Get CAT-Ready: Comprehensive Practice Questions for Exam Success- Day 28

CAT Question paper: CAT mock test online

This CAT question paper with solutions based on the CAT syllabus 2024 has been covered in 23 days, and consists of three Sections:

Part- A consists of 7 questions.

Part- B consists of 8 questions.

Part- C consists of 2 RCs with 5 questions each.

Part-1: CAT Exam Question Paper 2024 (Quantitative Aptitude)

Q1. A cistern contains 40 litres of Alcohol. 4 litres of alcohol are taken out of it and replaced by water. The process is repeated two more times. Find the proportion of water and alcohol in the resulting mixture.

1. 729 : 281

2. 271 : 729

3. 19 : 81

4. 81 : 19

Q2. A mixture worth Rs 7.41 a kg is formed by mixing two types of flour, one costing Rs 3.31 per kg while the other Rs 9.81 per kg. In what proportion must they have been mixed?

1. 5 : 12

2. 12 : 5

3. 24 : 41

4. 41 : 24

Q3. In the MP Zoo, there are Lions and ducks. If the heads are counted, there are 148, while the legs are 396. What will be the number of Lions in the zoo?

1. 136

2. 68

3. 50

4. 22

Q4. If 2x² + 3y² = 7xy, what is the ratio of x to y?

1. 1 : 4

2. 3 : 2

3. 4 : 5

4. 1 : 2

Q5. If the work done by (x + 2) boys in (x - 1) days is to the work done by (x + 2) women in (x – 3) days is in the ratio 9 : 10, then the number of women is:

1. 10

2. 12

3. 8

4. 15

Q6. If P = {8, 12, 16, 20, 24, 28, 32}, another set Q is formed whose elements are the average of all the possible pairs of the elements taken from set P. What is the average of all elements of set Q. [TITA]

Q7. A started a business with 30,000. After 3 months B joined him with 40,000. C joined them after one more month with 1,20,000 and left the partnership after 4 more months. At the end of the year, out of a total profit of 3,61,000, the share of C is _________ [TITA]

Part-2: CAT Exam Question Paper 2024: CAT DILR sample Questions (Logical Reasoning and Data Interpretation)

Direction (Q1-Q4):

A kid is promised by his father that starting the following Monday, pocket money of five rupees per day will be given every day in the morning. The kid has a school five days a week from Monday to Friday and wants to spend that amount on purchasing snacks during breaks in the school. He equally likes chocolate (Rs. 5), Samosa (Rs. 10) and pastry (Rs. 15). He purchases not more than one item on any day. He makes a purchase if he has a sufficient amount to purchase an item and he will not purchase the same item in the next two purchases. (Assume the kid did not have any other money and there are no holidays other than Saturdays and Sundays)

Q1. Which of the following is true with regard to the pattern in which the kid makes his purchases?

Ι. More data is required to identify a pattern.

ΙΙ. The pattern of the purchases is repetitive.

ΙΙΙ. If the first purchase of the kid is known, then the pattern will be repetitive.

1. Only Ι and ΙΙΙ

2. Only ΙΙ

3. Only Ι

4. Either I or ΙΙΙ

Q2. What is the maximum possible amount available with the kid on any Monday?

1. Rs. 15

2. Rs. 20

3. Rs. 25

4. Cannot be determined

Additional information for questions 3 and 4: During the second week, the kid tasted a complimentary fruit worth 5, and decided to add to the fruit his purchase list from the following Monday, along with the other three such that the price of every next purchase increases and decreases alternately.

Q3. Which of the following is definitely true?

1. The kid does not purchase on a Wednesday.

2. The kid does purchase on a Thursday

3. The kid does not purchase on a Friday

4. The kid does purchase on a Tuesday

Q4. What is the maximum possible amount available with the kid on any Monday (after he decides to eat the fruit)?

1. Rs. 15

2. Rs. 20

3. Rs. 25

4. Cannot be determined

Direction (Q5-Q8)

G, H, I, J, O, P, Q and S – are a group of eight family members. All are having dinner, sitting around a circular table, facing towards the centre of the table. Among them, there are four males and four females. No two females are adjacent to each other. Each married couple, except one, has at least one child and there are two unmarried persons.

P is the son-in-law of G, who is four places away from J. I is two places away to the left of his/ her only daughter. H is the sister-in-law of Q. P and O are seated on either side of J. G is the grandmother of S who is the nephew of H. No married person is seated adjacent to his/her spouse.

Q5. How is J related to O?

1. Granddaughter

2. Daughter

3. Grandson

4. Cannot be determined

Q6. Who is sitting three places away to the right of P?

1. H

2. Q

3. S

4. Cannot be determined

Q7. How is Q related to O?

1. Brother-in-law

2. Son-in-law

3. Daughter-in-law

4. Father-in-law.

Q8. Which of the following alternatives does not fit into the group where the second person in a pair is to the left of the first person?

1. GQ

2. HO

3. JP

4. SI

Part-3: CAT Exam sample paper 2024: CAT sample questions for VARC (Verbal Ability & Reading Comprehension)

Reading comprehension

A. Every autumn, when recruitment of new graduates and school leavers begins, major cities in Japan are flooded with students hunting for jobs. Wearing suits for the first time, they run from one interview to another. The season is crucial for many students, as their whole lives may be determined during this period.

B. In Japan, lifetime employment is commonly practised by large companies. While people working in small companies and those working for sub-contractors do not, in general, enjoy the advantages conferred by large companies, there is a general expectation that employees will, in fact, remain more or less permanently in the same job.

C. Unlike in many Western countries where companies employ people whose skills can be effective immediately, Japanese companies select applicants with potential who can be trained to become suitable employees. For this reason, recruiting employees is an important exercise for companies, as they invest a lot of time and money in training new staff. This is basically true both for factory workers and for professionals. Professionals who have studied subjects which are of immediate use in the workplace, such as industrial engineers, are very often placed in factories and transferred from one section to another. By gaining experience in several different areas and by working in close contact with workers, the engineers are believed, in the long run, to become more effective members of the company. Workers too feel more involved by working with professionals and by being allowed to voice their opinions. Loyalty is believed to be cultivated in this type of egalitarian working environment.

D. Because of this system of training employees to be all-rounders, mobility between companies is low. Wages are set according to educational background or initial field of employment, ordinary graduates being employed in administration, engineers in engineering and design departments and so on. Both promotions and wage increases tend to be tied to seniority, though some differences may arise later on as a result of ability and business performance. Wages are paid monthly, and the net sum, after the deduction of tax, is usually paid directly into a bank account. As well as salary, a bonus is usually paid twice a year. This is a custom that dates back to the time when employers gave special allowances so that employees could properly celebrate bon, a Buddhist festival held in mid-July in Tokyo, but on other dates in other regions. The festival is held to appease the souls of ancestors. The second bonus is distributed at New Year. Recently, bonuses have also been offered as a way of allowing workers a share in the profits that their hard work has gained. Many female graduates complain that they are not given equal training and equal opportunity in comparison to male graduates. Japanese companies generally believe that female employees will eventually leave to get married and have children. It is also true that, as well as the still-existing belief among women themselves that nothing should stand in the way of child-rearing, the extended hours of work often do not allow women to continue their careers after marriage.

E. Disappointed career-minded female graduates often opt to work for foreign firms. Since most male graduates prefer to join Japanese firms with their guaranteed security, foreign firms are often keen to employ female graduates as their potential tends to be greater than that of male applicants

Q1. What difference has the author stated between Western countries' hiring and Japanese hiring of professionals?

1. People in Japanese firms look for people who will work for more hours as compared to Western firms where people are allotted a certain number of hours.

2. Western nations' firms hire people with instant abilities but Japanese employers look for persons with potential who can be trained to become suitable workers.

3. Employers of Japanese companies want people who have mentioned more extracurriculars in their resumes.

4. All of the above

5. None of the above

Q2. Why do female graduates in Japan forgo joining Japanese firms in favour of foreign firms?

1. Japanese culture believes that females bring in lesser results as compared to men.

2. Because their local firms’ employers think that female employees would ultimately depart to marry and start a family.

3. Female graduates are keen to experience the work culture of foreign firms because of its novelty.

4. Both (a) and (c)

5. All of these

Q3. Large corporations frequently use ____in Japan.

1. Multiple interviews

2. Deduction of tax

3. Long hours and fewer wages

4. Lifetime employment

5. None of these

Q4. Among the following statements, which one is true about the Bon festival that is held in Japan?

1. The event is conducted to placate the spirits of those who have passed away.

2. Held in the middle of July in Tokyo but other regions have different dates.

3. This festival has inspired foreign firms in Japan to give bonuses twice a year.

4. Both (a) and (b)

5. None of these.

Q5. Select the synonym of crucial as highlighted in the passage.

1. Pivotal

2. Sedentary

3. Relegate

4. Aspire

5. None of these

Reading Comprehension

Most of these churches belonged to the catholic church, specifically the Syro-Malabar rite, forming a sizable chunk of the Christian population in the state. The ostensible reason for these large-scale demolitions was the space constraints in the age-old structures, but a more immediate reason was the kind of money coming in as donations and charity from the laity, growing prosperous on the back of a spike in prices of rubber among other cash crops. Towns with sizable Catholic populations in the Kottayam district such as Pala and Kanjirappally, would see a huge offtake of the newly launched cars back then. The era of prosperity, however, was short-lived as the Association of South East Asian Nations (ASEAN) India free trade agreement and other factors caused the prices of rubber and other cash crops to nosedive.

With the community’s collective bargaining power on the wane, its focus gradually shifted to the Muslim community’s newfound affluence on the back of West Asian remittances. The seeds of mistrust threatening to rip apart the social fabric of Kerala today were sown about a decade ago. There were _____ to love Jihad from the clergy even then, but it remained confined to catechism classes or drawing room conversations. The assault, in 2010, on Professor T.J. Joseph, whose palms were chopped off by Popular Front of India (PFI) extremists proved to be a seminal event, despite the Church going on the defensive and even victimising the professor in its aftermath. The fallout of this incident was contained by the swift intervention of civil society; yet, in hindsight, this was probably the point when Islamophobia began to take root among Christians in Central Travancore. The assembly election in 2011 saw the congress-led United Democratic Front(UDF) coming back to power but it also saw the eclipsing of the Church-backed Kerala Congress by the Indian Union Muslim League (IUML)in the power structure contributing to the churning.

When the ruling party came to power in New Delhi in 2014, the Sangh Parivar saw an opportunity to close ranks with the Christian community to reverse its electoral fortunes in Kerala. By 2016, as the Islamic State (IS) gained prominence, 21 Keralites- some Christian and Hindu converts among them- who had gone missing were traced to the terrorist outfit, sparking further anxiety within the Church. A spate of anti-Muslim propaganda began to circulate within Christian family networks and social media groups around that period.

Q6. Which of the following is/are the reason(s) for the destruction of Churches?

1. The conflicts on a religious basis caused the devastation of churches by non-Christian groups.

2. The old constructed Churches don’t have enough space.

3. An increase in the price of cash crops including rubber rendered an increase in donations and charity.

4. Both (b) and (c)

5. Both (a) and (b)

Q7. Which of the following is the reason behind the end of the affluence period?

1. There was high inflation caused by high rubber prices which made people out of pocket.

2. The price of cash crops declined sharply due to the government’s agreement of free trade with ASEAN countries.

3. High taxes and tariffs on exports and imports made rubber costlier and eventually declined in demand.

4. The lack of a proper stable market for cash crops caused turmoil and a decline in prices

5. None of these

Q8. When did Islamophobia start to establish itself among Christians?

1. The root of the establishment was sown about a decade ago which later thrived.

2. Only in 2010, when the assault on the professor took place and people started intervening.

3. Islamophobia was confined to catechism classes and in some other parts of Kerala's outskirts.

4. After the assembly elections in 2011, after which Congress-led United Demographic Front came into power.

5. None of these

Q9. Which of the following is the reason for contempt of Muslims in Kerala?

1. The expansion of Islamic religion in Christian-led Kerala was a cause of concern.

2. Keralites were against the prominence of Sangh Parivar whose perspective was election-winning only.

3. Keralites converted to Muslims and were later tracked down by the terrorist organisation

4. All of these

5. None of these

Q10. Which of the following is opposite in meaning to gradually as used in the passage?

1. Variations

2. Laud

3. Instantly

4. Malicious

5. None of these

Part-1: CAT Test Series 2024 (Quantitative Aptitude)

Solution 1: (B)

Final Proportion of Alcohol = Initial Proportion of Alcohol[1 - (Volume of alcohol taken out / Total volume)]n

n = number of replacements = 3

Initial Proportion of Alcohol = 40

Alcohol taken out = 4 litres

Volume after addition of water = 36 + 4 = 40

∴ Final Proportion of Alcohol = 40 × [ 1 - (4/40)]3 = 29.16 litres

Final amount of water = 40 - 29.16 = 10.84 litres

∴ Water : Alcohol = 10.84 : 29.16 = 271 : 729

Hence, the correct answer is 271 : 729.

Solution 2: (C)

Required ratio

= (Higher value – Mean value) : (Mean value – Lower value)

= (9.81 – 7.41) : (7.41 – 3.31)

= 2.4 : 4.1

= 24 : 41

Hence, the correct answer is 24 : 41.

Solution 3: [C]

Let the number of lions be x.
So, number of ducks be (148 - x).
Lions have 4 legs and ducks have two.
According to the question,
4x + (148 - x)× 2 = 396
⇒ 4x + 296 - 2x = 396
⇒ 2x = 100
∴ x = 50
Hence, the correct answer is 50.

Solution 4: (D)

2x² + 3y² = 7xy

Divide the above equation by xy.

2(x/y) + 3(y/x) = 7

Let a = x/y

So, 2a + 3/a = 7

⇒ 2a² -7a +3 =0

⇒ a = 3 or a = ½

So, x/y = 3/1 or ½ (It is in the options)

Hence, the correct answer is 1 : 2.

Solution 5: [B]

According to the question:

(x+2)(x-1)/(x+2)(x-3) = 9/7

⇒ (x-1)/(x-3)=9/7

∴ x = 10

So, number of women = x + 2 = 10 + 2 = 12

Hence, the correct answer is 12.

Solution 6:

Trick: Let P = {a, b, c}

Q = {(a+b)/2, (b+c)/2, (c+a)/2}

Average of elements of Q = {(a+b)/2+ (b+c)/2+ (c+a)/2}/3 = (a+ b+ c)/3

Therefore, the answer is = Average of {8, 12, 16, 20, 24, 28, 32} = 20

Hence, the correct answer is 20.

Solution 7:

A was in partnership for 12 months with Rs. 30000.

B was in partnership for 9 months with Rs. 40000.

C was in partnership for 4 months with Rs. 120000

Ratio of Profits of A, B, and C

= (30000 × 12) : (40000 × 9) : (120000 × 4)

= 36 : 36 : 48 = 3 : 3 : 4

∴ Share of C = 361000 × 4/(3 + 3 + 4) = 361000 × 4/10 = 144400

Hence, the correct answer is Rs. 144400.

Part-2: CAT Mock test series 2024: CAT DILR Solutions

Solutions (Q1-Q4):

Solution:

The kid receives Rs. 5 per day, ⇒ earns Rs. 35 per week, but earns a maximum of Rs. 25 in the first five days. Implies spends a maximum of Rs. 25 in the first five days ⇒ purchases only two items in the first week.

The amount available by next Monday is the sum of savings during the first five days and the amount earned during the weekend. The kid earns Rs. 10 on the weekend which is available for next Monday. Thus, from the second week onwards, he can purchase all the items at least once. The amount available on the second Monday will be among Rs. 15, Rs. 20 or Rs. 10.

Whatever items the kid purchases in the first week, the total amount the kid can spend up to the second week is the income of the first week and the first five days of the second week. i.e., Rs. 35 + Rs. 25 = Rs. 60.

By repeating the purchase of three items twice, the kid purchases all the items twice.

Starting the second week, in n weeks the kid purchases all the items at least n times and at most (n + k) times. In order for the purchases to make a pattern, n (35) = (n + k) (30) ⇒ n = 6k

⇒ for every 6 weeks, (k = 1), all the items would be purchased seven times.

Pastry = P = Rs. 15

Samosa = S = Rs. 10

Chocolate = C = Rs. 5

Answer 1: (B)

From the above, the given data is sufficient to determine that the pattern of the purchases is repetitive.

Hence only ΙΙ is true.

Answer 2: (C)

From the table, the maximum savings available on any Monday is Rs. 20, plus he would receive pocket money of Rs. 5, thus the maximum amount available on any Monday = Rs. 25.

Answer 3: (D)

Given that the kid makes a purchase as soon as he accumulates sufficient money to make his next purchase as per the defined conditions. With the new condition, the possible combinations in the five days of the week, for the kid to purchase the four items Chocolate (C), Fruit (F), Samosa (S) and Pastry (P) is F/C, S/P, C/F, __, P/S (No purchase on Thursday).

Hence, Only (D) is definitely true.

Answer 4: (A)

In the third week, opening balance = Rs. 10. Earns Rs. 25 during the five-week days. Spends Rs. 35 during five days. And earns Rs. 10 during the weekend. The kid starts with a balance of Rs. 10 every week. The maximum amount the kid has on any Monday in Rs. 15.

Solution: (Q5-Q8)

G is four places away from J ⇒ G and J are opposite each other. P and O are on either side of J. The representation will be as follows.

As P is a male, J must be a female and O must be a male. H is the sister-in-law of Q, and the spouse of P can be either H or Q.

Case (i): Let the spouse of P be Q. Then the representation will be as follows.

As I is two places away to the left of his/her daughter, I’s daughter must be Q and I must be the spouse of G and not next to her. The positions of I and Q in the circular arrangement are not possible.

∴ H is not the spouse of P.

Case (ii): H must be the spouse of P. The hierarchical representation will be as follows.

Here I can be the spouse of either G or Q. If I is the spouse of G, Then I must be two places away to the left of H. The position of I and H in the circular arrangement cannot be represented. ∴ I must be the spouse of Q. As J is female and O is male. O must be the spouse of G and J must be the daughter of I.

Finally, the circular arrangement representation is as follows.

Answer 5: (A)

Answer 6: (A)

Answer 7: (B)

Answer 8: (D)

Part-3: CAT Exam sample paper 2024: VARC Solutions

Answer 1: (B)

Explanation: This answer can be found in the second paragraph, “Unlike in many Western countries where companies employ people whose skills can be effective immediately, Japanese companies select applicants with potential who can be trained to become suitable employees.”

Answer 2: (B)

Explanation: D&E para mentions, “Disappointed career-minded female graduates often opt to work for foreign firms. Since most male graduates prefer to join Japanese firms with their guaranteed security, foreign firms are often keen to employ female graduates as their potential tends to be greater than that of male applicants.”

Answer 3: (D)

Explanation: in the first para, it is clearly mentioned, “In Japan, lifetime employment is commonly practised by large companies.”

Answer 4: (D)

Explanation: both statements (a) and (b) are correct about the Bon Festival.

For statement (a), look at para D, The festival is held to appease the souls of ancestors.

For statement (b) glance at the line just before the previous one, This is a custom that dates back to the time when employers gave special allowances so that employees could properly celebrate Bon, a Buddhist festival held in mid-July in Tokyo, but on other dates in other regions.

Answer 5: (A)

Answer 6: (D)

Explanation: refer to the first para, The ostensible reason for these large-scale demolitions was the space constraints in the age-old structures, but a more immediate reason was the kind of money coming in as donations and charity from the laity, growing prosperous on the back of a spike in prices of rubber among other cash crops.

Answer 7: (B)

Explanation: refer to the first para, The era of prosperity, however, was short-lived as the association of southeast Asian nations (ASEAN) India free trade agreement and other factors caused the prices of rubber and other cash crops to nosedive.

Answer 8: (B)

Explanation: refer to the second para, The assault, in 2010, on Professor T.J. Joseph, whose palms were chopped off by Popular Front of India (PFI) extremists proved to be a seminal event, despite the Church going on the defensive and even victimising the professor in its aftermath. The fallout of this incident was contained by the swift intervention of civil society; yet, in hindsight, this was probably the point when Islamophobia began to take root among Christians in Central Travancore.

Answer 9: (C)

Explanation: option (c) is correct and is inferred from the last para, By 2016, as the Islamic State (IS) gained prominence, 21 Keralites- some Christian and Hindu converts among them- who had gone missing were traced to the terrorist outfit, sparking further anxiety within the Church. A spate of anti-Muslim propaganda began to circulate within Christian family networks and social media groups around that period.

Answer 10: (C)

Study material for CAT 2024