# CAT Model Paper 11 Questions and Answers with Explanation Part 2

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8. Natural numbers are written on a blackboard. The following operation is then repeated until we will get only one number: In each repetition, any two numbers say a and b, currently on the blackboard are erased and a new number is written. But one number was missed by mistake. The sum obtained was 1525. Which number was missed?

(A) 15

(B) 25

(C) 20

(D) 10

Solution:

Missed number

9. What is the remainder when

is divided by 50?

(A) 46

(B) 6

(C) 56

(D) 5

Solution:

To find the remainder when an expression is divided by 50, we need to find the last two digits of that numbers.

Last two digit of the given expression are

10. A positive whole number M less than 100 is represented in base 2 notation, base 3 notation, and base 5 notation. It is found that in all three cases the last digit is 1, while in exactly two out of the three cases the leading digit is 1. Then M equals

(A) 31

(B) 63

(C) 75

(D) 91

Solution:

Option (D) - Since, the last digit in base 2, 3 and 5 is 1, the number should be such that on dividing by either 2, 3 or 5 we should get a remainder 1. The smallest such number is 31. The next set of numbers are 61, 91.

Among these only 31 and 91 are parts of the answer choices.

Among these, thus, all three forms have leading digit 1.

11. At a new index of 12 shares, the shares of HBL, Niposys and Brilliance have a weightage of 7%, 13% and 1% respectively. What is the increase in the price of the other shares, if the rise in these three is 9%, 10% and 4%, when the index rises by 6%?

(A) 4%

(B) 3.4%

(C) 6%

(D) None of these

Solution:

Option D

Let’s say the value of the index

HBL

Niposys

Brilliance

Others

Increased index value

Increased individual values

HBL

Niposys

Brilliance

Total

Others

Increase

12. has a circle centered on vertex C that passes through points A and E. If what is the distance between E and B?

(A) 2x

(B)

(C)

(D)

Solution:

Since, , it follow that ,

So,

13. The number of positive integer n in the range such that the product is not divisible by n is

(A) 5

(B) 7

(C) 13

(D) 14

Solution:

The question is asking you for all prime numbers between 12 and 40. There are 7 prime numbers.

14. A mixture of 125 liters of milk and water contains 20% water. What amount of water needs to be added to this milk-water mixure in order to increase the percentage of water to 25% of the new mixure?

(A) 7 L

(B) 5.66 L

(C) 8.33 L

(D) None of these

Solution:

We need to find out how much of solution of 100% water needs to be added to a solution containing 20% water to attain dilution of 25%.

This can be found out as follows.

Ratio

This is for 15 parts of a 20% water solution, one part of 100% water solution needs to be added. Therefore, for a solution of 125 liters. of water needs to be added.

15. In the figure, EAF is a common tangent to the circles at the point A. Chords AC and BC of the smaller circles are produced to meet the larger circle at G and D respectively. Which of the following must be true?

(A) 1 only

(B) 2 only

(C) 1 and 3 only

(D) 2 and 3 only