# CAT Model Paper 9 Questions and Answers with Explanation Part 2

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6. If this pattern continues, where would the number 289 appear?

(A) Row 17

(B) Row 18

(C) Row 19

(D) Row 20

Answer: A

Solution:

Perfect squares are the middle term of odd rows. should be middle term of 17^{th} now.

Alternate Solution:

There is 1 odd number in the 1^{st} row.

There are 2 odd numbers in the 2^{nd} row.

There are 3 odd number in the 3^{rd} row.

Hence this can be considered as a question where, n is the number of odd numbers.

As 289 will be term in the sequence, find a value which is close to the number.

which is equal to 153 and 17 numbers before 153 will be in the 17^{th} row.

7. A park has the shape of a regular hexagon of sides 2 m each. Ram walks a distance of 5 m around the perimeter. What is the direct distance between the start point and the end point?

(A)

(B)

(C)

(D)

Answer: B

Solution:

The starting point of Ram is A and end point is D.

Vertex angle for regular hexagon

In the angle ABC = angle

We know

Now, from -

Option (b) ; Alternate Solution:

The answer option will have to be between and 4 i.e. between and .

8. Every year Aman consume 250kg wheat and 90 kg rice. The price of wheat is 20 % of the price of rice and spends a total of ₹ 3500 on wheat and rice per year. If the price of rice is increased by 20 % then what is the percentage reduction of wheat consumption for the same expenditure of ₹ 3500? (Given that the price of wheat and consumption of rice is constant)

(A) 24 %

(B) 40 %

(C) 25 %

(D) 36 %

Answer: D

Solution:

Let the price of Wheat = X per kg. Then, the price of Rice = 5x per kg (As it is given that the price of Wheat is 20 % the price of rice)

Hence. The price of wheat be M kg, then

Let the new amount of wheat be M kg, then

(As price of rice instead of consuming 250kg of wheat, Aman can consume 50kg of rice.)

Hence,

Now,

X = 32

Therefore, change in consumption

Thus, percentage increase will be or 36 %

9. The sum of first n terms of a A. P. is 100 and sum of first n terms of another A. P. is 300. Find the ratio of common difference.

(A) 1: 6

(B) 1: 3

(C) 1: 1

(D) Cannot be determined

Answer: D

Solution:

If sums of the series are in ratio 1: 3, then the ratio of common difference will remain same.

For Example:- Let an A. P. 18, 19,20, 21,22 an other one 58, 59,60, 61,62 and another A. P. 54, 57,60, 63,66 sum of first A. P = 100 and sum of other A. P. = 300.

So, the ratio of common difference

10. Four equal jugs are filled with the mixture of sprit water. The ratio of sprit to water in four jugs is and . The mixture of the four jugs is emptied into a single vessel. What is the proportion of sprit to water in the vessel?

(A) 11: 21

(B) 11: 30

(C) 12: 24

(D) 3: 5

Answer: A

Solution:

Let x (in ml) be the volume of each jug.

Jug | 1^{st} | 2^{nd} | 3^{rd} | 4^{th} |

S: W | 1: 3 | 3: 5 | 5: 11 | 7: 9 |

S | ||||

W |