# CAT Model Paper 5 Questions and Answers with Explanation Part 6

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Q: 26. Directions:

Choose (1), if the question can be answered by one of the statements alone, but cannot be answered by using the other statement alone.

Choose (2), if the question can be answered by using either statement alone.

Choose (3), if the question can be answered by using both the statements together, but cannot be answered by using either statement alone

Choose (4), if the question cannot be answered even by using both the statements together

What is the date of birth of Kishan?

I. The month and the day of the month on which Kishan is born are co-primes and composite numbers, where the day of the month is odd.

II. The sum of day of the month on which Kishan is born is a composite number greater than 30

(A)

(B)

(C)

(D)

Ans: (D)

Solution

From I, the date of birth can be April 9^{th}_{,} 15th, 21^{st}, 25^{th} or 27^{th} or

Or June 25^{th} or August 9^{th}, 15^{th}, 21^{st}, 25^{th} or 27^{th} or September 25^{th} or October 9^{th}, 21^{st}, 27^{th} or December 25^{th}

From II, we get many possibilities

Combining I and II, we get either August 27^{th}_{,} or September 25^{th}

Hence, option D

Q: 27. 10 men can do a piece of work in days. men start the work and from the 2nd day onwards, at the start of each day, 1 extra man is added to complete the work. In how many days will the work be completed?

(A)

(B)

(C)

(D)

Ans: (A)

Solution:

Work completed in 1^{st} day, work completed in 2^{nd} day. Work done in 3^{rd}. In 16 days, 280/300 of the work will be completed. Work done on 17^{th} day with . Time taken on of the day

Total days days.

Hence option A

Q: 28. What is the remainder when is divided by ?

(A)

(B)

(C)

(D)

Ans: (B)

Solution

divided by is the same as divided by can be written as .

Now 27 or when divided by leaves remainder . Hence, the remainder is .

Again, can be written as .

when divided by leaves a remainder of . Hence, the remainder is or , which when divided by leaves a remainder of .

But the original divisor was and not. Hence the remainder is .

**Start Passage**

Directions for questions 29 to 30:

India and Australia play five cricket matches. The Indian team lost at least four wickets in each match. The following graph gives details about the total runs scored by Indian team at the fall of the first four wickets. For instance, in the first match, the Indian team’s score was when the first wicket was lost and when the second wicket was lost.

A partnership between two batsmen is defined as the total number of runs scored by the two batsmen as long as both of them are not out. An wicket partnership is defined as the number of runs scored between the fall of the wicket and the wicket. For example, in Match 1, the first wicket partnership was runs. Moreover, the number of runs scored by a player is always an integer. Assume that there are no extras in any of the matches.

Q: 29. In all the five matches, Indian batsman Virat Kohli came out to bat at the fall of the first wicket. What is the minimum number of runs that could have been scored by Virat Kohli if it is known that he scored at least half of the runs in any partnership that he was involved in?

(A)

(B)

(C)

(D)

Ans: (A)

Solution

Virat Kohli scores at least half the runs in every partnership he is involved in. Hence, if Virat Kohli has to score the minimum possible number of runs, he should be involved in as less number of partnerships as possible. That means Virat Kohli (who comes out to bat after the fall of the first wicket) should be the batsman to lose his wicket in each match. Therefore, Kohli’s contribution would be restricted to only the 2^{nd} wicket partnership in each match.

Wickets | Match 1 | Match 2 | Match 3 | Match 4 | Match 5 |

2 | 25 | 10 | 5 | 55 | 20 |

Since Kohli scores at least half the runs in every partnership he is involved in and the number of runs scored by a player is always an integer, he would score runs, runs, runs, runs and runs in matches one, two, three, four and five respectively.

Hence, minimum possible runs scored runs

Hence option A

Q: 30. In the fifth match, the Indian team went on to score a total of runs. By what percent is the contribution of the first four players who came out to bat more than that of the remaining players who came out to bat?

(A)

(B)

(C)

(D) Cannot be determined

Ans: (D)

Solution

The first four players to bat need not necessarily be the first four players to lose their wickets. It is possible that the fifth person to bat could be the fourth person to lose his wicket. Hence, it is impossible to find out the contribution made by the first four batsmen and therefore it is impossible to determine the contribution made by the other batsmen. Cannot be determined..

**End Passage**