Algebra - Simple Equations - Previous Year CAT/MBA Questions

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

7. SNAP 10th Dec 2023 Quant Slot 1 (Memory Based) | Algebra - Simple Equations omet Question

A and B have bags full of Rs. 1 coins. Total value of amount is 45. There was a hole in the bag due to which 5 one rupee coins were dropped from each bag. After this product of number of coins in the bag were 124. Find the product of number of coins in the two bags.

(a)
324
(b)
350
(c)
86
(d)
500

8. SNAP 10th Dec 2023 Quant Slot 2 (Memory Based) | Algebra - Simple Equations omet Question

At a certain place, there are some cows and some hen. The total number of heads is 408, and the total number of legs is 1024. What is the number of cows in the given place?

(a)
104
(b)
204
(c)
304
(d)
None of these

9. SNAP 10th Dec 2023 Quant Slot 2 (Memory Based) | Algebra - Simple Equations omet Question

A person has 20 and 50 rupee notes with him. If the total number of notes he has is 300 and the amount of money with him is Rs. 9000, then the number of 20 rupee notes with him is:

(a)
50
(b)
100
(c)
150
(d)
200

10. SNAP 17th Dec 2023 Quant (Memory Based) | Algebra - Simple Equations omet Question

Age of Raghu is 3 years more than four times the age of Hemant at present. Five years from now, age of Raghu will be 1 year more than thrice the age of Hemant. What is the age of Raghu at present?

(a)
32
(b)
35
(c)
36
(d)
None of these

11. SNAP 17th Dec 2023 Quant (Memory Based) | Algebra - Simple Equations omet Question

If trousers and 8 shirts cost Rs. 7350 while 3 trousers and 5 shirts cost Rs. 4475, what is the cost of 1 trouser?

(a)
Rs. 890
(b)
Rs. 950
(c)
Rs. 1025
(d)
Rs. 1115

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*

12. XAT 2021 QADI | Algebra - Simple Equations omet 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

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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

13. XAT 2021 QADI | Algebra - Simple Equations omet Question

What is the number of happy male shoppers?

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

14. XAT 2021 QADI | Algebra - Simple Equations omet 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

15. XAT 2021 DM | Algebra - Simple Equations omet 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

16. XAT 2021 DM | Algebra - Simple Equations omet 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

17. XAT 2021 DM | Algebra - Simple Equations omet 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.

18. XAT 2021 DM | Algebra - Simple Equations omet Question

The highest BMI among all patients is approximately

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

Answer: Option D

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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

19. XAT 2021 DM | Algebra - Simple Equations omet 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

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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

20. IIFT 23 Dec 2021 QA | Algebra - Simple Equations omet Question

The last two digits of the expression 1(1!)^1! + 2(2!)^2! + 3(3!)^3! + .... + 121(121!)^121!

(a)
61
(b)
71
(c)
81
(d)
91

21. IIFT 23 Dec 2021 QA | Algebra - Simple Equations omet Question

Find the set S that denotes the set of all values of 'α' for which the roots of the equation (1 - α)x² - 6αx + 8α = 0 is greater than 2.

(a)
$(\frac{2}{5}, \frac{1}{2})$
(b)
$(\frac{2}{5}, \frac{32}{68})$
(c)
$(\frac{32}{68}, 1)$
(d)
$(\frac{32}{68}, \frac{1}{2})$

Answer: Option D

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Text Explanation :

αf(x) = (1 - α)x² - 6αx + 8α = 0

Now roots are greater than 2 therefore,

$- \frac{b}{2 a}$ > 2

f(2) > 0

D > 0

$- \frac{b}{2 a}$ > 0

2(1 - α) > 0

$\frac{α}{α - 1}$ < 0

α ∈ (0, 1)

f(2) > 0

(1 − α ) 4 − 12α + 8α > 0
4 − 8α > 0

a < $\frac{1}{2}$

D > 0

36α² - 32α (1 - α) > 0

68α² - 32α > 0

α(68α - 32) > 0

α ∈ (-∞, 0) ∪ $(\frac{32}{68}, \infty)$

Taking the intersection of all we get α ∈ $(\frac{32}{68}, \frac{1}{2})$

22. IIFT 05 Dec 2021 QA | Algebra - Simple Equations omet Question

Find the value of $\sqrt{552 + \sqrt{552 + \sqrt{552 + . . .}}}$

(a)
26
(b)
-24
(c)
24
(d)
-26

Answer: Option C

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Text Explanation :

x = $\sqrt{552 + \sqrt{52 + \sqrt{552 + . . .}}}$

x² - 552 = $\sqrt{552 + \sqrt{52 + \sqrt{552 + . . .}}}$

x² - x - 552 = 0

(x - 24)(x + 23) = 0

x cannot be negative. Therefore, $\sqrt{552 + \sqrt{52 + \sqrt{552 + . . .}}}$ = 24

Answer is option C.

23. IIFT 05 Dec 2021 QA | Algebra - Simple Equations omet Question

If both the roots of the equation x² - 4ax + 3 - 3a + 4a² = 0 exceed 2, then the value of a:

(a)
a < 2
(b)
a < $\frac{3}{4}$
(c)
a > $\frac{5}{4}$
(d)
a > $\frac{7}{4}$

24. XAT 2020 QADI | Algebra - Simple Equations omet 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.

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

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Algebra - Simple Equations - Previous Year CAT/MBA Questions

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