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CAT Exam Focus on Ratio, Proportion, Selection-based Puzzle Questions and Strategies for RC & PYQs- Day 26
Edited By Team Careers360 | Updated on Sep 19, 2024 11:51 AM IST | #CAT
Welcome back, CAT 2024 candidates! The CAT exam for MBA admissions from 2025 to 2027 is scheduled for November 24. In this 60-day preparation guide series from Careers360, we'll cover the strategies for Day 26 to help you prepare effectively and succeed in the CAT 2024 entrance test.
This article focuses on questions about ratio and proportion, selection, and reading comprehension—key topics that frequently appear on the exam.
CAT 2024 QA Preparation Tips (Ratio and proportions CAT questions)
CAT Exam Important Topic: Strategy to Prepare “Algebra (CAT Ratio and Proportion Questions)” for CAT-2024
Comparing the quantities (a : b)
Dividing in the ratio by parts method
Learn the concept of the compounded ratio
Duplicate ratio of a : b is a2 : b2
Triplicate ratio of a b is a3: b3
Sub-duplicate ratio of a: b is a1/2: b1/2
Sub-triplicate ratio of a: b is a1/3: b1/3
Practice complex problems
This Story also Contains
- CAT 2024 QA Preparation Tips (Ratio and proportions CAT questions)
- CAT 2024 Preparation Tips: CAT DILR tips (Logical Reasoning and Data Interpretation)
- CAT Exam Preparation 2024: CAT exam tips for VARC (Verbal Ability & Reading Comprehension)
- Study resources for CAT 2024
New: CAT Preparation- 60-day Study Material by Experts
Latest: CAT Mock Test Series - 20 Sets, Questions with Solutions
Don't Miss: CAT 2024 Most Scoring Concepts PDF - VARC, DILR and QUANT
AT Exam Focus on Ratio, Proportion, Selection-based Puzzle Questions and Strategies for RC & PYQs- Day 26
Ratio and Proportion Definition:
Ratio and Proportion are fundamental concepts used to compare quantities and establish relationships between them. They are extensively used in various fields, including arithmetic, algebra, geometry, and real-life problem-solving. We have to learn the ratio and proportion formula, the difference between ratio and proportion, and practice various ratio and proportion problems on the ratio and proportion worksheet to have more grasp on this topic.
Examples of Ratio:
Fruit Basket : In a fruit basket, there are 4 apples and 6 oranges. The ratio of apples to oranges is 4 : 6, which can be simplified as 2 : 3.
Students in a Classroom: In a classroom, there are 30 boys and 20 girls. The ratio of boys to girls is 30 : 20, which can be simplified as 3 : 2.
Examples of Proportion:
Mixing Juice: To make a fruit juice mixture, you need to mix 2 cups of apple juice with 3 cups of orange juice. The proportion of apple juice to orange juice is 2 : 3.
Speed and Time: A car travels 300 miles in 5 hours. To find the proportion of speed to time, we divide the distance by time, which gives us 300 miles / 5 hours = 60 miles per hour.
Previous Year Ratio And Proportion Questions
Q1. The product of two positive numbers is 616. If the ratio of the difference of their cubes to the cube of their difference is 157 : 3, then the sum of the two numbers is:
[CAT Exam: 2019]
58
95
85
50
Answer: (D)
Let the numbers be x and y.
So, xy = 616
Also, (x3 – y3)/ (x-y)3 = 157/3
⇒ [(x - y) (x2+ y2+ xy)]/ (x-y)3 = 157/3
⇒ (x2+ y2+ xy)/ (x2 + y2 - 2xy) = 157/3
⇒ 3(x2 + y2) + 3xy = 157(x2 + y2) - 314xy
⇒ 154(x2 + y2) = 317xy
⇒ 154(x2 + y2) = 317 × 616
⇒ (x2 + y2) = 1268
We know that, (x + y)2 = x2 + y2 + 2xy
⇒ (x + y)2 = 1268 + 2 × 616
⇒ (x + y)2 = 2500
⇒ x + y = 50
Hence, the correct answer is 50.
Q2. Raju and Lalitha originally had marbles in the ratio 4 : 9. Then Lalitha gave some of her marbles to Raju. As a result, the ratio of the number of marbles with Raju to that with Lalitha became 5 : 6. What fraction of her original number of marbles was given by Lalitha to Raju? [CAT exam: 2018]
1/5
¼
7/33
6/19
Solution: (C)
Let Raju and Lalitha initially have 4x and 9x marbles with them.
Lalitha gave y marbles to Raju, then
(4x+ y)/ (9x – y) = ⅚
⇒ 24x + 6y = 45x – 5y
⇒ 11y = 21x
⇒ y = 21x/11
she gave a fraction of Lalitha’s original number of marbles to Raju = (21x/11)/ 9x =7/33
Q3. If the evaluation of company A and company B are in the ratio of 3 : 4 while that of B and C are in the ratio 2 : 1, then which one of the following is a possible value of evaluation of company A if the difference of evaluation of company B and company C is multiple of 14?
323 crores
268 crores
423 crores
420 crores
Solution: (D)
A : B : C = 3 : 4 : 2 (since A : B = 3 : 4 and B : C = 2: 1)
Then the evaluation of companies A, B, and C are 3y, 4y, and 2y respectively where y is a positive integer.
According to the question:
4y- 2y = 2y is multiple of 14
Evaluation of company A = 3y is a multiple of 7 and 3.
420 satisfies this condition.
Hence, the correct answer is 420 crores.
Q4. In a bag there are coins of three denominations of Re. 1, Rs. 2 and Rs. 5. The first two are in the ratio of 2 : 3 and the last two in the ratio of 4 : 5. If the total number of coins in the bag is less than 100, the total value of coins in the bag can be Rs. _____________. Fill in the blank.
107
214
321
Cannot be determined
Solution: D
In terms of number of coins, Re. 1 : Rs. 2 = 2 : 3 and Rs. 2 : Rs. 5 = 4 : 5.
∴ Re. 1 : Rs. 2 : Rs. 5 = 8 : 12 : 15
Total number of coins = 8 + 12 + 15 = 35 units
Thus the only integral possibilities below 100 coins in total are 35 coins or 70 coins.
If the total is 35, then Re. 1 = 8 coins, Rs.2 = 12 coins and Rs. 5 = 15 coins.
∴ Total Value = 8 + 24 + 75 = Rs. 107
If the total is 70, then Re.1 = 16 coins, Rs. 2 = 24 coins and Rs. 5 = 30 coins.
∴ Total Value = 16 + 48 + 150 = Rs. 214
Both the values are there in the options.
So, the content of the blank cannot be determined.
Hence, the correct answer is " Cannot be determined ".
CAT 2024: Prerequisite:
Fraction and comparison
Basics of calculations
CAT syllabus: References to Study (Theory):
How to Prepare for Quantitative Aptitude for CAT by Arun Sharma (7th Edition: Page No 281- 285)
https://www.youtube.com/watch?v=jfoJBivWlnQ (CareerRide YouTube Channel)
CAT syllabus References to Study (Practice):
How to Prepare for Quantitative Aptitude for CAT by Arun Sharma (7th Edition: Page No 286- 300)
CAT 2024 Preparation Tips: CAT DILR tips (Logical Reasoning and Data Interpretation)
CAT 2024 Syllabus Topic: Strategy to prepare Problem-Solving/Puzzle (Selection)
In this article, we make our strategy for the CAT exam through examples. Puzzles questions include “chess puzzles”, “sudoku puzzles”, “math puzzles”, “crossword puzzles”, “jigsaw puzzles”, etc.
CAT Previous Year Questions on Selection-based Puzzles:
Comprehension:
Princess, Queen, Rani and Samragni were the four finalists in a dance competition. Ashman, Badal, Gagan and Dyu were the four music composers who individually assigned items to the dancers. Each dancer had to individually perform in two dance items assigned by the different composers. The first items performed by the four dancers were all assigned by different music composers. No dancer performed her second item before the performance of the first item by any other dancers. The dancers performed their second items in the same sequence as their performance of their first items. [CAT exam: 2019]
The following additional facts are known.
No composer who assigned the item to the Princess assigned any item to the Queen.
No composer who assigned the item to Rani assigned any item to Samragni.
The first performance was by Princess; this item was assigned by Badal.
The last performance was by Rani; this item was assigned by Gagan.
The items assigned by Ashman were performed consecutively. The number of performances between items assigned by each of the remaining composers was the same.
CAT 2024 College Predictor
Know Your Chances for getting Calls from IIMs & other Top MBA Colleges through CAT Percentile, based on your category, academic profile, work-ex & CAT result.
Use NowQ1. Which of the following is true?
The second performance was composed by Dyu.
The third performance was composed by Ashman.
The second performance was composed by Gagan.
The third performance was composed by Dyu.
Q2. Which of the following is FALSE?
Samragni did not perform in any item composed by Ashman.
Princess did not perform in any item composed by Dyu.
Queen did not perform in any item composed by Gagan.
Rani did not perform in any item composed by Badal.
Q3. The sixth performance was composed of
Badal
Ashman
Dyu
Gagan
Q4. Which pair of performances were composed by the same composer?
The second and the sixth
The first and the seventh
The third and the seventh
The first and the sixth
Solution:
Trick 1: Look for concrete information first
P, Q, R, S (Four finalists)
A, B, G, D (Four Composers)
Each dancer performed on items by two different composers.
P and Q have no composer in common.
R and S have no composer in common.
First four performances on items by four different composers and so the last four.
Items by A for two consecutive performances i.e., Dance 4 and Dance 5.
P performed 1st (Item by B) and 5th.
R Performed 4th and 8th (Item by G).
Trick 2: Using the above information, draw a table for the selection.
D (2nd or 3rd item and 6th or 7th item)
G (2nd or 3rd)
B (6th or 7th)
Trick 3: Elimination of Possibilities
Clue:
The number of performances between items assigned by each of the remaining composers was the same.
Case 1: If item 2 is composed of G which is performed by Q (From table) then item 3 will be composed of D which is to be performed by S. Then item 6 is performed by Q and must be composed by D. Item 7 is performed by S and must be composed by B.
Now Sequence of items should be B G D A A D B G which is a violation of the above condition.
Case 2: If item 3 is composed of G which is performed by Q (From table) then item 2 will be composed of D which is to be performed by S. Then item 7 is performed by Q and must be composed by D. Item 6 is performed by S and must be composed by B.
Now Sequence of items should be B D G A A B D G which is a violation of the above condition.
The number of items between B and B is 4.
The number of items between D and D is 4.
The number of items between G and G is 4.
All conditions are satisfied.
Trick 4: Draw Final Table.
Answers:
Q1. (1)
Q2. (3)
Q3. (1)
Q4. (4)
CAT preparation: Prerequisite:
Ranking, Blood Relations, Directions
Puzzles on Selection (Basics)
CAT syllabus 2024: References to Study (Theory):
LRDI for CAT by Nishit K. Sinha
https://online.2iim.com › blogs › cat-preparation-strategy
Cat preparation-iQuanta (YouTube Channel)
CAT exam: References to Study (Practice):
Verbal and Non-Verbal Reasoning by R S Agrawal
CAT Exam Preparation 2024: CAT exam tips for VARC (Verbal Ability & Reading Comprehension)
CAT Exam Important Topic: Reading Comprehension Part-3 (Solving the Comprehension) for CAT Exam
In this section, we will make strategies for Solving Reading Comprehension with the help of the previous year's questions from the CAT Exam.
Previous Year Questions on RC from CAT:
Comprehension:
Read the passage and answer the question based on it.
Understanding where you are in the world is a basic survival skill, which is why we, like most species, come hard-wired with specialized brain areas to create cognitive maps of our surroundings. Where humans are unique, though, with the possible exception of honeybees, is that we try to communicate this understanding of the world with others. We have a long history of doing this by drawing maps – the earliest version yet discovered was scrawled on cave walls 14,000 years ago. Human cultures have been drawing them on stone tablets, papyrus, paper and now computer screens ever since.
Given such a long history of human map-making, it is perhaps surprising that is only within the last few hundred years that North has been consistently considered to be at the top. In fact, for much of human history, the north almost never appeared at the top,
according to Jerry Brotton, a map historian… “North was rarely put at the top for the simple fact that north is where the darkness comes from,” he says. “West is also very unlikely to be put at the top because the west is where the sun disappears.”
Confusingly, early Chinese maps seem to buck this trend. But, Brotton, says, even though they did have compasses at the time, that isn’t the reason that they placed north at the top. Early Chinese compasses were actually oriented to point south, which
was considered to be more desirable than the deepest darkest north. But in Chinese maps, the emperor, who lived in the north of the country was always put at the top of the map, with everyone else, his loyal subjects, looking up towards him. “In Chinese culture, the emperor looks south because it’s where the winds come from, it’s a good direction. North is not very good but you are in a position of subjection to the emperor, so you look up to him,” says Brotton.
Given that each culture has a very different idea of who, or what, they should look up to it’s perhaps not surprising that there is very little consistency in which way early maps pointed. In ancient Egyptian times, the top of the world was east, the position of
sunrise. Early Islamic maps favoured south at the top because most of the early Muslim cultures were north of Mecca, so they imagined looking up (south) towards it Christian maps from the same era (called Mappa Mundi) put east at the top, towards the Garden of Eden and with Jerusalem in the centre.
So, when did everyone get together and decide that the north was the top? It’s tempting to put it down to European explorers like Christopher Columbus and Ferdinand Magellan who were navigating by the North Star. But Brotton argues that these early explorers didn’t think of the world like that at all. “When Columbus describes the world, it is in accordance with the east being at the top,” he says “Columbus says he is going towards paradise, so his mentality is from a medieval Mappa Mundi.” We’ve got to remember, adds Brotton, that at the time, “no one knows what they are doing and where they are going.”
Q1. Which one of the following best describes what the passage is trying to do?
It questions an explanation of how maps are designed.
It corrects a misconception about the way maps are designed.
It critiques a methodology used to create maps
It explores some myths about maps
Answer: B
Trick: See the first 2-3 lines of the first paragraph and the last 2-3 lines of the last paragraph to get an idea of the passage.
Q2. Early maps did NOT put the north at the top for all the following reasons EXCEPT
the North was the source of darkness
the South was favoured by some emperors.
East and south were more important for religious reasons for some civilisations
East was considered by some civilisations to be a more positive direction
Answer: B
Trick: Search the given line in the paragraph
Option A: Given in the second paragraph (True)
Option C: From third paragraph (True)
Option D: From the third and fourth paragraph (True)
Q3. According to the passage, early Chinese maps placed north at the top because
the Chinese invented the compass and were aware of magnetic north
they wanted to show respect to the emperor.
the Chinese emperor appreciated the winds from the south.
north was considered the most desirable direction.
Answer: B
Trick: Search the question in the passage
See the third paragraph to find the answer.
CAT 2024: Prerequisite:
Tenses and Parts of Speech
Comprehension reading skills
CAT Tricks/Strategies to Solve the Comprehension:
Read first then attempt
After reading the questions, refer to the paragraph.
Rationale (Eliminate wrong options generally with words like ‘never’, ‘always’, and ‘maybe’
CAT exam 2024: References to Study (Theory):
How to Prepare for Verbal Ability & Reading Comprehension for CAT by Meenakshi Upadhyay and Arun Sharma (9th Edition)
CAT exam: References to Study (Practice):
CAT Previous year Papers.
2iim (Web)
Study resources for CAT 2024
CAT 2024 Quantitative Aptitude Study Material PDF - Geometry and Mensuration | CAT 2024 preparation tips with 30-day study material by Experts |
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Questions related to CAT
Have a question related to CAT ?
Top MBA colleges based on CAT, XAT, SNAP, and NMAT scores include some of India’s best institutions. For CAT, the IIMs (Ahmedabad, Bangalore, Calcutta) and FMS Delhi are highly regarded. XAT results in prestigious colleges like XLRI Jamshedpur and XIMB. SNAP is known for Symbiosis Institutes, such as SIBM Pune and SCMHRD. NMAT scores open doors to NMIMS Mumbai, SPJIMR Mumbai, and ISB Hyderabad. Each exam has unique eligibility requirements, and their cutoffs vary, so it's important to research the specific criteria and select based on your preferences and strengths.
Ankit 17 January,2025
Hello,
Here are important points regarding your query :-
- Opportunity for candidates: IIM Kashipur might be inviting candidates for further consideration, regardless of initial CAT scores.
- Broadening applicant pool: They may aim to review diverse profiles beyond just percentile.
- Different criteria: Other factors like academic performance, work experience, and diversity may contribute to the decision.
- Possibility of screening: The email could be a formality, and actual shortlisting will depend on various selection criteria.
- No guarantee of shortlist: The invitation doesn’t ensure selection; many institutes offer preliminary applications before filtering through comprehensive evaluations.
Hope it helps !
Prachi Kumari 13 January,2025
Hi,
Based on the previous year analysis, According to your CAT 2024 percentile some of the colleges in which you have chances to get a seat includes:
- ISBR Business School
- SOIL Institute of Management
- Birla Institute of Management Technology
- GD Goenka University
- The ICFAI University
- Great Lake Institute of Management
- Jaipur National University
You can predict more colleges using the CLAT 2024 college predictor tool .
Hope this information will help you
Devraj 12 January,2025
Hello Greetings
With a CAT 2024 percentile of 68.28%, you may face a challenging time getting into IIT Delhi, as their cutoffs are typically higher. However, being an SC female student, you may be eligible for relaxation in the cutoff criteria .
To give you a better idea, here are some general CAT cutoff percentiles for IITs and other top B-schools:
- *IIT Delhi*: Typically above 90 percentile for general category students.
- *Newer IIMs*: Such as IIM Vishakapatnam, IIM Shillong, and IIM Udaipur, may have lower cutoffs, around 80-90 percentile.
- *Other top B-schools*: Like IMT Ghaziabad, XIM Bhubaneswar, and TAPMI, may also consider students with lower percentiles.
It's essential to note that CAT cutoffs can vary from year to year, and other factors like your academic background, work experience, and performance in the personal interview (PI) and written ability test (WAT) also play a significant role in the admission process.
To explore more options and predict your chances of getting into various colleges, you can use online CAT college predictor tools .
Have a great day
Sakshi Badoni 09 January,2025
Hello Greetings
Considering your 82.58 percentile in CAT and 22 months of industry experience in IT and Financial analysis, you have several options for General Management PGDM or PGPM programs.
*Decent Colleges Accepting Low CAT Percentile:*
- _SPJIMR_: Offers PGDM and PGPM programs, accepting CAT scores, with a minimum eligibility criterion of 50% aggregate in graduation ¹ ².
- _SOIL_: Provides PGPM and PGDM programs, considering CAT scores, with a focus on experiential learning ³.
- Other institutes like _IMT Ghaziabad_, _XIMB_, and _IRMA_ might also accept candidates with lower CAT percentiles, but this may vary depending on the program and intake.
*Key Factors to Consider:*
- _Work Experience_: With 22 months of experience, you might be eligible for PGPM programs, which typically require more work experience than PGDM programs ¹.
- _Career Gap_: Explain your career gap effectively in your application, highlighting any relevant activities or skills gained during that period.
- _Profile-Based Selection_: Some institutes consider profiles, including work experience, academic background, and extracurricular activities, in addition to CAT scores ¹.
*Next Steps:*
1. Research the institutes mentioned above and their programs.
2. Review the eligibility criteria, admission process, and fees for each program.
3. Prepare your application, ensuring you effectively communicate your strengths, work experience, and career goals.
4. Be prepared for interviews, focusing on your profile, experience, and motivation for pursuing a PGDM or PGPM program.
Remember, a lower CAT percentile doesn't necessarily limit your options. Focus on showcasing your strengths, experience, and fit with the program to increase your chances of admission.
Have a great day
Sakshi Badoni 09 January,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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