Stalwart Career Institute

Get access to the detailed solutions to the previous years questions asked in IIM IPMAT exam

1 CAT 2023 Slot 2 - Quant

For any natural numbers m, n and k, such that k divides both m + 2n and 3m + 4n, k must be a common divisor of 

m and n

m and 2n

2m and 3n

2m and n




m and 2n



2 CAT 2023 Slot 2 - Quant

The sum of all possible values of x satisfying the equation  is

3

5/2

3/2

1/2




1/2



3 CAT 2023 Slot 2 - Quant

Any non-zero real numbers x, y such that y ≠ 3 and x/y < (x+3)/(y-3), will satisfy the condition

If y > 10, then – x > y

x/y < y/x

If x < 0, then – x < y

If y < 0, then – x < y




If y < 0, then – x < y



4 CAT 2023 Slot 2 - Quant

Let a, b, m and n be natural numbers such that a > 1 and b > 1. If am bn = 144145, then the largest possible value of n – m is

579

580

289

290




579



5 CAT 2023 Slot 2 - Quant

Let k be the largest integer such that equation (x - 1)2 + 2kx + 11 = 0 has no real roots. If y is a positive real number, then the least possible value of k/4y + 9y is




6



6 CAT 2023 Slot 2 - Quant

The number of positive integers less than 50, having exactly two distinct factors other than 1 and itself, is




15



7 CAT 2023 Slot 2 - Quant




7



8 CAT 2023 Slot 2 - Quant

Pipes A and C are fill pipes while pipe B is a drain pipe of a tank. Pipe B empties the full tank in one hour less than the time taken by pipe A to fill the empty tank. When pipes A, B and C are turned on together, the empty tank is filled in two hours. If pipes B and C are turned on together when the tank is empty and pipe B is turned off after one hour, then pipe C takes another one hour and 15 minutes to fill the remaining tank. If pipe A can fill the empty tank in less than five hours, then the time taken, in minutes, by pipe C to fill the empty tank is

60

90

75

120




90



9 CAT 2023 Slot 2 - Quant

Anil borrows Rs 2 lakhs at an interest rate of 8% per annum, compounded half-yearly. He repays Rs 10320 at the end of the first year and closes the loan by paying the outstanding amount at the end of the third year. Then, the total interest, in rupees, paid over the three years in nearest to

40991

45311

33130

51311




51311



10 CAT 2023 Slot 2 - Quant

Ravi is driving at a speed of 40 km/h on a road. Vijay is 54 meters behind Ravi and driving in the same direction as Ravi. Ashok is driving along the same road from the opposite direction at a speed of 50 km/h and is 225 meters away from Ravi. The speed, in km/h, at which Vijay should drive so that all the three cross each other at the same time, is

67.2

58.8

61.6

64.4




61.6



11 CAT 2023 Slot 2 - Quant

Minu purchases a pair of sunglasses at Rs 1000 and sells to Kanu at 20% profit. Then, Kanu sells it back to Minu at 20% loss. Finally, Minu sells the same pair of sunglasses to Tanu. If the total profit made by Minu from all her transactions is Rs 500, then the percentage of profit made by Minu when she sold the pair of sunglasses to Tanu is

26%

31.25%

52%

35.42%




31.25%



12 CAT 2023 Slot 2 - Quant

The price of a precious stone is directly proportional to the square of its weight. Sita has a precious stone weighing 18 units. If she breaks it into four pieces with each piece having distinct integer weight, then the difference between the highest and lowest possible values of the total price of the four pieces will be 288000. Then, the price of the original precious stone is

972000

1296000

1944000

1620000




1296000



13 CAT 2023 Slot 2 - Quant

In a company, 20% of the employees work in the manufacturing department. If the total salary obtained by all the manufacturing employees is one-sixth of the total salary obtained by all the employees in the company, then the ratio of the average salary obtained by the manufacturing employees to the average salary obtained by the non-manufacturing employees is

4 : 5

6 : 5

5 : 6

5 : 4




4 : 5



14 CAT 2023 Slot 2 - Quant

A container has 40 liters of milk. Then, 4 liters are removed from the container and replaced with 4 liters of water. This process of replacing 4 liters of the liquid in the container with an equal volume of water is continued repeatedly. The smallest number of times of doing this process, after which the volume of milk in the container becomes less than that of water, is




7



15 CAT 2023 Slot 2 - Quant

If a certain amount of money is divided equally among n persons, each one receives Rs 352. However, if two persons receive Rs 506 each and the remaining amount is divide equally among the other persons, each of them receive less than or equal to Rs 330. Then maximum possible value of n is




16



16 CAT 2023 Slot 2 - Quant

Jayant bought a certain number of white shirts at the rate of Rs 1000 per piece and a certain number of blue shirts at the rate of Rs 1125 per piece. For each shirt, he then set a fixed market price which was 25% higher than the average cost of all the shirts. He sold all the shirts at a discount of 10% and made a total profit of Rs 51000. If he bought both colors of shirts, then the maximum possible total number of shirts that he could have bought is




407



17 CAT 2023 Slot 2 - Quant

A triangle is drawn with its vertices on the circle C such that one of its sides is a diameter of C and the other two sides have their lengths in the ratio a : b. If the radius of the circle is r, then the area of the triangle is






18 CAT 2023 Slot 2 - Quant

In a rectangle ABCD, AB = 9 cm and BC = 6 cm. P and Q are two points on BC such that the areas of the figures ABP, APQ and AQCD are in geometric progression. If the area of the figure AQCD is four times the area of triangle ABP, then BP : PQ : QC is

2 : 4 : 1

1 : 2 : 4

1 : 1 : 2

1 : 2 : 1




2 : 4 : 1



19 CAT 2023 Slot 2 - Quant

The area of the quadrilateral bounded by the Y-axis, line x = 5, and the lines |x – y| – |x – 5| = 2, is




45



20 CAT 2023 Slot 2 - Quant

If p2 + q2 - 29 = 2pq - 20 = 52 - 2pq, then the difference between the maximum and minimum possible value of (p3 - q3) is

243

378

189

486




378



21 CAT 2023 Slot 2 - Quant

If both the series a1, a2, a….. and b1, b2, b3….. be in arithmetic progression such that the common differences of both the series are prime numbers. If a5 = b9, a19 = b19 and b2 = 0 then a11 equals

86

84

79

83




79



22 CAT 2023 Slot 2 - Quant

Let an and bn be two sequences such that an = 13 + 6(n - 1) and bn = 15 + 7(n - 1) for all natural numbers n. Then, the largest three digit integer that is common to both these sequences, is




967



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Stalwart Career Institute

Stalwart Career Institute: Your Premier Destination for CAT, IPMAT, CMAT, and CUET Coaching in Indore

Welcome to Stalwart Career Institute, the best coaching institute in Indore, offering specialized coaching for CAT, IPM, CMAT, and CUET. Positioned as your definitive pathway to prestigious B-Schools across the country, we are dedicated to providing unparalleled guidance and support to fuel your MBA aspirations.

Why Opt for Stalwart Career Institute for Your MBA Aspirations?

  1. Proven Excellence: As a trusted name in management education, Stalwart Career Institute empowers students through Best-in-Class Teaching and Technology-Enabled Learning.
  2. Impressive Results: Our commitment to delivering quality education is evidenced by numerous success stories and admissions to renowned B-Schools, including IIMs, IIFT, MDI Gurugram, SCMHRD, SIBM Pune, NMIMS, MICA, GIM Goa, IMT Ghaziabad, and more.
  3. Dedication to Excellence: We showcase our dedication through comprehensive study materials and online tests, designed to instill confidence in every student facing MBA entrance exams.

Why Stalwart Career Institute Excels in CAT, IPMAT, CMAT, and CUET Coaching

  1. Experienced Faculties: Our instructors, CAT/XAT toppers with years of teaching expertise, impart invaluable knowledge to students.
  2. Dynamic Study Material: We annually update our content to align with the latest exam patterns, offering the largest question bank (Online + Offline) to students.
  3. National Online Test Series: Recognizing the significance of online tests, our in-house web portal features a variety of tests, including topic tests, sectional tests, video capsules, full-length tests, online magazines, and more.
  4. Mentorship Program: Beyond academics, we provide guidance and mentorship to students, both academically and mentally, ensuring they are well-prepared to crack national-level tests.
  5. GD/PI/WAT Training: Converting a call into admission is paramount. At Stalwart Career Institute, we place equal emphasis on GD/PI/Essay writing alongside core academic subjects.

Courses Offered:

  • CAT Coaching in Indore: Comprehensive coaching program covering Verbal Ability, Quantitative Aptitude, Data Interpretation, and Logical Reasoning.
  • IPMAT Coaching in Indore: Specialized coaching for Integrated Program in Management Aptitude Test (IPMAT), encompassing Quantitative Ability, Verbal Ability, and Logical Reasoning.
  • CMAT Coaching in Indore: Tailored coaching for the Common Management Admission Test (CMAT), addressing Quantitative Techniques, Data Interpretation, Logical Reasoning, Language Comprehension, and General Awareness.
  • CUET Coaching in Indore: Customized coaching for the Common University Entrance Test (CUET), covering relevant subjects and preparing students for the unique challenges of the exam.

Online Courses:

  • CAT Coaching Online: Interactive sessions covering the entirety of CAT’s syllabus, with recorded sessions for flexible learning.
  • IPMAT Coaching Online: Specialized coaching sessions dedicated to the IPMAT syllabus, accessible anytime, anywhere.
  • CMAT Coaching Online: Engaging online sessions designed to thoroughly prepare you for CMAT, including comprehensive study material and practice tests.
  • CUET Coaching Online: Tailored online coaching sessions for CUET, ensuring comprehensive preparation for this distinct examination.

Preparation Books:

To complement our coaching programs, we recommend the following preparation books:

  • CAT Preparation Books: Curated materials focusing on Verbal Ability, Quantitative Aptitude, Data Interpretation, and Logical Reasoning.
  • IPMAT Preparation Books: Essential resources covering Quantitative Ability, Verbal Ability, and Logical Reasoning for IPMAT.
  • CMAT Preparation Books: Comprehensive guides addressing Quantitative Techniques, Data Interpretation, Logical Reasoning, Language Comprehension, and General Awareness for CMAT.
  • CUET Preparation Books: Specialized books catering to the unique syllabus and requirements of the Common University Entrance Test.

Stalwart Career Institute offers a seamless blend of classroom and online courses, ensuring flexibility and accessibility for students aiming to excel in CAT, IPM, CMAT, CUET, and more. Choose the mode of learning that suits your schedule and preferences while receiving the same high-quality education and guidance. Your aspirations, our expertise – a winning combination for your MBA dreams.