Navigating CAT : Unlocking the Power of Linear Equations, Direction, and Future Tense - Day 13

Navigating CAT : Unlocking the Power of Linear Equations, Direction, and Future Tense - Day 13

Edited By Team Careers360 | Updated on Sep 19, 2024 03:24 PM IST | #CAT

We're back with the strategy for Day 13 of our CAT 2024 preparation. Today, we'll focus on tackling CAT algebra questions. Stick to our 60-day CAT exam preparation schedule to maintain a steady flow, plan, and structure for your studies.

Quantitative Aptitude for CAT 2024

Algebra (Linear Equation) And CAT Algebra Questions

Linear Equations is an important part of Algebra as well as for the CAT exam. You can expect 1 or 2 algebra questions for the CAT Exam.

Linear equations are mathematical statements which are used to find the value of some unknown variable(s). Graphically linear equations always form a straight-line curve.

What is a linear equation?

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable.

Linear Equations can have one or more variables.

The general form of a linear equation is based on the variables.

Types/ Representation of Linear Equations for CAT

  • Linear Equations in One Variables : ax + b = 0 a ≠ 0 and x is the variable.

  • Linear Equations in Two Variables : ax + by + c = 0 a ≠ 0, b ≠ 0, x and y are the variables.

  • Linear Equation in three variables: ax + by + cz + d = 0 a ≠ 0, b ≠ 0, c ≠ 0, x, y, z are the variables.

  • Slope intercept form: y = mx + b; m = slope of the line b = y-intercept

  • Point Slope form: (y - y1) = m(x - x1)

This Story also Contains
  1. Quantitative Aptitude for CAT 2024
  2. CAT Logical Reasoning and Data Interpretation
  3. CAT Exam VARC (English grammar questions for CAT on tenses)
  4. Study material for CAT 2024
Navigating CAT : Unlocking the Power of Linear Equations, Direction, and  Future Tense - Day 13
Navigating CAT : Unlocking the Power of Linear Equations, Direction, and Future Tense - Day 13

To Solve Linear Equations, the Number of variables cannot be greater than the number of equations.

CAT linear equation questions can be categorised into the following types:

  • Questions that involve calculations of some unknown variables.

  • CAT linear arrangement questions that involve calculations of the number of solutions/ Types of solutions.

Methods of solving Linear Equations:

  • Method of Substitution: It involves picking one equation from the pair of linear equations in two variables and writing one variable in terms of the other. Then substitute that value in the other equation.

  • Elimination Method: It involves adding or subtracting the equations to eliminate one of the variables, making it possible to solve for the remaining variable.

  • Graphical Method: This method visually shows the solution to a pair of linear equations by plotting the lines and finding their intersection point.

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CAT Previous Year Algebra Questions for CAT exam

Question 1. When you reverse the digits of the number 13, the number increases by 18. How many other two-digit numbers increase by 18 when their digits are reversed?

[CAT Question Paper 2013]

  1. 7

  2. 5

  3. 6 (Correct answer)

  4. 8

Solution:

Let the number be (10a + b), so when the digits of the number are reversed, the number becomes (10b + a).

According the question, (10b + a) – (10a + b) = 18

⇒ 9 (b – a) = 18

⇒ b – a = 2

So, the possible pairs of (x, y) are

(1, 3), (2, 4), (3, 5), (4, 6), (5, 7), (6, 8), and (7, 9).

13 is already there, so other possible numbers are 24, 35, 46, 57, 68, and 79.

So, the total number of possible numbers (except 13) is 6.

Question 2. Let k be a constant. The equations kx + y = 3 and 4x + ky = 4 have a unique solution if and only if [CAT Question Paper 2020]

  1. k ≠ 2

  2. |k| = 2

  3. k = 2

  4. |k| ≠ 2 (Correct answer)

Solution:

For a unique solution,

a1/ a2 ≠ b1/ b2

⇒ k / 4 ≠ 1 / k

⇒ k2 ≠ 4

⇒ |k| ≠ 2

Question 3. The cost of 12 apples and 15 oranges is INR 660. The cost of 15 apples and 21 oranges is INR 870. Find the cost of one apple.

  1. INR 25

  2. INR 15

  3. INR 30

  4. INR 20

Solution:

Let the cost of one apple be x and one orange is y.

According to the question,

12x + 15y = 660 .......(1)

And, 15x + 21y = 870 ........(2)

Multiplying equation (1) by 5 and equation (2) by 4, we get,

60x + 75y = 3300 and 60x + 84y = 3480

Subtracting these equations, we get,

75y - 84y = 3300 - 3480

⇒ 9y = 180

⇒ y = 20

Putting this value in (1), we get,

12x + 15(20) = 660

⇒ 12x + 300 = 660

⇒ 12x = 360

⇒ x = 30

Hence, the correct answer is INR 30.

Question 4. The cost of 3 pieces of bread and 1 packet of juice at a certain store is Rs. 323.50. At the same store, the cost of 5 pieces of bread and 1 packet of juice is Rs. 433.50. What will be the cost of 2 pieces of bread and 2 packets of juice at this store?

  1. Rs. 427

  2. Rs. 350

  3. Rs. 403

  4. Rs. 433

Solution:
Let the cost of one bread be b and the cost of one packet of juice be j.

The cost of 3 breads and 1 packet of juice.

⇒ 3b + j = 323.50---(1)

The cost of 5 breads and 1 packet of juice.

⇒ 5b + j = 433.50---(2)

Subtracting the first equation from the second,

⇒ 2b = 433.50 - 323.50 = 110

⇒ b = 110/2 = 55

Substituting b = 55 into the first equation,

⇒ 3 × 55 + j = 323.50

⇒ j = 323.50 - 165 = 158.50

So, the cost of one bread is Rs. 55 and the cost of one packet of juice is Rs. 158.50.

Therefore, the cost of 2 breads and 2 packets of juice is,

⇒ 2b + 2j = 2 × 55 + 2 × 158.50 = 110 + 317 = 427

Hence, the correct answer is Rs. 427.

Prerequisite To Algebra Practice Questions:

For this topic, students must have knowledge of the following while preparing through Algebra practice questions:

  • Speed Maths/ Vedic Maths.

  • Unitary Method

  • Variables and constants.

Tips to Prepare Linear Equations for CAT Exam:

Use the Elimination method by making the coefficient of one variable equal in two equations.

See the solution either as consistent or inconsistent.

  • If two lines intersect exactly at one point, then the system of equations has only one Unique solution.

  • If two lines coincide or stay on the same line and overlap completely, then the system of equations has infinitely many solutions.

  • If two lines are parallel and never intersect each other, then the system of equations has no solution. In this case, the slopes of the two lines are the same but their intercepts are different.

If a1x + b1y + c1 = 0 and a2 x + b2y + c2 = 0 are two linear equations,

Then,

  • a1 / a2 ≠ b1/ b2 to have a unique solution.

  • a1/ a2 = b1/ b2 = c1/ c2 to have to have infinitely many solutions.

  • a1/ a2 = b1/ b2 ≠ c1/ c2 to have no solution.

References to Study (Theory):

  • NCERT Class 9-10

  • Quantitative Aptitude for CAT by N K Sinha

  • 2iim (You-Tube)

References to Study (Practice) CAT Algebra Questions:

  • Quantum CAT by S K Verma

  • https://iim-cat-questions-answers.2iim.com

  • Previous Year's Question Papers

CAT Logical Reasoning and Data Interpretation

Direction Sense (LR)

Direction Sense Consists of the following types of questions in CAT:

  • To Find the direction of a person after taking some turns from its initial position.

  • To find the distance between the initial and final position.

  • Questions on Shadow.

  • Questions on the direction of the hands of the clock.

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Basic Concepts of Direction Sense:

  1. Basic Directions

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  1. Concept of Shadow

Facing of a Person

Direction of Shadow (Morning)

Direction of Shadow (Evening)

North

West

East

East

West

East

South

East

West

West

East

West

3. Distance between initial and final positions will be calculated by using Pythagoras theorem.

Direction Senses test tricks:

Draw a direction diagram.

You can count the number of rotations to find the final direction with respect to the initial direction

1 Right turn = 3 left turns = to the right of initial direction

2 Right turns = 2 left turns = to the opposite of initial direction

3 Right turns = 1 left turn = to the left of initial direction

4 Right turns = 4 left turns = in the same direction of initial direction

3. (Hypotenuse)2 = (Base)2 + (Perpendicular)2 (For right triangle)

4. Draw the distances in proportion while drawing a distance diagram.

Now we have to practise some direction sense aptitude questions, direction sense test questions pdf, and direction sense test MCQ to have a better understanding of this concept.

Questions that can help you to build the concept of Direction Sense (Based on CAT):

Question 1. Raju, a child labourer is looking for his uncle. He went 60 metres in the West before turning to his left. He went 20 metres before turning to his right again to look for his uncle at his home 30 metres from this point. His uncle was not there. From here he went 60 metres to the South before meeting his uncle at a grocery shop. What is the smallest distance between the starting point and his uncle’s position (nearest to its integer value)? [TITA]

Solution:

For such questions, always remember that when a person moves to his left side, he will move in anti- clockwise direction and when a person moves to his right side, he will move in a clockwise direction.

1695700370671

Vertical distance = 20 + 60 = 80 metres

Horizontal distance = 30 + 60 = 90 metres

Distance between initial and final position= 802 + 902 = √14500 = 120 m (Approx)

Question 2. A is in the West of B which is in the north of C. If P is in the south of A, then in which direction of B, is P?

  1. North-East

  2. West

  3. South

  4. South- West

Solution: (D)

1695700370224

P is in the south-west of B. (Even P can be anywhere in the line above it)

Prerequisite for CAT Logical Reasoning:

To Prepare the questions based on direction sense, a student must have the knowledge of

  1. Knowledge of basic direction

  2. Pythagoras theorem

References to Study (Theory):

  • A New Approach to Reasoning by B.S. Sijwali & S. Sijwali Arihant

  • wifistudy (YouTube Channel)

References to Study (Practice):

  • Verbal and Non-Verbal Reasoning by R S Aggarwal. (Basic)

  • LRDI for CAT and GMAT by Nishit K Sinha. (Advance)

  • Previous Year's Question Papers

CAT Exam VARC (English grammar questions for CAT on tenses)

Tenses Part-3 (Future Tense)

As discussed in the previous two articles, tenses are divided into three types. Today we are going to discuss the future Tense and future tense formulas.

Future Tense: Future tense is used to describe the event that will have to occur in the coming time.

Future tense can further be divided into four categories to indicate the action as follows:

Simple Future Tense/ Future Indefinite Tense: denotes habitual action in the coming time. The action is supposed to be finished in the future but its time is not definite.

Formula: Subject + Will + Verb(present form) + Object

Example: Geetha will go abroad to study.

Future Perfect Tense: it refers to an action that will have to be completed on a later date or day but its time is known.

Formula: Subject + Will be + Verb(Present participle) + Object

Example: Geetha will have reached Delhi by next week.

Future Continuous Tense: denotes an action that will be in progress in the future.

Formula: Subject + Will have + Verb(Past participle) + Object

Example: Geetha will be coming to us in the next hour.

Future Perfect Continuous Tense: denotes an action that is under work or incomplete but will be finished in the coming time.

Formula: Subject + Will have been + Verb(Present participle) + Object

Example: Geetha will have been here by next week.

Students can make a past present future tense chart or practice on the simple future tense worksheet to understand it better.
Also, read simple future tense formulas and simple future tense examples to know better.

Tenses Exercise With Answers on Future Tense: [Based on PYQs]

Question 1. Mother dolphins whistle to their calves frequently after birth so that the calves will learn to recognize their distinctive whistle. [Sentece correction]

[Previous Year Question]

  1. learn to recognise their distinctive whistle.

  2. learn to recognise their distinctive whistle.

  3. will learn to recognise their distinctive whistle.

  4. learn to recognise their mother's distinctive whistle.

Solution: (d)

Simple present tense for the verb ‘learn’ should be used in place of future verb ‘will learn’ as the verb ‘whistle’ used in the main clause is in simple present tense.

Question 2. By the end of this year, she_______worked for AJ production house for eighteen years. [Fill in the blanks]

  1. Will work

  2. Had been working

  3. Will have been working

  4. Will be working

Solution: (c)

Future perfect continuous tense should be used since work will be completed in the coming time and work is underway.

Prerequisite

  • Basic Knowledge of Nouns, Pronouns and Verbs.

  • Basic knowledge of subject-verb agreement.

  • Knowledge of the use of helping verbs (Will/Will be/ Shall be/ Will have/ Shall have/Will have been)

Tips to Prepare Error correction in Future tenses:

  • Learn the rules of all types of future tenses.

  • Do basic exercises on Future tense.

  • Try to make new sentences by yourself.

  • Attempt Mock-Tests.

References to Study (Theory):

  • Advanced English Grammar by Martin Hewings

  • Learn English with Rebecca · engVid (YouTube Channel)

  • References to Study (Practice):

  • Purdue Online Writing Lab

  • How to Prepare for Verbal Ability & Reading Comprehension for CAT by Meenakshi Upadhyay and Arun Sharma (9th Edition)

  • Practise Sample Question Papers.

Study material for CAT 2024

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MBA Exams Computer Based Mock Test 2024 - CAT, MAT, XAT, SNAP, NMAT

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We will be back with Day 14 tomorrow. Do practice and be focused.

Thank You

All the best.

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Questions related to CAT

Have a question related to CAT ?

With a 59.95 percentile in CAT 2024 and ST category, you can expect calls from newer IIMs like IIM Bodh Gaya, IIM Jammu, and IIM Sirmaur, as they have lower cutoffs for reserved categories. Non-IIM options like IIT Madras (MBA), NIT Trichy (MBA), and state universities like Delhi School of Economics (DSE) might also consider your profile. Apply to institutions that prioritize diversity and offer ST reservation. Ensure your application highlights strong academics and achievements.

For more details you can visit the link given below

https://bschool.careers360.com/cat-percentile-predictor


Hi,

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  • GITAM School of Business, Hyderabad
  • Institute of Management Technology, Hyderabad
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For more information about the colleges in which you have chances to get a seat you can predict using MBA college predictor tool provided below

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Hope this information will help you

Hi,

With a CAT 2024 score of 93.94 percentile, you have a good chance of getting calls from several IIMs. Here are some possibilities:

IIMs:

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CAT exam is conducted every year for purpose of admission to various prestigious business school and management institutes in India. The exam is also considered among toughest entrance exams in India. The exam rats the logical skills of the candidates. You can get the college list based on your CAT score by simply visiting CAT College Predictor 2024

Hi Sonu,

Preparing for CAT 2025 through self-study requires the right study materials, a structured plan, and consistent effort. CAT Syllabus comprises of Quantitative Aptitude (QA), Data Interpretation and Logical Reasoning (DILR), Verbal Ability and Reading Comprehension (VARC).

You can get more detailed information in the mentioned website of Careers360, it will be helpful enough for preparation of CAT 2025.

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All the best for your CAT preparation.

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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:

Two friends Moloy and Niloy passed out from the Purulia Institute of Science and Technology with B.Tech degrees in Mechanical Engineering, but even after a year placement was hard to find. So they decided to take the challenge head-on, came down to Kolkata, rented a garage space on Park Street, and having an affinity towards making people enjoy good food, started their firm named 'B.Tech Bread-Omlette Wala'. 

They started with three items on the menu. One was the French Toast which could be prepared in 3 minutes. The second was the Egg Tortillas which took 15 minutes to prepare. Any one of Moloy and Niloy could prepare any one of them at a time. The third was the Egg Bhurji with French Fries. This however was prepared on an automated fryer which could prepare 3 servings at a time and took 5 minutes irrespective of the number of servings equal to or below 3. The fryer did not need anyone to attend to it, and the time to put in the raw ingredients could be neglected. So one could tend to the preparation of other items while the Egg Bhurji with French Fries were being prepared. 

They wanted to serve the orders as early as possible after the order was given. The individual items in any order were served as and when all the items were ready, and the order was then considered closed. None of the items on the menu were prepared in advance in anticipation of future orders. 

On the first day, 3 groups of customers came in and ordered at 6.00 pm, 6.10 pm, and 6.13 pm. The first order was for a plate of Egg Tortillas, two plates of French Toast, and three plates of Egg Bhurji with French Fries. The second order was for a plate of French Toast and two plates of Egg Bhurji with French Fries. The third order was for a plate of Egg Tortilla and a plate of Egg Bhurji with French Fries. 

On the backdrop of the above information answer the questions given :

Question: 

Assuming that the next customer's order could only be attended to when the previous customer's order was closed, at what time would the first customer's order be considered closed ?

 

Option: 1

6.15 pm

 

 


Option: 2

6.17 pm

 


Option: 3

6.18 pm

 


Option: 4

6.20 pm


Directions for question :

Six sticks of equal lengths were kept in the vertical position in an empty flower-vase, to be arranged at the six corners of a regular hexagon. The two ends of each of the sticks were of different colours. 

The top ends of the sticks were one of each of the following colours – Red, Cyan, Pink, Brown, Black and Green. The bottom ends were one of each of the following colours – Blue, Yellow, White, Orange, Purple and Grey. Both the sets of colours mentioned were in no particular order.

It was also known that :

a) The stick with the red colour was opposite to the stick with the blue colour

b) There were exactly two sticks whose both ends had colours whose names started with the same letter

c) The stick with the grey colour was adjacent to the stick with the white colour

d) The stick with the cyan colour was adjacent to both the sticks with the brown colour and the one with the blue colour

e) The stick with the purple colour was adjacent to both the sticks with the grey colour and the one with the green colour

f) The stick with the white colour was opposite to the stick with the green colour

Question :

What was the colour of the bottom end of the stick having brown colour at the top end ?

Option: 1

 White 

 


Option: 2

Yellow 


Option: 3

Black

 


Option: 4

Grey


Directions for question:

Two friends Moloy and Niloy passed out from the Purulia Institute of Science and Technology with B.Tech degrees in Mechanical Engineering, but even after a year placement was hard to find. So they decided to take the challenge head-on, came down to Kolkata, rented a garage space on Park Street, and having an affinity towards making people enjoy good food, started their firm named 'B.Tech Bread-Omlette Wala'. 

They started with three items on the menu. One was the French Toast which could be prepared in 3 minutes. The second was the Egg Tortillas which took 15 minutes to prepare. Any one of Moloy and Niloy could prepare any one of them at a time. The third was the Egg Bhurji with French Fries. This however was prepared on an automated fryer which could prepare 3 servings at a time and took 5 minutes irrespective of the number of servings equal to or below 3. The fryer did not need anyone to attend to it, and the time to put in the raw ingredients could be neglected. So one could tend to the preparation of other items while the Egg Bhurji with French Fries were being prepared. 

They wanted to serve the orders as early as possible after the order was given. The individual items in any order were served as and when all the items were ready, and the order was then considered closed. None of the items on the menu were prepared in advance in anticipation of future orders. 

On the first day, 3 groups of customers came in and ordered at 6.00 pm, 6.10 pm, and 6.13 pm. The first order was for a plate of Egg Tortillas, two plates of French Toast, and three plates of Egg Bhurji with French Fries. The second order was for a plate of French Toast and two plates of Egg Bhurji with French Fries. The third order was for a plate of Egg Tortilla and a plate of Egg Bhurji with French Fries. 

On the backdrop of the above information answer the questions given :

Question: 

Assuming that the next customer's order could only be attended to when the previous customer's order was closed, at what time would the third customer's order be considered closed ?

 

Option: 1

6.28 pm

 


Option: 2

6.35 pm

 


Option: 3

6.38 pm


Option: 4

6.45 pm


Directions for question:

Two friends Moloy and Niloy passed out from the Purulia Institute of Science and Technology with B.Tech degrees in Mechanical Engineering, but even after a year placement was hard to find. So they decided to take the challenge head-on, came down to Kolkata, rented a garage space on Park Street, and having an affinity towards making people enjoy good food, started their firm named 'B.Tech Bread-Omlette Wala'. 

They started with three items on the menu. One was the French Toast which could be prepared in 3 minutes. The second was the Egg Tortillas which took 15 minutes to prepare. Any one of Moloy and Niloy could prepare any one of them at a time. The third was the Egg Bhurji with French Fries. This however was prepared on an automated fryer which could prepare 3 servings at a time and took 5 minutes irrespective of the number of servings equal to or below 3. The fryer did not need anyone to attend to it, and the time to put in the raw ingredients could be neglected. So one could tend to the preparation of other items while the Egg Bhurji with French Fries were being prepared. 

They wanted to serve the orders as early as possible after the order was given. The individual items in any order were served as and when all the items were ready, and the order was then considered closed. None of the items on the menu were prepared in advance in anticipation of future orders. 

On the first day, 3 groups of customers came in and ordered at 6.00 pm, 6.10 pm, and 6.13 pm. The first order was for a plate of Egg Tortillas, two plates of French Toast, and three plates of Egg Bhurji with French Fries. The second order was for a plate of French Toast and two plates of Egg Bhurji with French Fries. The third order was for a plate of Egg Tortilla and a plate of Egg Bhurji with French Fries. 

On the backdrop of the above information answer the questions given :

Question: 

Suppose Moloy and Niloy had decided to process multiple orders at the same time, however strictly prioritising a first come first serve basis, when would the second customer's order be considered closed ?

Option: 1

6.20 pm

 

 


Option: 2

6.18 pm


Option: 3

6.15 pm

 


Option: 4

6.12 pm


Directions for question:

Two friends Moloy and Niloy passed out from the Purulia Institute of Science and Technology with B.Tech degrees in Mechanical Engineering, but even after a year placement was hard to find. So they decided to take the challenge head-on, came down to Kolkata, rented a garage space on Park Street, and having an affinity towards making people enjoy good food, started their firm named 'B.Tech Bread-Omlette Wala'. 

They started with three items on the menu. One was the French Toast which could be prepared in 3 minutes. The second was the Egg Tortillas which took 15 minutes to prepare. Any one of Moloy and Niloy could prepare any one of them at a time. The third was the Egg Bhurji with French Fries. This however was prepared on an automated fryer which could prepare 3 servings at a time and took 5 minutes irrespective of the number of servings equal to or below 3. The fryer did not need anyone to attend to it, and the time to put in the raw ingredients could be neglected. So one could tend to the preparation of other items while the Egg Bhurji with French Fries were being prepared. 

They wanted to serve the orders as early as possible after the order was given. The individual items in any order were served as and when all the items were ready, and the order was then considered closed. None of the items on the menu were prepared in advance in anticipation of future orders. 

On the first day, 3 groups of customers came in and ordered at 6.00 pm, 6.10 pm, and 6.13 pm. The first order was for a plate of Egg Tortillas, two plates of French Toast, and three plates of Egg Bhurji with French Fries. The second order was for a plate of French Toast and two plates of Egg Bhurji with French Fries. The third order was for a plate of Egg Tortilla and a plate of Egg Bhurji with French Fries. 

On the backdrop of the above information answer the questions given :

Question: 

Suppose Moloy and Niloy had decided to process multiple orders at the same time, however strictly prioritising a first come first serve basis, when would the third customer's order be considered closed ?

 

Option: 1

6.22 pm

 


Option: 2

6.25 pm


Option: 3

6.28 pm 


Option: 4

6.30 pm


Directions for question:

Two friends Moloy and Niloy passed out from the Purulia Institute of Science and Technology with B.Tech degrees in Mechanical Engineering, but even after a year placement was hard to find. So they decided to take the challenge head-on, came down to Kolkata, rented a garage space on Park Street, and having an affinity towards making people enjoy good food, started their firm named 'B.Tech Bread-Omlette Wala'. 

They started with three items on the menu. One was the French Toast which could be prepared in 3 minutes. The second was the Egg Tortillas which took 15 minutes to prepare. Any one of Moloy and Niloy could prepare any one of them at a time. The third was the Egg Bhurji with French Fries. This however was prepared on an automated fryer which could prepare 3 servings at a time and took 5 minutes irrespective of the number of servings equal to or below 3. The fryer did not need anyone to attend to it, and the time to put in the raw ingredients could be neglected. So one could tend to the preparation of other items while the Egg Bhurji with French Fries were being prepared. 

They wanted to serve the orders as early as possible after the order was given. The individual items in any order were served as and when all the items were ready, and the order was then considered closed. None of the items on the menu were prepared in advance in anticipation of future orders. 

On the first day, 3 groups of customers came in and ordered at 6.00 pm, 6.10 pm, and 6.13 pm. The first order was for a plate of Egg Tortillas, two plates of French Toast, and three plates of Egg Bhurji with French Fries. The second order was for a plate of French Toast and two plates of Egg Bhurji with French Fries. The third order was for a plate of Egg Tortilla and a plate of Egg Bhurji with French Fries. 

On the backdrop of the above information answer the questions given :

Question: 

A fourth customer comes in and orders two plates of French Toast at 6.24 pm. Suppose Moloy and Niloy had decided to process multiple orders at the same time, however strictly prioritising a first come first serve basis. For exactly how many minutes would one of the friends be idle from 6.00 pm till serving the last customer, assuming that the four customers were the only ones to have come in within the period being discussed ?

Option: 1

9

 


Option: 2

13


Option: 3

18


Option: 4

21


Directions for question:

Two friends Moloy and Niloy passed out from the Purulia Institute of Science and Technology with B.Tech degrees in Mechanical Engineering, but even after a year placement was hard to find. So they decided to take the challenge head-on, came down to Kolkata, rented a garage space on Park Street, and having an affinity towards making people enjoy good food, started their firm named 'B.Tech Bread-Omlette Wala'. 

They started with three items on the menu. One was the French Toast which could be prepared in 3 minutes. The second was the Egg Tortillas which took 15 minutes to prepare. Any one of Moloy and Niloy could prepare any one of them at a time. The third was the Egg Bhurji with French Fries. This however was prepared on an automated fryer which could prepare 3 servings at a time and took 5 minutes irrespective of the number of servings equal to or below 3. The fryer did not need anyone to attend to it, and the time to put in the raw ingredients could be neglected. So one could tend to the preparation of other items while the Egg Bhurji with French Fries were being prepared. 

They wanted to serve the orders as early as possible after the order was given. The individual items in any order were served as and when all the items were ready, and the order was then considered closed. None of the items on the menu were prepared in advance in anticipation of future orders. 

On the first day, 3 groups of customers came in and ordered at 6.00 pm, 6.10 pm, and 6.13 pm. The first order was for a plate of Egg Tortillas, two plates of French Toast, and three plates of Egg Bhurji with French Fries. The second order was for a plate of French Toast and two plates of Egg Bhurji with French Fries. The third order was for a plate of Egg Tortilla and a plate of Egg Bhurji with French Fries. 

On the backdrop of the above information answer the questions given :

Question: 

Had Niloy been absent on that day, and assuming that the next customer's order could only be attended to when the previous customer's order was closed, at what time would the fourth customer's order (refer to the previous question) be considered closed ?

Option: 1

6:38 pm

 


Option: 2

6:42 pm

 


Option: 3

6:47 pm


Option: 4

6:49 pm


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

Directions for question:

The Jadavpur University’s Prince Anwar Shah Road hostel consists of two large separate buildings, one for the ladies and the other for the gents, while having a common kitchen and dining hall. It is the hostel of the CS and the EEC department of engineering students of the university.

In recognition of the growing dissatisfaction and hence complaints among the inmates of the hostel regarding the menu served for dinner, the Dean of the engineering department, Dr Aparesh Sanyal, personally decided to investigate the matter. He set about collecting information about the preference of dinner among the inmates, separately from the gents and the ladies wing of the hostel.

Dr Sanyal was able to gather the following partial information :  

 

Hostel inmates

Menu preference for dinner

Total

Egg Meal

Fish Meal

Chicken Meal

Gents

   

20

 

Ladies

     

64

Total

 

60

   

 

The Warden of the hostel was consulted, who after investigation declared that the following facts were clear :

1. Forty percent of the hostel inmates were ladies

2. One-third of the gentlemen inmates preferred an egg meal for dinner

3. Half the hostel inmates preferred either fish meal or chicken meal

Question:

What proportion of the lady hostel inmates preferred a fish meal for dinner ?

 

 

Option: 1

0.25

 

 


Option: 2

0.50

 


Option: 3

0.75

 


Option: 4

1.00 


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