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CAT Exam Focus on Ratio, Proportion, Selection-based Puzzle Questions and Strategies for RC & PYQs- Day 26

CAT Exam Focus on Ratio, Proportion, Selection-based Puzzle Questions and Strategies for RC & PYQs- Day 26

Edited By Irshad Anwar | Updated on Sep 14, 2023 03:27 PM IST | #CAT

Welcome Back CAT 2023 aspirants, CAT exam 2023 for MBA admission 2024-2026 will be held on November 26. In this CAT 2023 60 days preparation guide series of Careers360, we will discuss the strategies of day 26 that can help you prepare well and crack CAT entrance test 2023.

This Article includes questions related to ratio and proportion, selection and reading comprehension. These topics are very important and recurringly come in exams. CAT Preparation 2023 in 60 days

Part-1: CAT 2023 QA Preparation Tips (Ratio and proportions CAT questions)

CAT Exam Important Topic: Strategy to Prepare “Algebra (CAT Ratio and Proportion Questions)” for CAT-2023

  1. Comparing the quantities (a: b)

  2. Dividing in the ratio by parts method

  3. Learn the concept of compounded ratio

  4. Duplicate ratio of a: b is a2: b2

  5. Triplicate ratio of a: b is a3: b3

  6. Sub-duplicate ratio of a: b is a1/2: b1/2

  7. Sub-triplicate ratio of a: b is a1/3: b1/3

  8. Practice complex problems

CAT Exam Focus on Ratio, Proportion, Selection-based Puzzle Questions and Strategies for RC & PYQs- Day 26
CAT 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.

Examples of Ratio:

  1. 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.
  2. 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.
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Ratio And Proportion Previous Year 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]

  1. 58

  2. 95

  3. 85

  4. 50

Answer: [4]

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

⇒ [(x+ y)2- xy]/ [(x+ y)2- 4xy] = 157/3

Let x+ y= a

⇒ [a2- 216]/ [a2- 4x 216] = 157/3

⇒ 3a2- 648 = 157a2- 4x 216 x 157

On solving, we get a = 50.

Or, x+ y = 50


Q2. Ratio Proportion CAT Questions

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. 1/5

  2. ¼

  3. 7/33

  4. 6/19

Solution: [3]

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 fraction of Lalitha’s original number of marbles to Raju = (21x/11)/ 9x =7/33

CAT 2023: Prerequisite:

  1. Fraction and comparison
  2. Basics of calculations

CAT syllabus: References to Study (Theory):

  1. How to Prepare for Quantitative Aptitude for CAT by Arun Sharma (7th Edition: Page No 281- 285)
  2. https://www.youtube.com/watch?v=jfoJBivWlnQ (CareerRide YouTube Channel)

CAT syllabus References to Study (Practice):

  1. How to Prepare for Quantitative Aptitude for CAT by Arun Sharma (7th Edition: Page No 286- 300)
  2. CAT Previous year Papers.
  3. CAT Sample Papers.

Part-2: CAT 2023 Preparation Tips: CAT DILR tips (Logical Reasoning and Data Interpretation)


CAT 2023 Syllabus Topic: Strategy to prepare Problem-Solving/Puzzle (Selection)

In this article, we make our strategy for CAT exam through examples.

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.

  1. No composer who assigned the item to Princess, assigned any item to Queen.

  2. No composer who assigned the item to Rani, assigned any item to Samragni.

  3. The first performance was by Princess; this item was assigned by Badal.

  4. The last performance was by Rani; this item was assigned by Gagan.

  5. The items assigned by Ashman were performed consecutively. The number of performances between items assigned by each of the remaining composers was the same.

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Q1. Which of the following is true?

  1. The second performance was composed by Dyu.

  2. The third performance was composed by Ashman.

  3. The second performance was composed by Gagan.

  4. The third performance was composed by Dyu.


Q2. Which of the following is FALSE?

  1. Samragni did not perform in any item composed by Ashman.

  2. Princess did not perform in any item composed by Dyu.

  3. Queen did not perform in any item composed by Gagan.

  4. Rani did not perform in any item composed by Badal.


Q3. The sixth performance was composed of

  1. Badal

  2. Ashman

  3. Dyu

  4. Gagan


Q4. Which pair of performances were composed by the same composer?

  1. The second and the sixth

  2. The first and the seventh

  3. The third and the seventh

  4. 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 selection

1694683121937

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

1694683121795


Answers:

Q1. (1)

Q2. (3)

Q3. (1)

Q4. (4)

CAT preparation: Prerequisite:

  • Ranking, Blood Relations, Directions
  • Puzzles on Selection (Basics)

CAT syllabus 2023: 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):

Part-3: CAT Exam Preparation 2023: 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 previous year 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 o 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?

  1. It questions an explanation of how maps are designed.
  2. It corrects a misconception about the way maps are designed.
  3. It critiques a methodology used to create maps
  4. It explores some myths about maps

Ans: 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

  1. the North was the source of darkness

  1. the South was favoured by some emperors.

  1. East and south were more important for religious reasons for some civilisations

  1. East was considered by some civilisations to be a more positive direction

Ans: 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

  1. the Chinese invented the compass and were aware of magnetic north

  1. they wanted to show respect to the emperor.

  1. the Chinese emperor appreciated the winds from the south.

  1. north was considered the most desirable direction.

Ans: B

Trick: Search the question in the passage

See the third paragraph to find the answer.

CAT 2023: 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 ‘may be’

CAT exam 2023: 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)

We will be back with CAT Preparation Day 27 of the CAT exam preparation guide 2023 for 60 days tomorrow. Do practice and be focused.

Thank You, All the best.

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View All

1-radian measures 600. (True/False)

Option: 1

True


Option: 2

False


$111111^2$ = 

Option: 1

123456654321


Option: 2

123454321


Option: 3

123454321


Option: 4

12345654321


1111112 =___________ 

Option: 1

 123456654321


Option: 2

1234554321


Option: 3

123454321


Option: 4

12345654321


159702 is divisible by

Option: 1

7


Option: 2

9


Option: 3

11


Option: 4

6


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

What best can be said about the number of satellites serving C? 

Option: 1

Must be between 450 and 725 

 


Option: 2

Cannot be more than 800 
 


Option: 3

Must be between 400 and 800 

 


Option: 4

Must be at least 100 


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

What is the minimum possible number of satellites serving B exclusively? 

Option: 1

100


Option: 2

200


Option: 3

500


Option: 4

250


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

If at least 100 of the 1600 satellites were serving O, what can be said about the number of satellites serving S? 

Option: 1

At most 475 

 


Option: 2

Exactly 475 
 


Option: 3

At least 475 

 


Option: 4

No conclusion is possible based on the given information 


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

 If the number of satellites serving at least two among B, C, and S is 1200, which of the following MUST be FALSE? 

Option: 1

The number of satellites serving C cannot be uniquely determined 

 


Option: 2

The number of satellites serving B is more than 1000 
 


Option: 3

All 1600 satellites serve B or C or S 

 


Option: 4

The number of satellites serving B exclusively is exactly 250 


2839155 is divisible by

Option: 1

2


Option: 2

7


Option: 3

55


Option: 4

None of the above


'a' for which x^{2}-ax+9= 0 can be written as square of a linear factor is

Option: 1

6


Option: 2

-6,6


Option: 3

\left ( 6,\infty \right )


Option: 4

\left ( -\infty,-6 \right )


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