Stalwart Career Institute

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

1 CAT 2023 Slot 1 - Quant

If x and y are real numbers such that x2 + (x  2y  1)2 = – 4y(x + y), then the value x – 2y is 

1

2

– 1

0




1



2 CAT 2023 Slot 1 - Quant

Let n be the least positive integer such that 168 is a factor of 1134n. If m is the least positive integer such that 1134n is a factor of 168m, then m + n equals

24

12

9

15




15



3 CAT 2023 Slot 1 - Quant

3√31

2√7

3√7

4√5




3√7



4 CAT 2023 Slot 1 - Quant

If x and y are positive real numbers such that logx?(x2 + 12) = 4 and 3  logy? x = 1,  then x + y equals

10

68

20

11




10



5 CAT 2023 Slot 1 - Quant

The number of integer solutions of equation 2|x|(x2 + 1) = 5x2 is




3



6 CAT 2023 Slot 1 - Quant

The equation x3 + (2r + 1) x+ (4r  1)x + 2 = 0 has – 2 as one of the roots. If the other two roots are real, then the minimum possible non-negative integer vale of r is




2



7 CAT 2023 Slot 1 - Quant

Let α and β be the two distinct roots of the equation 2x2 – 6x + k = 0, such that (α + β) and αβ are the distinct roots of the equation x2 + px + p = 0. Then, the value of 8(k – p) is




6



8 CAT 2023 Slot 1 - Quant

In an examination, the average marks of 4 girls and 6 boys is 24. Each of the girls has the same marks while each of the boys has the same marks. If the marks of any girl is at most double the marks of any boy, but not less than the marks of any boy, then the number of possible distinct integer values of the total marks of 2 girls and 6 boys is

21

19

20

22




21



9 CAT 2023 Slot 1 - Quant

The salaries of three friends Sita, Gita and Mita are initially in the ratio 5 : 6 : 7, respectively. In the first year, they get salary hikes of 20%, 25% and 20%, respectively. In the second year, Sita and Mita get salary hikes of 40% and 25%, respectively, and the salary of Gita becomes equal to the mean salary of the three friends. The salary hike of Gita in the second year is

26%

30%

28%

25%




26%



10 CAT 2023 Slot 1 - Quant

The minor angle between the hours hand and minutes hand of a clock was observed at 8 : 48 AM. The minimum duration, in minutes, after 8 : 48 AM when this angle increases by 50% is

24/11

36/11

4

2




24/11



11 CAT 2023 Slot 1 - Quant

Brishti went on an 8 hour trip in a car. Before the trip, the car had travelled a total of x km till then, where x is a whole number and is palindromic, i.e. x remains unchanged when its digits are reversed. At the end of the trip, the car had travelled a total of 26862 km till then, this number again being palindromic. If Brishti never drove at more than 110 km/hr, then the greatest possible average speed at which she drove during the trip, in km/hr, was

90

80

100

110




100



12 CAT 2023 Slot 1 - Quant

Gita sells two objects A and B at the same price such that she makes a profit of 20% on object A and a loss of 10% on objects B. If she increases the selling price such that objects A and B are still sold at an equal price and a profit of 10% is made on object B, then the profit made on object A will be nearest to

42%

49%

45%

47%




47%



13 CAT 2023 Slot 1 - Quant

A mixture P is formed by removing a certain amount of coffee from a coffee jar and replacing the same amount with cocoa powder. The same amount is again removed from mixture P and replaced with same amount of cocoa powder to from a new mixture Q. If the ratio of coffee and cocoa in the mixture Q is 16:9, then the ratio of cocoa in mixture P to that in mixture Q is

4 : 9

1 : 3

5 : 9

1 : 2




5 : 9



14 CAT 2023 Slot 1 - Quant

Anil invests Rs 22000 for 6 years in a certain scheme with 4% interest per annum, compounded half-yearly. Sunil invests in the same scheme for 5 years, and then reinvests the entire amount received at the end of 5 years for one year at 10% simple interest. If the amounts received by both at the end of 6 years are same, then the initial investment made by Sunil, in rupees, is




20808



15 CAT 2023 Slot 1 - Quant

The amount of job that Amal, Sunil and Kamal can individually do in a day, are in harmonic progression. Kamal takes twice as much time as Amal to do the same amount of job. If Amal and Sunil work for 4 days and 9 days, respectively, Kamal needs to work for 16 days to finish the remaining job. Then the number of days Sunil will take to finish the job working alone, is




27



16 CAT 2023 Slot 1 - Quant

Arvind travels from town A to town B, and Surbhi from town B to town A, both starting at the same time along the same route. After meeting each other, Arvind takes 6 hours to reach town B while Surbhi takes 24 hours to reach town A. If Arvind travelled at a speed of 54 km/hr, then the distance, in km, between town A and town B is




972



17 CAT 2023 Slot 1 - Quant

A quadrilateral ABCD is inscribed in a circle such that AB : CD = 2 : 1 and BC : AD = 5 : 4. If AC and BD intersect at the point E, then AE : CE equals

2 : 1

1 : 2

8 : 5

5 : 8




8 : 5



18 CAT 2023 Slot 1 - Quant

Let C be the circle x2 + y2 + 4x - 6y - 3 = 0 and L be the locus of the point of intersection of a pair of tangents to C with the angle between the two tangents equal to 60°. Then, the point at which L touches the line x = 6 is

(6, 6)

(6, 4)

(6, 8)

(6, 3)




(6, 3)



19 CAT 2023 Slot 1 - Quant

In a right-angled triangle ?ABC, the altitude AB is 5 cm, and the base BC is 12 cm. P and Q are two points on BC such that the areas of ?ABP, ?ABQ and ?ABC are in arithmetic progression. If the area of ?ABC is 1.5 times the area of ?ABP, the length of PQ, in cm, is




2



20 CAT 2023 Slot 1 - Quant

For some positive and distinct real numbers x, y and z, if 1/(√y+√z) is the arithmetic mean of 1/(√x+√z) and 1/(√x+√y), then the relationship which will always hold true, is

x, y and z are in arithmetic progression 

√x,√y and √z are in arithmetic progression 

y, x and z are in arithmetic progression 

√x,√z and √y are in arithmetic progression 




y, x and z are in arithmetic progression 



21 CAT 2023 Slot 1 - Quant

The number of all natural numbers up to 1000 with non-repeating digits is

738

648

504

585




738



22 CAT 2023 Slot 1 - Quant

A lab experiment measures the number of organisms at 8 am every day. Staring with 2 organisms on the first day, the number of organisms on any day is equal to 3 more than twice the number on the previous day. If the number of organisms on the nth day exceeds one million, then the lowest possible value of n is




19



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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.