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The CAT Exam Roadmap: Navigating Success through Practice Set Questions- Day 20
Edited By Team Careers360 | Updated on Nov 07, 2024 09:18 AM IST | #CAT
Practice sets are very crucial from an exam point of view. On day 20 Career’s 360 has prepared this practice test to give the candidates exposure to the actual exam pattern. Students may refer to it and practice more papers in the following days using our articles. You may prepare for the CAT test in an organized way by following our 60-day CAT exam preparation strategy. Make sure to improve your test-taking skills by practising with these CAT practice questions every day.
CAT 2025: VARC, DILR, and Quant: MCQs & Weightages | Chapter-wise MCQs
CAT 2025 Study Material: VARC | Quantitative Aptitude | 60 Days Study Material by Experts
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This Story also Contains
- CAT Sample Paper with solutions PDF
- CAT Exam: Sample Papers: Answers and Solutions
- CAT Exam: Sample Papers: Answers and Solutions
- CAT Exam: Sample Papers: Answers and Solutions
- Free Ebooks for CAT Preparation 2024
CAT Sample Paper with solutions PDF
This CAT Sample paper consists of three Sections:
Part- A consists of 9 questions.
Part- B consists of 7 questions.
Part- C consists of 9 questions.
Quantitative Aptitude
Q1. For the given pair (x, y) of positive integers, such that (-x + 3y/2) = 7 and x < 210. How many integer values of y satisfy the given conditions? (CAT previous year questions)
340
341
342
1024
Q2. A quadratic function f(x) attains a maximum of 12 at x = 1. The value of the function at x = 0 is 7. What is the value of f (x) at x = -11? (CAT previous year questions)
-805
-719
-859
-883
CAT 2025: VARC, DILR, and Quant MCQs & Weightages
Comprehensive CAT prep guide with focused practice on Verbal Ability, Data Interpretation & Logical Reasoning, and Quantitative Aptitude.
Download NowQ3. If the roots of the equation in y i.e. y3 – ay2 + by – c = 0 are three consecutive integers, then the smallest possible value of b (nearest to its integer value) is ______________ [TITA]
Q4. The sum of the integers in the solution set of |x2 - 7x| > 5 is: (CAT exam model paper)
10
15
20
0
Q5. The equation x2 + ax + (3-b) = 0 has real roots. What is the minimum value of a2 + b2? (CAT previous year questions)
0
2
4
8
Q6. X is p% less than Y and Z is p% more than Y. If X is 2.5p% more than Z, then find p.
(Note: p ≠ 0) - (CAT previous year questions)
20
40
60
50
Q7. The value of the base of a triangle for which area is minimum if the relation between the perpendicular distance from the vertex and the base is p = 7b2 - 84 is _______________ (where b represents base and p represents perpendicular distance) [TITA]
Q8. Let f (x) = max (2x + 1, 3 − 4x), where x is any real number. Value of f(x) at x = 7.5 is: (CAT exam model paper)
-11
- 27
16
43
Q9. Let g (x) be a function such that g (x + 1) g (x) = 12 for every real x. Then what is the value of g (11) g (0)? (CAT exam model paper)
1
12
1/12
6
Logical Reasoning
Direction (Q1-Q3):
Four friends Arun, Bittu, Cirag and Dheeraj went for an excursion with their wives Priya, Renu, Sharita and Varti, not necessarily in the same order. Each couple hails from a different city, including Madurai, Cutnee, Kurnool, and Hapur, but they are not necessarily in that order. They went to Delhi to visit the Pinkfort, where they sat in a row. Each wife always sat to the immediate right of her husband.
(CAT practice questions)
(i) Bittu sat to the immediate right of Priya.
(ii) Dheeraj is from Hapur and Priya is not from Madurai.
(iii) Renu and her husband were sitting to the immediate right of the couple that hailed from Cutnee.
(iv) Chirag and his wife were sitting to the immediate left of the couple from Kurnool and Chirag was sitting to the immediate right of Sharita.
(v) Arun sat to the immediate right of Renu, who is not from Madurai.
Q1. Who is Dheeraj’s wife?
Sharita
Priya
Varti
Renu
Q2. Which couple is from Cutnee?
Varti and Bittu
Dheeraj and Renu
Chirag and Priya
Arun and Sharita
Q3. Who is the husband in the couple, who is seated second in the row from left to right?
Arun
Bittu
Chirag
Dheeraj
Direction (Q4- Q7) (CAT practice questions)
A cube is formed by joining 216 smaller and identical cubes. The bigger cube is painted black colour on all its faces. From the bigger cube, 64 smaller cubes from a corner were taken out and the cube formed by joining these 64 smaller cubes is painted pink in all its faces. Again, this cube is fitted back into its usual position in the large cube.
Q4. How many smaller cubes have no faces painted?
Q5. How many smaller cubes have three faces painted?
Q6. How many smaller cubes have only two faces painted?
Q7. How many smaller cubes have only one face painted?
VARC (CAT solved papers)
In the questions below, find the phrase with an error.
Q1: If I had known, I would lend you my car.
I will lend you my car
I would lent you my car
I would have lent you my car
No improvement needed
Q2. You have no trouble at school, if you had done your homework.
You would have had no trouble at school.
You will have no trouble at school.
You would had no trouble at school
No improvement needed
Q3. If you had done better at your interview, you get that job.
You will get that job.
You would get that job.
You would have got that job.
No improvement needed
Choose appropriate sentence
Q4. While the guests danced, the thieves broke into the house.
While the guests have danced
While the guests were dancing
While the guests had danced
No improvement needed
Error detection - (CAT exam paper sample)
Q5. Take a shower (a)/ you will (b)/ feel better. (c) / No error (d)
(a)
(b)
(c)
(d)
Q6. Whenever I look (a)/ at the moon, my heart (b)/ fills with the pleasure. (c)/ No error(d)
(a)
(b)
(c)
(d)
Q7. The whole block of flats (a)/ including two shops were (b)/ destroyed in fire. (c)/ No error (d)
(a)
(b)
(c)
(d)
Q8. The man who cannot (a)/ believe his senses and the man who cannot (b)/ believe anything else are insane. (c)/ No error(d)
(a)
(b)
(c)
(d)
Fill the blank with the correct Article:
Q9. If you go by __ train you can have quite__ comfortable journey, but make sure you get ___ express, not __ train that stops at all the stations.
a, an, a, the
an, a, the, a
No article, an, a, the
No article, a, an, a
CAT Exam: Sample Papers: Answers and Solutions
Part-A: Quantitative Aptitude
Answer 1: (B)
3y/2 = 7 + x
⇒ y = (14 + 2x)/3; for y to be integer (14 + 2x) should be divisible by 3
So, x = 2; y = 6
When x= 5, y = 8
When x = 8, y = 10
When x = 11, y = 12 and so on…
So, there is an AP in x with the first term being 2 and the common difference is 3.
nth term in x must be less than or equal to 210 i.e., 1024.
Therefore, 2 + (n-1)3 ≤ 1024
⇒ n ≤ (1022/3) +1
Therefore, n must be 341.
Hence, there can be 341 solutions.
Answer 2: (D)
If the function gets the maximum of 12 at x = 1
f(x) = a(x – 1)2 + 12
So, f (0) = a + 12 = 7 [Given]
⇒ a = –5
f(x) = –5(x – 1)2 + 12
So, f(-11) = –5(-12 – 1)2 + 12 = –845 + 12 = –833
Hence, the correct answer is –833.
Answer 3:
Let roots be (n - 1), n and (n + 1).
In a cubic equation, the coefficient of y divided by the coefficient of y3 represents the sum of the product of roots taken two at a time.
So, b = the sum of the product of roots taken two at a time
n(n - 1) + (n + 1)n + (n - 1) (n + 1) = b
⇒ n2 - n + n2 + n + n2 - 1 = b
⇒ 3n2 - 1 = b
The value of b will be minimal when the value of n2 is minimum.
i.e., n2 = 0
So, 3 × 0 - 1 = b
∴ b = -1
Hence, the correct answer is -1.
Answer 4: (D)
|x2 - 7x| > 5
⇒ x2 - 7x > 5 or x2 - 7x < -5
Case 1:
⇒ x2-7x > 5
⇒ x2 - 7x – 5 > 0
⇒ x > [(7±√69)/2], which gives two solutions x > 7 or x < 0 (for x to be integer).
Case 2:
⇒ x2 - 7x < -5
⇒ x2 - 7x + 5 < 0
⇒ x < [(7±√29)/2], which gives two solutions x < 7 or x > 0 (for x to be integer).
So, x = [1, 2, 3, 4, 5, 6]
There is no common solution in both cases.
Hence, the correct answer is 0.
Answer 5: (D)
For real roots; a2 – 4(3 – b) ≥ 0
⇒ a2 + 4b – 12 ≥ 0
⇒ a2 + 4b + b2 – b2 – 12 ≥ 0
⇒ a2 + b2 ≥ b2 – 4b + 12
⇒ a2 + b2 ≥ b2 – 4b + 4 + 8
⇒ a2 + b2 ≥ (b – 2)2 + 8
At b = 2, a2 + b2 has the minimum value. i.e., 8.
Hence, the correct answer is 8.
Answer 6: (A)
X = (100 – p) Y/100
Z = (100 + p) Y/100
X = (100 + 2.5p) Z/100
From 1st and 2nd relation, we get X = Z (100 – p) / (100 + p)
So, Z (100 – p) / (100 + p) = (100 + 2.5p) Z/100
⇒ 100(100 – p) = (100 + p) (100 + 2.5p)
⇒ – 100p = 100p – 250p + 2.5p2
⇒ 50p = 2.5p2
⇒ p = 20
Hence, the correct answer is 20.
Answer 7:
Area = ½ (base) (height) = ½ b (7b2 - 84) = 7b3/2 - 84b1/2
For Area to be minimum, find dA/db = 21/2 b2 – 42 = 0
⇒ b2 = 4
⇒ b = 2 or b = -2
Now find d2A/db2 = 21b
At b = 2; d2A/db2 = 42, which is greater than 0.
So, at b = 2, we get the minimum value of Area.
Hence, the correct answer is 2.
Answer 8: (C)
f(x) = max (2 × 7.5 + 1, 3 – 4 × 7.5) at x = 7.5
⇒ f(x) = max (16, -27) at x = 7.5
Hence, the correct answer is 16.
Answer 9: (B)
For x = 0; g(1) = 12/g(0)
Similarly g(2) = 12/g(1), which gives g(2) = g(0)
g(3) = g(1) and so on.
Therefore, g(11) = g(9) = g(7) = ……= g(1) = 12/g(0)
⇒ g (11) g (0) = 12
Hence, the correct answer is 12.
CAT Exam: Sample Papers: Answers and Solutions
Part B - Logical Reasoning
Solution 1-3:
Males: Arun, Bittu, Cirag and Dheeraj
Females: Priya, Renu, Sharita and Varti
Cities: Madurai, Cutnee, Kurnool and Hapur
Regarding the couples, the wife always sits to the immediate right of her husband.
From (i), Bittu is not the husband of Priya.
From (ii), Dheeraj is from Hapur.
From (iii), Renu is not from Cutnee.
From (iv), Cirag is not from Kurnool and is not the husband of Sharita.
From (v), Arun is not married to Renu and Renu is not from Madurai.
Possibility Table
HUSBAND | WIFE | CITY |
Bittu | Priya | Hapur |
Dheeraj | Sharita, Reno, Priya, Varita | Hapur |
Chirag | Sharita, Renu, Priya or Varita | Hapur, Kurnool, Mudrai or Cutnee |
Arun | Renu | Hapur, Cutnee, Madurai or Kurnool |
So, according to the table, there were two possibilities for Chirag's wife either Priya or Varita so we will consider these cases one by one.
Case I: If we consider Priya as Chirag’s wife and Priya can’t be from Madurai so they must be from Cutnee.
So, the arrangement could look like this:
------ Sharita Chirag --- Priya Bittu---Renu Arun-------
Now after this arrangement only one man and one woman is left so we can consider the woman as Arun’s wife and the man as Sharita’s Husband
Dheeraj ------ Sharita Chirag --- Priya Bittu---Renu Arun-------Varti
This arrangement fulfils all the conditions, so it is not required to consider any other case.
Answer 1: Dheeraj is married to Sharita. [Which is option (A)]
Answer 2: Chirag and Priya are from Cutnee. [Which is option (C)]
Answer 3: Chirag and his wife are seated second in the row. [Which is option (C)]
Solution 4 to 7:
Answer 4: By assuming a 4 × 4 × 4 cube is also not painted with pink colour, the number of cubes with no faces painted is = (6 – 2)3 = 64. Of these 64 smaller cubes now, in the second, third and fourth layers leftmost 9 cubes are painted pink, on the bottom surface four smaller cubes are painted pink and on the fourth layer back six smaller cubes are painted.
Hence, the total number of cubes with no face painted = 64 – 19 = 45
Answer 5: The number of cubes which are three faces painted before removing 64 smaller cubes = 8 and after painting with pink colour to those 64 smaller cubes seven new cubes will have three faces painted.
Hence, the total number of cubes with three faces painted = 8 + 7 = 15
Answer 6: The number of smaller cubes painted on two faces in the larger cube after removing 4 × 4 × 4 is illustrated as shown below.
9 edges with four smaller cubes with two faces painted = 9 × 4 = 36; 3 edges with one cube with two faces painted = 3 × 1 = 3
In the pink cube, there are 24 cubes on 12 edges which are painted on two faces.
Hence, the number of cubes with two faces painted = 36 + 3 + 24 = 63
Answer 7: The number of cubes with one face painted in the larger cube = 3 × 16 + 3 × 7 = 69. Number of cubes with one face painted in the 4 × 4 cube = 6 × 4 = 24
Hence, the total number of smaller cubes with one face painted = 69 + 24 = 93
CAT Exam: Sample Papers: Answers and Solutions
Part-C: VARC
Answer 1: (C)
if clause: had known (past perfect), Main clause: would/ could have lent.
Answer 2: (A)
if clause: had done (past perfect), the main clause: would/ could/ might have had.
Answer 3: (C)
if clause: had done (past perfect), the main clause: would/ could/ might have had.
Answer 4: (B)
The previous event is simple past, then the next event must be past continuous for continuous action.
Answer 5: D
“take a shower” is an idiomatic phrase. Hence, No error.
Answer 6: (C)
“with pleasure” is an idiomatic phrase. With pleasure replaced with “pleasure”.
Answer 7: (B)
“was” is used instead of “were”. The whole block is considered a singular subject and the singular subject takes a singular verb.
Answer 8: (D)
when two nouns get added with the use of ‘and’ and a possessive adjective article is used before both nouns then we use a plural verb but when the possessive adjective article is used with only one noun then it is considered to be one and hence singular verb is used.
Answer 9: (D)
No article is used between By and Means of transport.
Before comfortable “a” should be used.
Before “express”, “an” will be used as there is a vowel at the start.
Before “train”, “a” will be used.
Free Ebooks for CAT Preparation 2024
300+ Phrasal Verbs List for CAT Exam, Types With Examples & Practice Questions | CAT Quantitative Aptitude Questions with Answers PDF |
Frequently Asked Questions (FAQs)
1. What is a quadratic function?
A quadratic function is a degree two polynomial function in which the variable's maximum exponent is 2.
2. What are the roots of a quadratic equation?
The roots are the values of 'x' for which the quadratic equation is true, indicating where the graph intersects the x-axis.
3. How many roots can a quadratic equation have?
There can be 1, 0, or 2 roots in a quadratic equation.
4. What are real roots?
Real roots are real-valued equation solutions. This implies that they may be positive, negative, or zero, but not imaginary or complex. The real roots of the equation x^2-4=0 are x=2 and x=-2, which are both real values that satisfy the equation. Simply said, real roots are the values of a variable that satisfy the equation and may be found on the number line.
5. Do these practice tests help me to score well?
Yes absolutely, practices will make you better, helping in increase of speed and accuracy.
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Questions related to CAT
Have a question related to CAT ?
Although, it's very unlikely that you will secure a seat in top ABM with CAT 67 percentile. Here's is a breakdown to your question:
· CAT Percentile vs. Score: A CAT score of 67 typically translates to a percentile in the range of 90-95 percentile based on the provided data from previous years. While this is a decent score overall, it falls short of the cutoffs for most top-tier ABM programs.
· Cutoffs for Top ABM Institutes:
- IIM Lucknow: For their PGP-ABM program, the qualifying CAT cutoff for the general category is around 85 percentile . However, the actual cutoff for shortlisting for the Written Ability Test (WAT) and Personal Interview (PI) stages is likely to be higher.
- IIM Ahmedabad: While they also offer an ABM program (PGP-FABM), their minimum qualifying CAT cutoff is around 80 percentile , but the final admission cutoffs are usually much higher, often in the 99+ percentile range for general candidates.
- MANAGE (National Institute of Agricultural Extension Management): Their cutoff in CAT percentile has been around 70 for the general category in recent years. With a 67 percentile, you might have a slim chance here, but it's still competitive.
- CCS NIAM (National Institute of Agricultural Marketing, Jaipur): They consider CAT scores with a significant weightage (30-51% in their selection criteria). While they don't explicitly state a cutoff, it's reasonable to assume it would be higher than 67 percentile for a good chance of admission.
· Overall Good CAT Score: Generally, a CAT percentile of 90 and above is considered a good score for securing admission to decent MBA programs in India. For top-tier institutes, a percentile of 95 and above is often preferred.
· MBA Colleges Accepting 60-70 Percentile: While there are MBA colleges that accept CAT scores in the 60-70 percentile range, these are generally not the top-ranked or most sought-after ABM programs. The focus of those lists is on general MBA programs, not specifically ABM.
While securing a seat in ABM can be tough, you can research about other colleges, consider other examinations, to improve your application profile.
You Got This !
Aman Kar 16 April,2025
Hello,
achieving a 99.99 pecentile in the CAT exam significantly enhances your prospects for admission to JBIMS, which evaluates candidates using an application rating(AR) score, which includes
-entrance exam score (CAT/MH-CET/CMAT) : 60% weightage
-Past Academic Record (PAR) : 15% weightage (https://cracku.in/colleges/jbims/admission-process/?utm_source=chatgpt.com)
-Extra-curricular Activities/Work Experience : 20% weightage (https://jbims.edu/uploads/announcement/Revised_M_Sc__Finance_Admission_Procedure_Batch_2024-26.pdf?utm_source=chatgpt.com)
-Diversity (Academic/Gender): 5% weightage
while ahigh CAT percentile is crucial, a lower academic record may impact your overall AR score. Nonetheless, exceptional performance in other areas, such as entrance exams and extracurricular activities, can help offset weaker academic credentials. it's advisable to review JBIMS's detailed admission criteria and consider strengthening other aspects of your application to enhance your chances
Riya Dhoot 10 April,2025
To find the 2024 MHT CET answer key, you'll need to check the official Maharashtra State Common Entrance Test Cell website. This is the primary source for all official announcements and documents related to the MHT CET exam. After the exam concludes, the CET Cell typically releases a provisional answer key.
Once released, the provisional answer key will likely be available as a downloadable PDF file. You'll need to navigate to the official website, look for the MHT CET section, and find the link related to the answer key. This link might be labelled "MHT CET 2024 Answer Key" or something similar.
After downloading the answer key, you can compare your responses with the official answers. If you find any discrepancies or have objections, the CET Cell usually provides a window for raising objections. You'll likely need to pay a specified fee for each objection raised. The official website will provide instructions on how to submit your objections, which may involve logging into your candidate portal and following the provided steps.
Finally, after considering all objections, the CET Cell will publish a final answer key. This final version is considered definitive, and the MHT CET results will be based on it. Keep an eye on the official website for all updates and announcements regarding the 2024 answer key.
I hope this helps.
SUKRITI GUPTA 13 April,2025
Greetings! Here's a detailed response to your query
Okay, so you're a bit confused about what to put in those CAT, FMS, DSE, and IIFT forms regarding your 12th scores. Since you did CBSE, they usually only consider your final 12th standard marks.
Even though you did great in 11th, scoring 495 out of 500, for these entrance exam forms, they're specifically asking about your 12th board exam marks .You mentioned you got 400 out of 500 in 12th, which comes out to 80%.
Therefore, when filling out the forms for CAT, FMS, DSE, and IIFT, you should enter 80% as your 12th percentage. The aggregate of 11th and 12th isn't typically what they're looking for in these sections. They want to know how you performed in your final board exams. So, stick with the 80% from your 12th results. Good luck with your applications!
SUKRITI GUPTA 05 April,2025
Greetings! Here's a detailed response to your query:-
Determination of the best time to start the journey of CAT examination is based on individual factors like your current skill level, knowledge ,potential, learning pace and availability. To give yourself the best chance of success on the CAT exam , which usually takes place in November, it's advisable to begin studying between January and March of that same year. This 8 to 12-month preparation window is widely recommended by experts. But if you're managing your college along with the CAT preparations make sure you start from 2nd year onwards. It will hep you manage stress and you'll have ample amount of time to get along with the syllabus , pattern and various practice and mocks .
You'll be able to build a strong foundation in each sections and be able to know your strengths and weaknesses in different topics. The CAT syllabus is extensive, and early preparation allows for thorough coverage. Assess your learning speed and adjust your preparation timeline accordingly.
Essentially, while the ideal start time is subjective, beginning your CAT preparation well in advance is generally considered the most effective strategy for achieving optimal results.
SUKRITI GUPTA 01 April,2025
Popular CAT Questions
Directions for question :
M/s Deloitte Touche Tohmatsu Limited, one of the top four audit and accounting firms in the world with headquarters at London, UK, and with an operational presence in 153 countries, hires Management Trainees (MT) from all the premier management institutes of India thrice every year, in the months of January, May and September.
Each new group of Management Trainees (MT) have to go through a four month rigorous training schedule, after which they have to pass through a test consisting of a written assessment and a case-analysis. The top hundred ranked Management Trainees (MT) based on the performance in the test are confirmed as Management Executives (ME). The rest are given the opportunity of undergoing the training for four months one more time along with the next batch of Management Trainees (MT) and then passing through the subsequent test consisting of the written assessment and case-analysis. The Management Trainee (MT) who fails to get confirmed as a Management Executive (ME) the second time is fired.
The scatter-graph below depicts the number of Management Trainees (MT) at Deloitte taking the tests from January 2020 till May 2022, and the vis-à-vis hired Management Trainees (MT) at Deloitte who were fired :
It is also known that for the month of September 2019 at Deloitte, 96 hired Management Trainees (MT) failed to be confirmed as a Management Executive (ME) the first time, and that 36 hired Management Trainees (MT) were fired.
Question :
In which test did the minimum number of Management Trainees (MT) get confirmed as a Management Executive (ME) in the second attempt ?
Option: 1
September 2020
Option: 2
May 2021
Option: 3
January 2021
Option: 4
January 2022
Directions for question:
The bar-graph given below shows the foreign exchange reserves of Nepal (in million Rupees) from 2014 to 2021. Answer the following questions based on the graph :
Question:
What was the percentage increase (rounded to the nearest integer, if deemed necessary) in the foreign exchange reserves in 2020 over 2016 ?
Option: 1 None
Option: 2 None
Option: 3 None
Option: 4 None
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Marketing Manager
A marketing manager is a person who oversees a company or product marketing. He or she can be in charge of multiple programmes or goods or can be in charge of one product. He or she is enthusiastic, organised, and very diligent in meeting financial constraints. He or she works with other team members to produce advertising campaigns and decides if a new product or service is marketable.
A Marketing manager plans and executes marketing initiatives to create demand for goods and services and increase consumer awareness of them. A marketing manager prevents unauthorised statements and informs the public that the business is doing everything to investigate and fix the line of products. Students can pursue an MBA in Marketing Management courses to become marketing managers.
2 Jobs Available
SEO Analyst
An SEO Analyst is a web professional who is proficient in the implementation of SEO strategies to target more keywords to improve the reach of the content on search engines. He or she provides support to acquire the goals and success of the client’s campaigns.
2 Jobs Available
Digital Marketing Executive
Digital marketing is growing, diverse, and is covering a wide variety of career paths. Each job function aids in the development of effective digital marketing strategies and techniques. The aims and objectives of the individuals who opt for a career as a digital marketing executive are similar to those of a marketing professional: to build brand awareness, promote company services or products, and increase conversions. Individuals who opt for a career as Digital Marketing Executives, unlike traditional marketing companies, communicate effectively through suitable technology platforms.
2 Jobs Available
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