Crack CAT 2023 with Practice Set -2: Top Questions and Expert Tips -Day 8

Hi aspirants, Hope all the aspirants have started to follow the schedule we prepared for you for 60 days on how to prepare for CAT exam. We are done with the strategy on CAT preparation for day 1 to day 7. On the basis of the CAT syllabus we covered in the first seven days, we invite you to take the CAT sample paper (CAT exam questions with answers) which is given below and track your progress with self-analysis. CAT exam questions and answers prepared for the students to get a learning experience of the syllabus in different ways and how they can prepare it well.

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We have prepared a 60-day preparation plan, syllabus, schedule, and activity on a daily basis. Students will be updated every day here with an article, based on the divided CAT syllabus along with the CAT exam questions with answers. Students can also download the pdf of the online CAT mock test free for all - CAT exam previous year question papers with answers

Part-A: Quantitative Aptitude for CAT 2023

Cat Exam Aptitude Questions

Q1. If 138! is divisible by 7n, then find the maximum value of n.

1. 24

2. 20

3. 21

4. 22

Q2. Find the smallest natural number n such that n! is divisible by 1430.

1. 3

2. 13

3. 11

4. 124

Q3. Find the remainder when 591 is divided by 626.

1. 125

2. 1

3. 49

4. 7

Q4. n is a number, such that 2n has 8 factors and 3n has 6 factors. 6n has.

1. 24

2. 48

3. 12

4. Cannot be determined

Q5. How many pairs of positive integers x, y exist such that LCM (x, y) - HCF (x, y) = 42? [TITA]

Q6. 8 different brands of pairs of shoes counting 16, 64, 48, 88, 92, 60, 120, and 44 were ordered by a newly opened store. They need to be packed in such a way that each box has the same brand of pair of shoes and the number of pairs of shoes in each box is also the same. What is the minimum number of boxes required to pack?

1. 129

2. 64

3. 48

4. 133

Q7. Mr Kaju Srivastava is worried about the Expenditure on PNG. The price of PNG has increased by 30%. By what percent should he reduce the consumption of PNG so that he is able to maintain his Expenditure on PNG?

1. 33.33 %

2. 21 %

3. 23 %

4. 14.28 %

Q8. Of the population over 18 yrs in Singapore, 36% of men and 45% of women are married. What percentage of the total population of age more than 18 yrs are men? (Assume that no man marries more than one woman and vice versa)?

1. 44.44%

2. 55.55%

3. Cannot be determined

4. None of these

Directions for Questions 9 to 10: Read the following and answer the questions that follow.

Vande Bharat express has 4 AC-I coaches having 24 berths each, 6 AC-II Coaches having 45 berths each, and 3 AC-III Coaches having 64 berths each. There are no general Coaches on the train. If Rs 2000 is the cost of an AC -III berth from Delhi to Jammu. Following information in addition to above information is given:

AC-I berth is 20% expensive than AC-II berths.

AC-II berth is 20% more expensive than AC-III berths.

answer the following questions:

Q9. The value of the maximum revenue possible from Vande Bharat Express between Delhi to Jammu is

1. More than Rs.1.5 million

2. less than Rs.1.5 million

3. More than Rs. 1 million

4. Between Rs 1 to 1.5 million

Q10. What percent of revenue is generated from AC-I tickets in the previous question?

1. 24.23%

2. 21.13%

3. 22.23%

4. 28.9%

CAT Practice Papers: Answers And Solutions

Part A (Quantitative Aptitude)

CAT entrance exam question papers with answers:

Ans1: (c)

To find the maximum value of ‘n’, we have to count the number of 7s in 138!

So, n = [138/7] + [138/49], where [x] = maximum integer function

So, n = 19 + 2 =21

Ans 2: (b)

Do Prime factorization of 1430

i.e. 1430 = 13 x 11 x 5 x 2

n! must be 13 or greater since before 13, n! do not contain any 13.

So, the answer must be n = 13 (13! Will contain at least one 5, one 2, one 11 and one 13)

Ans 3: (a)

When 54 i.e. 625 divided by 626, the remainder is -1.

591 = (54x22) x53 = (625²²) x125

Rem (591/626) = Rem {(625²²) x125/ 626} = Rem {(-1)²² x125/626} = 125

Ans 4: (c)

2n has 8 factors. So, 2n must be of the form of one of the following:

2n = axbxc (no of factors = 2x2x2 = 8, here a, b and c are prime numbers)

Or

2n = axb³ (no of factors = 2x4 = 8, here a and b are prime numbers)

It is clear from here a= 2.

3n has 6 factors. So, 3n must be of the form of one of the following:

3n = b⁵ (no of factors = (5+1) = 6, where b is a prime numbers)

Or

3n = cxb² (no of factors = 2x3 = 6, here c and b are prime numbers)

It is clear from here b = 3.

Here c will be a prime number other than 2 and 3.

Case 1:

2n = ax b³= 2n = 2x3³; both cases of 3n will not be possible. So 2n cannot be ax b³.

Case 2:

2n = axbxc = 2x3xc; 3n = cxb² = cx3² is possible

So, n = 3xc

6n = 2x3^2×c

No of factors = (1+1) x (2+1) x (1+1) = 2x3x2 = 12

Ans 5: 10 possible pairs are there.

Solution is as follows:

Let x = h x a; y = h x b, where h is HCF of x and y; a and b are co-primes

LCM = h x a x b

ATQ

h x a x b – h = 42

h (a x b - 1) = 42

Total possible pairs in a and b are 10.

Therefore, 10 pairs in x and y exist.

Ans 6: (d)

Take the HCF of the number of pairs of shoes and divide the total number of pair of shoes by HCF to find the minimum number of boxes required.

HCF (16, 64, 48, 88, 92, 60, 120, 44) = 4

Number of boxes are required = (16+64+48+88+92+60+120+44)/4 = 133

Since n is even, unit digit of 42n + 1 = 4 (Since 4^odd is always gives 4 as unit digit)

and unit digit of 4n = 6 (Since 4^odd is always gives 6 as unit digit)

Ans 7: (c)

Price is increased by 30% means, if initial price was Rs 10 then new price will be Rs. 13

E₂ (New Expenditure) = E₁ (old Expenditure)

Using,

E₂/E₁ = (New Price/ Old Price) x (New Consumption/ Old Consumption)

1 = 13/10 x(New Consumption/ Old Consumption)

So, (New Consumption/ Old Consumption) = 10/13

We can say consumption will reduce from 13 to 10 i.e. 23.07%

Ans 8: (b)

Let there are 100x and 100y men and women respectively (Age more than 18 yrs)

Married Men = Married Women

i.e. 36x = 45y

So, x = 5y/4

Total Men = 100x = 100x5y/4 = 125y

Total Population (more than 18yrs) = 125y + 100y = 225y

Men = 125y × 100/225y % = 55.55%.

Ans 9: (d)

Cost of AC-III berth = Rs 2000

Cost of AC-II berth = Rs 2400

Cost of AC-I berth = Rs 2880

Maximum revenue is when all the berths are filled

Revenue from AC-III Coaches = 3x64x2000 = Rs 384000

Revenue from AC-II Coaches = 6x45x2400 = Rs 648000

Revenue from AC-I Coaches = 4x24x2880 = Rs 276480

Total revenue = Rs 384000 + Rs 648000 + Rs 276480 = Rs 1308480

Ans 10: (b)

Revenue from AC-I coaches = Rs 276480

Total Revenue = Rs. 1308480

Share of AC-I = 276480 × 100/1308480 = 21.13%

Part-B: LRDI Sets For CAT 2023

Direction (Q1-Q3):

The graph below informs about the total area and the population density for 8 different countries. The area of all countries is the same for the two years 2002 and 2008 and is shown by the bar graph, read off from the right-hand Y-axis. The population density is dividing the total population of the country by the area and is depicted by the line graphs and is read off the left-hand Y-axis. The two line graphs refer to the population density in the years 2002 and 2008.

Q1. How many countries had a higher population in 2008 as compared to 2002?

1. 8

2. 7

3. 6

4. Cannot be determined.

Q2. Find the increase in the population of F from 2002 to 2008.

1. 5.44 mn

2. 5.44 lacs

3. 5,440

4. Cannot be determined

Q3. The country with the largest population in 2008 among the given countries is

1. A

2. E

3. F

4. Cannot be determined

Population Density = Thus, the Population of a country can be found by multiplying the population density by the area.

CAT Practice Papers: Answers And Solutions

Part B (LRDI)

1. c

Since for all countries, the area remains the same over the two years, 2002 and 2008, then if population density has increased from 2002 to 2008, the population has increased and if population density has decreased, then the population has decreased. The number of countries having a population density in 2008 more than that in 2002 is 6 (except B and E)

2. a

The increase in the population of F = (70 – 62) × 680,000 i.e. 8 × 680,000 = 5,440,000 i.e. 5.44 mn.

3. b

Since the area has remained the same in 2002 and 2008, the percentage increase in the population is the same as the percentage increase in the population density. Thus, the required percentage growth is percentage growth from 46 to 56 i.e. a decrease of 10/46 i.e., 10/46 x100 = 21.73%

The country with the largest population is going to be one that has a higher population density as well as a higher area. Looking for this combination in the graph, the choices are narrowed down to E and F. (Each of the rest of the countries has both the area and the population density lower than one of these two countries)

Population of E in 2008 = 76 × 600 = 45600 thousand.

Population of F in 2008 = 70 × 680 = 47600 thousand.

Thus, in 2008, the highest population is F.

Directions for questions 4 to 7: Answer the questions on the basis of the information given below.

The following table gives the details of the production of 4 crops in India from the years 2007 to 2010. Winter and Summer refer to two different seasons of sowing and harvesting in the year. All 4 crops are produced in both seasons and the break-up across the two seasons is also given in the table.

Further, the table also gives the yield of the crops across the seasons and the years. Yield is defined as the production of the crop per hectare of the area under cultivation.

Production figures are in million tonnes and the Yield is in tons/hectare.

Q4. In 2008, for how many of the four crops is the yield in the summer season more than the yield in the Winter season?

1. 1

2. 2

3. 3

4. 4

Q5. In which year did the area under cultivation of Rice in the Winter season increase by the greatest rate?

1. 2007

2. 2008

3. 2009

4. 2010

Q6. Arrange the following in increasing order of their magnitudes

I. the area under cultivation of Jowar in the Summer season in the year 2009

II. the area under cultivation of Maize in the Winter season in the year 2007

III. the area under cultivation of Pulses in the Summer season in the year 2010

1. I,II, III

2. I, III, II

3. II, III, I

4. III, II, I

Q7. The area under cultivation of which crop was the highest in the Winter season of 2008?

1. Rice

2. Jowar

3. Maize

4. Pulses

CAT Practice Papers: Answers And Solutions

Part B (LRDI)

Solutions:

Since , and we are given Production and Yield figures, so re-arranging the relation to get area, we have . With the units given, we will get the area in million hectares.

4. c

Just check the table where the yield in second row is more then the yield in the first row in 2008

We see that for Rice, Maize and Pulses, the yield in Summer is more than the yield in Winter.

5. b

The area under cultivation of rice in Winter season in successive years can be found as . And we have to find in which year the growth rate is the greatest. Just by solving the above fraction, we found that in 2008 we have the highest growth rate

6. a

I. Area = = 4.46

II. Area = =6.4

III. Area = =10.51

Thus, increasing order will be I, II, III

7. a

The area for Rice, Jowar, Maize and Pulses is found as

Part-C : VARC for CAT 2023

In the questions below, find the phrase with error.

Q1: As Franklin ran (a)/ next the street, he wondered (b)/ what he should buy.(c)/ No Error (d)

1. (a)

2. (b)

3. (c)

4. (d)

Ans: B.

“Along the street” should be there in place of “next the street”

Q2. Hardly had he visited(a)/ his friend’s house(b) when got invited(c). No Error(d)

1. (a)

2. (b)

3. (c)

4. (d)

Ans: A

In interrogative sentences, the first form of the verb should be used.

‘Visit’ should be there

Q3. This view has been taken (a)/ by one of the ablest persons (b)/ who has written on this subject (c)/. No error(d)

1. (a)

2. (b)

3. (c)

4. (d)

Ans. C

‘Have’ in place of ‘has’ should be there. (Plural verb should come with plural noun)

Q4. Due to population, Indian(a)/ agriculture are in pressure to raise(b)/ more and more crops. (c) /No Error(d)

1. (a)

2. (b)

3. (c)

4. (d)

Ans: B

‘Under pressure’ will be there in place of ‘in pressure’.

Q5. We must have(a)/ sympathy for the needy (b)/ and the poor. (c)/ No Error(d)

1. (a)

2. (b)

3. (c)

4. (d)

Ans: D

for the needy (use of definite article)

Q6. Prince Charles is a heir (a)/ to the throne(b)/ of Great Britain. (c)/ No Error(d)

1. (a)

2. (b)

3. (c)

4. (d)

Ans. A

‘an’ in place of ’a’ due to the vowel sound of an heir.

Q7. The roads of Agra(a)/ are wider and cleaner(b)/ than Noida. (c)/ No Error (d)

1. (a)

2. (b)

3. (c)

4. (d)

Ans. C

“than those of Noida” will be the correct phrase. (Comparison should be with similar things.)

Q8. The teacher asked(a)/ the student’s father to (b)/ put his sign on the report card. (c)/ No Error(d)

1. (a)

2. (b)

3. (c)

4. (d)

Ans. C

‘Signature’ in place of ‘sign’

Hope everyone learned the concepts and will practice more!

Keep practicing, keep learning, see you on Day 9

Thank you

All the Best