of the triangle ABC?

Question 6

Two circles whose radii are 8 cm. and 3 cm. are externally tangent. What is the distance between the point of tangency of the circles and a line externally tangent to both of them?

Question 7

Consider the following four statements A, B, C and D.
A) A horse is gentle if it has been well trained. 
B) A horse is gentle only if it has been well trained.
C) Some horses are gentle even though they have not been well trained.
D) Some horses that are well trained are not gentle.
Which one of the following statements is correct?

Question 8

The number of positive integers n in the range 2 < n < 20, such that (n - 1)! is not divisible by n is:

Question 9

The number of squares that can be formed using the adjacent squares of a chess board is:

Question 10

If log 3, log (2x – 1) and log (2x+1 + 7) are in arithmetic progression, then a possible value of x is:

Question 11

If then the value of is

Question 12

A family decides to have children until it has four children of the same sex. Assume that, for this family, the probability of a new-born being a boy is p and that of being a girl is q = 1 – p. What is the probability that the family will end up having seven children?
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Nov 20CAT & MBA