Algebra - Simple Equations - Previous Year CAT/MBA Questions

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1. XAT 2024 QADI | Algebra - Simple Equations XAT Question

In a small college, students are allowed to take only one specialization. Traditionally, only two specializations are offered: Science and Arts. Students enrolled to specialize in Science must take Physics and Mathematics subjects, while students enrolled to specialize in Arts must take Economics and Political Science subjects. Students enrolled in Science are not allowed to take either Economics or Political Science, while students enrolled in Arts are not allowed to take either Physics or Mathematics.

Recently, the college has started a third specialization called MatEco that requires students to take Economics and Mathematics. However, MatEco students would not be allowed to take either Physics or Political Science. When the college opens this new specialization for enrolment, it allows students, originally enrolled in Science or Arts, to switch to MatEco. From among the students originally enrolled in Arts, 20 students switch to MatEco. This makes the number of Science students twice the number of Arts students. After this, from among the students who originally enrolled in Science, 45 students switch to MatEco. This makes the number of Arts students twice the number of Science students.

In total, how many students, from among those originally enrolled in Science or Arts, are now taking Economics?

(a)
45
(b)
65
(c)
80
(d)
95
(e)
None of the remaining options is correct.

2. XAT 2024 QADI | Algebra - Simple Equations XAT Question

Consider the system of two linear equations as follows: 3x + 21y + p = 0; and qx + ry – 7 = 0, where p, q, and r are real numbers.

Which of the following statements DEFINITELY CONTRADICTS the fact that the lines represented by the two equations are coinciding?

(a)
p and q must have opposite signs
(b)
The smallest among p, q, and r is r
(c)
The largest among p, q, and r is q
(d)
r and q must have same signs
(e)
p cannot be 0

Read the following scenario and answer the TWO questions that follow.

Aman has come to the market with Rs. 100. If he buys 5 kilograms of cabbage and 4 kilograms of potato, he will have Rs. 20 left; or else, if he buys 4 kilograms of cabbage and 5 kilograms of onion, he will have Rs. 7 left. The per kilogram prices of cabbage, onion and potato are positive integers (in rupees), and any type of these vegetables can only be purchased in positive integer kilogram, or none at all.

3. XAT 2024 QADI | Algebra - Simple Equations XAT Question

Aman decides to buy only onion, in whatever maximum quantity possible (in positive integer kilogram), with the money he has come to the market with.

How much money will he be left with after the purchase?

(a)
Rs. 12
(b)
Rs. 9
(c)
Rs. 7
(d)
Rs. 5
(e)
Re. 1

4. XAT 2024 QADI | Algebra - Simple Equations XAT Question

Aman decides to buy only onion and potato, both in positive integer kilogram, in such a way that the money left with him after the purchase will be insufficient to buy a full kilogram of either of the two vegetables.

If all such permissible combinations of purchases are equally likely, what is the probability that Aman buys more onion than potato?

(a)
3/10
(b)
5/6
(c)
2/9
(d)
7/20
(e)
4/10

5. XAT 2023 QADI | Algebra - Simple Equations XAT Question

Raju and Sarita play a number game. First, each one of them chooses a positive integer independently. Separately, they both multiply their chosen integers by 2, and then subtract 20 from their resultant numbers. Now, each of them has a new number. Then, they divide their respective new numbers by 5. Finally, they added their results and found that the sum is 16. What can be the maximum possible difference between the positive integers chosen by Raju and Sarita?

(a)
67
(b)
58
(c)
49
(d)
40
(e)
None of the above

6. XAT 2023 QADI | Algebra - Simple Equations XAT Question

There are three sections in a question paper and each section has 10 questions. First section only has multiple-choice questions, and 2 marks will be awarded for each correct answer. For each wrong answer, 0.5 marks will be deducted. Any unattempted question in this section will be treated as a wrong answer. Each question in the second section carries 3 marks, whereas each question in the third section carries 5 marks. For any wrong answer or un-attempted question in the second and third sections, no marks will be deducted. A student’s score is the addition of marks obtained in all the three sections. What is the sixth highest possible score?

(a)
92.5
(b)
94
(c)
95.5
(d)
95
(e)
None of the above

Read the following scenario and answer the three questions that follow.
A company awards incentives to its employees for successful project performances. It rates successful project performance in categories A*, A, B, and C. Employees, in solo projects rated A*, A, B, and C, are awarded incentives ₹6 lakh, ₹5 lakh, ₹3 lakh, and ₹1 lakh respectively. When a project has multiple team members, the following scheme is used to award the incentives:

For example, for a project rated A, with three members, the team lead gets ₹4 lakh, and the other team members get ₹2.5 lakh each. A project always has a single team lead. Six employees: Altaf, Bose, Chakrabarthi, Dipa, Ernie, and Fatima receive a total of ₹45 lakh in incentives by participating in a total of eight different projects that does not involve any other person. Not all six employees are involved in all eight projects.
The following are additionally known about these eight projects:
1. One project involves all six employees. Four projects involve three each, and the rest, two each.
2. Exactly three projects are rated C, for which a total of ₹4.8 lakh is paid.
3. Only one project is rated A*

7. XAT 2021 QADI | Algebra - Simple Equations XAT Question

Total amount of money paid for projects rated A (in lakhs of Rupees) is:

(a)
19
(b)
15
(c)
16
(d)
17
(e)
18

Answer: Option E

Text Explanation :

Total percentage incentive when number of team members = 1 = 100%
Total percentage incentive when the number of team members = 2 =160%
Total percentage incentive when the number of team members = 3=180%
Total percentage incentive when the number of team members = 4= 190%
Total percentage incentive when the number of team members >4 = 200%
From 1, Number of people in 8 different projects = 6, 3, 3, 3, 3, 2, 2, 2 respectively
From 2, Given, exactly three projects are rated C and 4.8 lakh is paid in total
A minimum of 3 lakhs has to be paid for rating C => 3 *1.6 = 4.8lakhs ⇒ All 2 member teams have been rated C
From 3, one project has been rated A*. Let that project be handled by the team of 3 members ⇒ Incentives = 180% of 6 = 10.8 lakh
Now remaining 6, 3, 3, 3 should be either rated A or B and the total incentives should be equal to 45 - 10.8 - 4.8 = 29.4 lakhs
Let us assume 6 has been rated B ⇒ Incentives = 200% of 3 = 6 lakhs
The remaining 23.4 lakhs should come from 180% $\frac{23.4}{1.8}$ = 13 lakhs

Hence the remaining 3,3,3 can be rated as A, A, B
Hence final ratings are and total payouts are
6 - B - 6lakhs
3- A - 9 lakhs
3-A - 9 lakhs
3-B - 5.4 lakhs
3-A* - 10.8lakhs
2-C - 1.6 lakhs
2-C - 1.6 lakhs
2-C - 1.6 lakhs

Read the following scenario and answer the three questions that follow.
A quick survey at the end of a purchase at buyagain.com asks the following three questions to each shopper:
1. Are you shopping at the website for the first time? (YES or NO)
2. Specify your gender: (MALE or FEMALE)
3. How satisfied are you? (HAPPY, NEUTRAL or UNHAPPY)

240 shoppers answer the survey, among whom 65 are first time shoppers. Furthermore:
i. The ratio of the numbers of male to female shoppers is 1 : 2 while the ratio of the numbers of unhappy, happy and neutral shoppers is 3 : 4 : 5
ii. The ratio of the numbers of happy first-time male shoppers, happy returning male shoppers, unhappy female shoppers, neutral male shoppers, neutral female shoppers and happy female shoppers is 1 : 1 : 4 : 4 : 6 : 6
iii. Among the first-time shoppers, the ratio of the numbers of happy male, neutral male, unhappy female and the remaining female shoppers is 1 : 1 : 1 : 2, while the number of happy first-time female shoppers is equal to the number of unhappy first-time male shoppers

8. XAT 2021 QADI | Algebra - Simple Equations XAT Question

What is the number of happy male shoppers?

(a)
10
(b)
15
(c)
5
(d)
20
(e)
40

9. XAT 2021 QADI | Algebra - Simple Equations XAT Question

Which among the following is the lowest?

(a)
Number of neutral first-time female shoppers
(b)
Number of unhappy first-time female shoppers
(c)
Number of unhappy first-time male shoppers
(d)
Number of neutral first-time male shoppers
(e)
Number of happy returning male shoppers

10. XAT 2021 DM | Algebra - Simple Equations XAT Question

Which among the following cannot be determined uniquely?

(a)
The number of first-time happy male shoppers
(b)
The number of returning male shoppers
(c)
All the numbers can be determined uniquely
(d)
The number of returning unhappy female shoppers
(e)
The number of first-time neutral male shoppers

11. XAT 2021 DM | Algebra - Simple Equations XAT Question

Find z, if it is known that:

a: -y² + x² = 20

b: y³ - 2x² - 4z ≥ -12 and

c: x, y and z are all positive integers

(a)
Any integer greater than 0 and less than 24
(b)
24
(c)
We need one more equation to find z
(d)
6
(e)
1

12. XAT 2021 DM | Algebra - Simple Equations XAT Question

An encryption system operates as follows:

Step 1. Fix a number k (k ≤ 26).
Step 2. For each word, swap the first k letters from the front with the last k letters from the end in reverse order. If a word contains less than 2k letters, write the entire word in reverse order.
Step 3. Replace each letter by a letter k spaces ahead in the alphabet. If you cross Z in the process to move k steps ahead, start again from A.
Example: k = 2: zebra → arbez → ctdgb.
If the word “flight” becomes “znmorl” after encryption, then the value of k:

(a)
5
(b)
4
(c)
7
(d)
Cannot be determined uniquely from the given information
(e)
6

Read the following scenario and answer the three questions that follow.
The following plot describes the height (in cm), weight (in kg), age (in years) and gender (F for female, M for male) of 20 patients visiting a hospital.

A person’s body mass index (BMI) is calculated as weight (in kg) divided by squared height (measured in square metres). For example, a person weighing 100 kg and of height 100 cm (1m) will have a BMI of 100. A person with BMI less than or equal to 18.5 is considered as underweight, above 18.5 but less than or equal to 25 as normal weight, above 25 but less than or equal to 30 as overweight, and above 30 as obese.

13. XAT 2021 DM | Algebra - Simple Equations XAT Question

The highest BMI among all patients is approximately

(a)
20
(b)
33
(c)
30
(d)
27
(e)
23

Answer: Option D

Text Explanation :

For the highest BMI, weight should be as high as possible and height as little as possible.
Hence it is possible with the person with a weight of 69 kg and a height of 1.6m

His BMI will be ( ${(\frac{69}{1.6})}^{2}$ ) = 27

14. XAT 2021 DM | Algebra - Simple Equations XAT Question

The BMI of the oldest person considered as normal weight is approximately

(a)
20
(b)
25
(c)
22
(d)
24
(e)
19

Answer: Option A

Text Explanation :

The BMI of 1st oldest person = ( $(\frac{40}{1.5})$ )² = 17.77
The BMI of next oldest person = ( $(\frac{61}{1.75})$ ) = 19.9

15. XAT 2020 QADI | Algebra - Simple Equations XAT Question

A shop sells bags in three sizes: small, medium and large. A large bag costs Rs.1000, a medium bag costs Rs.200, and a small bag costs Rs.50. Three buyers, Ashish, Banti and Chintu, independently buy some numbers of these types of bags. The respective amounts spent by Ashish, Banti and Chintu are equal. Put together, the shop sells 1 large bag, 15 small bags and some medium bags to these three buyers. What is the minimum number of medium bags that the shop sells to them?

(a)
7
(b)
5
(c)
9
(d)
4
(e)
10

Read the following paragraph carefully and answer the question that follows:

Vindhya, Shabnam and Amala are interning at a software organization as part of the requirement of their B-school curriculum.
The organization has allotted each of them a project based on their area of specialization. In the first meeting with the HR head, they are informed of a PPO possibility (pre-placement offer, i.e., an offer to join the company after their MBA), based on their performance. All of them are eager to convert their internship into a job offer.
Each of them is assigned a mentor who evaluates the intern's performance along with the HR head.

16. XAT 2020 DM | Algebra - Simple Equations XAT Question

In the second week of her eight-week internship, Amala realizes that the project requires inputs from subjects she studied in her third trimester. However, during the third trimester, Amala was significantly distracted by an inter-college sports meet, affecting her grasp of the subjects.
Which of the following is the MOST appropriate way forward for Amala?

(a)
Amala should realize that she may not get a PPO and so focus on networking with the experienced talent in the organization.
(b)
Amala, after studying the organization for a week, should design her own project and pitch it to her mentor.
(c)
Amala should request her mentor to allocate a different project because of her limited familiarity with the inputs required.
(d)
Amala should seek Shabnam’s help who performed well in the third trimester.
(e)
Amala should disclose to the mentor her limited understanding of the required inputs and seek his suggestions.

17. XAT 2020 DM | Algebra - Simple Equations XAT Question

Vindhya’s project is about understanding employee perception regarding the organization’s HR policies. Against her own instinct, she is suggested by her mentor to interview only the good performers identified by his office because poor performers, he believes, usually crib against the policies.
Which of the following courses of action will BEST enable Vindhya to provide the organization with a complete picture?

(a)
Vindhya should report this restraint to the HR head requesting her immediate intervention in the project.
(b)
Vindhya should request the HR Head to allot her another mentor without divulging the reason.
(c)
Vindhya should ignore her mentor’s directive, collect data from all, but compile reports separately for the good performers and the poor performers.
(d)
Vindhya should meet only those identified by her mentor, but also collect information from them as why their other colleagues are disgruntled.
(e)
Vindhya should completely comply with her mentor’s suggestion.

18. XAT 2020 DM | Algebra - Simple Equations XAT Question

Shabnam, who is working on sales executives’ work-life balance, has collected the following details about their frequent travels:

Frequent meetings help strengthen relationships with key customers.
Travelling has no effect on the personal lives of the sales executives as most of them are single.
Travel enhances the financial health of the sales executives since their fixed salaries are low.
Frequent travel has no significant impact on market budget, given the current high margins from sales.
The sales executives have the autonomy to decide the frequency of their travel.

Shabnam thinks that the frequency of travel is higher than required.
Which of the following combinations of the above reasons can enable Shabnam BEST substantiate her thinking?

(a)
2, 3 and 5
(b)
1, 3 and 5
(c)
2, 3 and 4
(d)
1, 2 and 4
(e)
3, 4 and 5

Read the following paragraph carefully and answer the question that follows:

Two industrial towns, Jayanagar and Ramnagar, about 15 kms. apart, are similar in land area, population, ethnic diversity and per capita incomes.
Jagdeep Singh owns a bakery named Le Baguette in Jayanagar. He specializes in croissants, masala bread and whole wheat bread; eggless cakes are also a favorite.
Among the four bakeries in Jayanagar, Jagdeep’s bakery with a market share of 30% is second only to the oldest Le Croissant bakery whose market share is 40%. Le Croissant commands a loyal customer base and does not offer eggless varieties.

19. XAT 2020 DM | Algebra - Simple Equations XAT Question

Jagdeep has decided to open a branch in Ramnagar. Which of the following facts about Ramnagar will BEST support his decision?

(a)
Ramnagar is served by 4 bakeries, with the two largest bakeries having market shares of 55% and 25% respectively.
(b)
3% of Le Baguette’s current revenue comes from Ramnagar.
(c)
Le Croissant’s Ramnagar branch struggles with a market share of 10%.
(d)
Jagdeep has managed to acquire a big space in Ramnagar at a nominal rent.
(e)
Before starting his own bakery, Jagdeep was supplying bread to most bakeries in Ramnagar.

20. XAT 2020 DM | Algebra - Simple Equations XAT Question

Jagdeep wishes to open a 100% eggless branch in Ramnagar. To explore feasibility, he collected the following facts:

Eggless products account for 30% of Le Baguette’s sales.
At least 20% of all bakery sales in Ramnagar is from eggless products.
The eggless varieties of Le Baguette contain minute traces of egg.
Le Baguette currently makes 3% of its revenue from Ramnagar customers and all of it comes from eggless products.
Le Croissant’s Ramnagar branch struggles with a market share of 10%.

From the combinations below, in the DESCENDING order of effectiveness, choose the one that BEST supports Jagdeep’s decision.

(a)
4, 3, 2
(b)
5, 4, 1
(c)
2, 1, 3
(d)
2, 4, 1
(e)
5, 2, 1

21. XAT 2020 DM | Algebra - Simple Equations XAT Question

From a newspaper, Jagdeep has learnt that Americans use their own ovens to bake ready-to-bake products, sold by some bakeries. This idea is apparently catching up in Indian metros as well. Jagdeep wants to try this out in his bakery. He has gathered the following facts:

US bakeries that also sell ready-to-bake products earned higher revenues compared to those that do not.
Around 7% of Jagdeep’s regular customers own baking ovens in their homes.
The sale of baking ovens in India is forecast to increase by 12% every year, for the next three years.
50% of Jagdeep’s regular customers are fulltime working couples.
In Indian metros, ready-to-bake products give higher profit margins compared to finished products.

Select the BEST of the following sequences of the above facts, in DESCENDING order of effectiveness, to support Jagdeep.

(a)
2, 5, 1, 3, 4
(b)
3, 4, 5, 1, 2
(c)
1, 5, 3, 2, 4
(d)
3, 2, 1, 4, 5
(e)
2, 3, 5, 1, 4

Read the following paragraph carefully and answer the question that follows:

A Multinational Company (MNC) sources pristine natural spring water from Bori, a village in Satpura mountains. The unprocessed natural spring water is directly bottled by the MNC. The company brands it as “Natural Spring Water” and sells at 50% premium vis-a-vis other brands that sell processed water.
The local panchayat, under the Panchayati Raj Act, 1992 controls the spring water usage. Hence, the company signed a 30-year contract with the panchayat for exclusive access to the spring water for business purposes. This contract contributes 50% to the panchayat’s revenues besides providing 250 jobs in the panchayat. The spring also meets domestic and agricultural needs of the people of Bori and the surrounding villages

22. XAT 2020 DM | Algebra - Simple Equations XAT Question

Chanchala owns a small parcel of farming land in Bori. She grows cannabis in some part of her land and earns a significant amount of money from it. Soon after the bottling plant was commissioned, Chanchala, instigated by a landlord with a vested interest, starts accusing the MNC of robbing her of water and impacting her livelihood.
She threatens to take the MNC to court.
Which of the following options will BEST solve the MNC’s problem?

(a)
Promise to employ Chanchala’s 17-year-old son as he turns 18.
(b)
Compensate the monetary loss as perceived by Chanchala.
(c)
Get the villagers employed by the MNC to persuade Chanchala not to sue.
(d)
Request the panchayat to excommunicate Chanchala for cultivating cannabis.
(e)
Buy Chanchala’s produce at a premium of 30% to the market price.

23. XAT 2020 DM | Algebra - Simple Equations XAT Question

The MNC has spotted traces of chemicals in their fortnightly water quality analysis. The MNC realizes that this is due to the contaminated agricultural runoff, flowing into the spring from the nearby fields where farmers use pesticides and fertilizers. This requires an immediate solution. Which of the following options will BEST resolve the situation for the MNC?

(a)
Since the customers trust the MNC to do what is good for them, remove the contaminants and continue to brand as “Natural Spring Water”.
(b)
Continue bottling the natural spring water without processing since the villagers drink it as it is.
(c)
Source water from an uncontaminated natural spring 150 kms away at an addition of 50% to the total cost.
(d)
Close down the bottling plant until the problem is resolved and inform the media that customer interests override profit concerns.
(e)
Rebrand “Natural Spring Water” as “Purified Spring Water” after removing the contaminants through charcoal filtering.

24. XAT 2020 DM | Algebra - Simple Equations XAT Question

The MNC is concerned about chemical contamination of the natural spring water due to the agricultural runoff with pesticides and fertilizers. The MNC is looking for a sustainable solution to this contamination.
Which of the following courses of action will BEST solve the issue?

(a)
Acquire all agricultural land in the natural spring’s catchment and afforest them.
(b)
Negotiate with the Panchayat to gain control of the entire spring and provide alternate sources of irrigation for farming.
(c)
Move to another state with unexploited natural springs.
(d)
Coax the farmers in the natural spring’s catchment to move to organic farming.
(e)
Change branding from “Natural Spring Water” to “Processed Drinking Water”.

Read the following paragraph carefully and answer the question that follows:

When Deepti opened the package, she was aghast. She received cotton pillow covers instead of satin pillow covers, she had ordered. Deepti ordered them for her father from a popular ecommerce website that hosted products of many sellers.
Confused, Deepti contacted the seller’s office using the details given on the package. The seller’s representative profusely regretted and promised to send the satin pillow covers at no extra cost. He added that Deepti need not return the cotton covers she received. Deepti happily accepted the deal.

A few days later, Deepti received another package from the seller. Unfortunately, this package also contained cotton pillow covers. Completely disillusioned with the seller’s professionalism, Deepti decided to put to use these cotton pillow covers also.

25. XAT 2020 DM | Algebra - Simple Equations XAT Question

A few days later, Deepti received an email from the e-commerce website, requesting her to share feedback about the seller. Deeply frustrated with the overall online purchasing experience, she deliberately ignored it. Later that evening, over supper, her father opined that the balcony curtains needed to be changed. He suggested that they be bought from a local shop. “If something went wrong, we could at least yell at the seller,” he added.
Deepti stared at her laptop and began writing her feedback.
What would Deepti DEFINITELY achieve by giving feedback?

(a)
Release her frustration
(b)
Prove a point to her father
(c)
Coerce the e-commerce website to punish the seller
(d)
An act of social service
(e)
Instigate people against the seller

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Algebra - Simple Equations - Previous Year CAT/MBA Questions

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