# CAT Model Paper 10 Questions and Answers with Explanation Part 2

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9. Taps to a tank are switched on in the following manner. Tap 1 for the first hour. Tap 2 for the next two hrs and so on. The number indicated on each tap (1 for Tap number 1,2 for tap number 2 …) indicates its flow rate in litre/hr. These taps are filling a tank whose capacity is more than 1000litre. Moreover the capacity cannot be expressed as a difference of squares of two numbers. Find the tap no that fills the tank assuming that the tank՚s capacity is minimum.

(A) 11

(B) 12

(C) 13

(D) 14

Answer: D

Solution:

The smallest number possible is 1002 (this is a number; it cannot be expressed as difference of squares) .

Therefore, our equation becomes.

i.e.. when the 14^{th} tap is open the tank gets filled.

10. A group of 100 people play carom, snooker and chess. 90 people play chess, 80 people play snooker and 80 people play carom. Find the maximum number of people who play all 3 games, if each person plays at least one game.

(A) 80

(B) 70

(C) 75

(D) 65

Answer: C

Solution:

Using the Maxima of all shortcut

11. The milk and water in two vessels A and B are in the ration and respectively. In what ration the liquids in both the vessels be mixed to obtain a new mixture in vessel C consisting half milk and half water?

(A)

(B)

(C)

(D)

Answer: B

Solution:

Suppose in the vessels A & B, one litre of liquid is present.

So, amount of milk in vessel

Amount of milk in vessel .

The required mixture in vessel C should be milk.

So, let the ration be .

Applying allegation:

.

12. Which of the following is the factor of f (x) ?

(A)

(B)

(C)

(D)

Answer: A

Solution:

Use the reverse gear approach.

Option (a)

Option (b)

Option (c)

Option (d)

Hence the answer is option (a)

13: If x, y, z are positive numbers such that , where [p] denotes the greatest integer less than or equal to p and {p} denotes the fractional part of p, e. g. [1.23] . The numerical value of is

(A) 7

(B) 8

(C) 9

(D) None of these

Answer: C

Solution:

Adding the three equations we get,

Subtracting first eq. from the above eq.

We get {y} subtracting second eq. from the above eq. subtracting third eq. from the above eq.

14. Anil looked up at the top of a lighthouse from his boat, and found the angle of elevation to be . After salling in a straight line 50m towards the lighthouse, he found that the angle of elevation changed to . Find the height of the lighthouse.

(A) 25

(B)

(C)

(D) + 1)

Answer: B

Solution:

Now since

Also,

Thus or