CAT Model Paper 8 Questions and Answers with Explanation Part 2

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Q: 7. Find the sum of the 1st 30 terms of the series:

(A)

(B)

(C)

(D) None of these

Ans: C

Solution:

Since , we can write the sum as:

Since , we can write the sum as:

Q: 8. A person wrote the 1st 10000 natural numbers, next to each other, in the ascending order, from left to right. Find the total number of digits he wrote.

(A) 38894

(B) 38893

(C) 10000

(D) None of these

Ans: A

Solution:

The correct choice is (A).

Natural Numbers
Natural numbers

NO.

Single digit Numbers

9

1

9

2 digit Numbers

90

2

180

3 digit Numbers

900

3

2700

4 digit Numbers

9000

4

36000

10000

1

5

5

Total

38894

Q: 9. Given, which of the following is definitely true about N?

I. N is a perfect square when n is prime.

II. N is always divisible by .

III. For , N leaves a remainder of 3 when divided by 10.

(A) Only I

(B) Only II

(C) Only I & II

(D) Only II & III

Ans: D

Solution:

For is not true.

. Since onwards all expressions are divisible by 3, II is true.

For , unit digit of N is always 3. Hence III is true.

Q: 10. Two swimmers starts swimming simultaneously from the same point, one towards the south and the other towards the east. After two hours the shortest distance between them is . The speed of the slower swimmer is of that of the faster swimmer. What is the speed of the faster swimmer?

(A)

(B)

(C)

(D)

SOLUTION

Let the speed of the swimmers be respectively.

So, distances travelled by them in 2 hrs are 8x km and km respectively.

Using Pythagoras theorem,

Q 10 Image of Pythagoras Theorem

Q 10 Image of Pythagoras Theorem

.

Q: 11. Harish Chandra wrote 50 numbers on the black board. Varadhan deleted several numbers which added to and replaced the deleted numbers with 10 numbers that had an average of . As a result of this operation the average amount of the original group of numbers became identical to the new group of numbers so formed after deletion and addition. Harish Chandra now wrote the deleted numbers once again on the black board and recalculated the average (also taking into consideration the 10 new numbers added by Varadhan). The new average was . What was the average of the original group of 50 numbers?

(A)

(B)

(C)

(D) Cannot be determined

Ans: B

Solution:

In this problem, the deletion process has been given to confuse the students since the deleted numbers are actually being re inducted any way. So the problem boils down to a simple case of 50 numbers having an average A (say) being taken along with 10 more numbers so that the final average of the group of 60 numbers is 270.

Hence, we have

or

Start Passage

Answer the questions based on the information provided below.

Every day the Kolkata stock exchange opens at 10:00 hours and closes at 15:30 hours. A person can trade shares during this entire time every day. In the table below the share prices of four different companies are given at every hour of trading on a particular day. All the prices are in rupees.

Q_12-to-14_Table of All the Prices Are in Rupees
Q_12-to-14_Table of All the Prices are in Rupees

10:00

11:00

12:00

13:00

14:00

15:00

15:30

REL

899.8

901

885.9

882.9

882

874

875

SBI

1333

1330

1328

1343

1349

1334

1306

BHEL

230.2

227.3

215.4

214

210.2

211.5

210.7

TATA

300.5

290.9

291.4

290.2

290.8

295.2

292.3

Q: 12. Mr. Parekh bought shares of a company at hours and sold them at hours. If he made the maximum possible loss that he could have made, then which company did he pick?

(A) REL

(B) SBI

(C) BHEL

(D) TATA

Ans: A

Solution:

The correct choice is (A). For 1 share,

For REL

From SBI

From BHEL

From TATA

Q: 13. Mr. Jhunjhunwala’s strategy is to buy 50 shares of each company at a specific time and sell all of them at hours. At what time should he have made the purchase to minimize his losses?

(A)

(B)

(C)

(D)

Ans: D

Solution:

Refer to the table given below:

Q_13_Mr. Jhunjhunwala’S Strategy is to Buy 50 Shares of Each Company at a Specific
Q_13_Mr. Jhunjhunwala’s Strategy is to buy 50 Shares of Each Company at a Specific

10

15.3

Loss

12

15.3

Loss

13

15.3

Loss

15

15.3

Loss

REL

899.8

875

-24.8

885.9

875

-10.9

882.9

875

-7.9

874

875

1

SBI

1333

1306

-27

1328

1306

-22

1343

1306

-37

1334

1306

-28

BHEL

230.2

210.7

-19.5

215.4

210.7

-4.7

214

210.7

-3.3

211.5

210.7

-0.8

TATA

300.5

292.3

-8.2

291.4

292.3

0.9

290.2

292.3

2.1

295.2

292.3

-2.9

Total loss

-79.5

-36.7

-46.1

-30.7

He must buy at 15.00

Q: 14. Mr. Ajay buys the shares of one of the companies at 10.00 hours and sells all of them at 15.30 hours. Which company should he choose so that the percentage change in the price is the minimum?

(A) REL

(B) SBI

(C) BHEL

(D) TATA

Ans: B

Solution:

Refer to the table below:

Q_14_Table of the Shares of One of the Companies
Q_14_Table of the Shares of One of the Companies

10

15.3

Change

Change %

REL

899.8

875

-24.8

2.80%

SBI

1333

1349

-27

2.10%

BHEL

230.2

210.2

-19.5

8.50%

TATA

300.5

290.8

-8.2

2.70%

He must buy the shares of SBI.

End Passage

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