# CAT Model Paper 7 Questions and Answers with Explanation Part 4

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Q: 23. ABCD is a cyclic quadrilateral drawn inside a circle with AB parallel to DC where CD is the diameter of the circle. Side and diagonal . Calculate AB in terms of a and b

(A)

(B)

(C)

(D) None of these

Ans: A

Solution:

Consider the following figure,

By question, and is the centre of the circle. is dropped perpendicular to and OB is joined. Let the radius of the circle be r and . Now area of triangle This is because ABCD is a cyclic quadrilateral as well as a trapezium hence it is an isosceles trapezium and and is a right angled triangle as DC is the diameter of the circle as well as the hypotenuse of triangle DBC. Hence, now BP is a perpendicular dropped on DC, so, triangle OBP is a right angled triangle. . Therefore using Pythagoras theorem, we get,

Therefore as given in option A

Q: 24. Altitudes AM and BN are drawn in triangle ABC (M lies on BC and N lies on AC) . MN is joined. If angle , calculate angle MNC

(A)

(B)

(C)

(D) Cannot be determined

Ans: C

Solution:

Consider the following figure

We have, the right angle triangles AMC and BNC have equal acute angles at the vertex C. Hence they must be similar. Hence … (1) . Now triangle ABC and MNC share the same angles C. thus using (1) , we infer that they must be similar angle as given in

Answer the questions on the basis of the information given below:

The following pie-charts give details about the number of readers of a newspaper as a percentage of the total number of readers of all the six newspapers put together for the cities Mumbai and New Delhi in the year 2012. Each person reads exactly one newspaper. The total number of readers in Mumbai is and the total number of readers in New Delhi is . Readership details of some of the newspapers are missing in the pie-charts below.

Q: 25. If in each city, the number of readers of a newspaper is not less than of the total number of readers of all the six newspapers put together, then what is the maximum percentage by which the number of ‘Economic Times’ readers of Mumbai is more than the number of ‘The Hindu’ readers of New Delhi?

(A)

(B)

(C)

(D)

Ans: B

Solution:

In Mumbai,

gives

In Delhi,

Mumbai and Delhi readership are in the ratio of ET in Mumbai and % of TH in Delhi readership are in the ratio

Readers of ET in Mumbai and Readers of TH in Delhi are in the ratio 25: 8

Max.

Q: 26. The number of Deccan Chronicle readers in each city is not more than the number of Economic Times readers of that city but it is not lesser than the number of Indian express readers of that city. Which of the following can be the difference between the number of Deccan Chronicle readers of Mumbai and New Delhi?

(A)

(B)

(C)

(D)

Ans: A

Solution:

In Mumbai,

In Delhi,

TH has to be minimum implies DC can only be

The Mumbai and Delhi Readers hip are in the ratio DC in Mumbai

DC in Delhi Difference is

Only first option lies in this range.

Q: 27. By approximately what percent is the total number of Indian Express readers in both the cities less than that of the total number of Hindustan Times readers in both the cities?

(A)

(B)

(C)

(D)

Ans: B

SOLUTION

The Mumbai and Delhi Readers hip are in the ratio

i.e. in Mumbai is and in Delhi is

HT in Mumbai is and in Delhi is

Percentage

Q: 28. Let . Then which of the following is true?

(I) ,

(II) ,

(III)

(A) Only I

(B) Only III

(C) Only I & II

(D) None of these

Ans: C

Solution:

Subtracting,

Hence, either .