Algebra - Simple Equations - Previous Year CAT/MBA Questions
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Garima had only Rs. 200, Rs. 500 and Rs. 2000 notes in her wallet. She goes to shoppers Stop, purchases some dresses and gives half of her Rs. 2000 notes & in turn receives same number of Rs. 200 notes. She then goes to a restaurant and gives all her Rs. 500 notes and receives thirty Rs. 2000 notes, which increases the number of Rs. 2000 notes she had by 75%. If now she has fifty Rs. 200 notes, what were the original number of Rs. 2000 and Rs. 200 notes she had at the start?
- (a)
60, 10
- (b)
60, 15
- (c)
80, 10
- (d)
80, 15
Answer: Option C
Text Explanation :
Let Garima initially have (2n) notes of Rs. 2,000.
After the first transaction (in which she gives away half her notes), Garima has n notes of Rs. 2,000.
Now, Garima gets 30 notes of Rs. 2,000 which increases her number of Rs. 2,000 notes by three-fourth.
∴ n + 30 = n + (3n/4)
∴ (3n/4) = 30 i.e. n = 40
∴ Initial number of Rs. 2,000 notes = 2n = 80
This eliminates options 1 and 2.
Let Garima initially have x notes of Rs. 200.
She then gets n notes of Rs. 200, thereby taking the total notes of Rs. 200 to 50.
∴ x + n = 50
∴ x + 40 = 50 i.e. x = 10
∴ Initial number of Rs. 200 notes = x = 10
Hence, option (c).
Workspace:
In a survey on the viewership of the TV channels, 73% of those surveyed viewed at least one of the three Channels: Star Plus, Sab TV, and Sony. 38% of those surveyed viewed Star Plus, 39% viewed Sony, and 23% viewed Sab TV. 11% of all those surveyed viewed all the three channels. What percentage of those surveyed, viewed more than one of the three TV channels?
- (a)
16
- (b)
38
- (c)
27
- (d)
Data Inadequate
Answer: Option A
Text Explanation :
Let there be 100 people surveyed in all.
Let a, b, c correspond to people who watched only Star Plus, only Sony and only SAB TV.
Let d, e, f correspond to people who watched only Star Plus and Sony, only Sony and SAB TV and only SAB TV and Star Plus.
Let g correspond to people who watched all three channels.
73% people i.e. 73 people watched atleast one channel.
∴ a + b + c + d + e + f + g = 73 … (i)
Number of people watching Star Plus, Sony and SAB TV is 38%, 39% and 23% respectively i.e. 38, 39 and 23.
∴ a + d + f + g = 38 … (ii)
b + d + e + g = 39 … (iii)
c + e + f + g = 23 … (iv)
Adding (i), (ii) and (iii):
(a + b + c) + 2(d + e + f) + 3g = 39 + 38 + 23 = 100 … (v)
Solving (i) and (v), we get:
(d + e + f) + 2g = 100 – 73 = 27
Number of people surveyed who watch more than one channel = (d + e + f) + g
Also, number of people who watch all channels = g = 11
∴ (d + e + f) + g + 11 = 27
∴ (d + e + f) + g = 16
∴ Required % = (16/100) × 100 = 16%
Hence, option (a).
Workspace:
The square root of 1
- (a)
- (b)
- (c)
1
- (d)
None of the above
Answer: Option A
Text Explanation :
Instead of solving algebraically, solve the question by first substituting x = 1. You will get one original value and three values in the options. Square each value from the options and match it with the original value of the expression.
Original expression:
Option 1:
Now, square this value.
Hence, option (a).
Workspace:
- (a)
2
- (b)
4
- (c)
12
- (d)
16
Answer: Option B
Text Explanation :
log2x × log(x/64)2 = log(x/16)2
It is clear that x has to be a power of 2 to solve the equation i.e. x ≠ 12.
Hence, option (c) is eliminated.
If x = 16, then the base of the RHS (i.e. x/16) becomes 1, which is not possible for a logarithm i.e. x ≠ 16. Hence, option (d) is eliminated.
If x = 2, then you get (x/64) = (x/16); which is not possible.
Hence, x = 4
Hence, option (b).
Workspace:
"Music probably does something interesting," explains neuropsychologist Catherine Loveday of the University of Westminster. "It stimulates the brain in a very powerful way, because of our emotional connection with it." Unlike brain-games, playing an instrument is a rich and complex experience. This is because it's integrating information from senses like vision, hearing, and touch, along with fine movements. This can result in long-lasting changes in the brain. This can also be applicable in the business world.
Go through the following statements:
- Playing a musical instrument is a unique experience involving vision, hearing and touch.
- Instrumental musicians are far more creative than vocalists.
- Playing brain games does not integrate various senses and movements as much as playing a musical instrument.
- Integrating the five senses is critical in the business world.
Which of the above statements can definitely be interpreted based on the passage above?
- (a)
Statement 1 only
- (b)
Statement 1 and 2
- (c)
Statement 3 only
- (d)
Statement 1 and 3
- (e)
Statement 3 and 4
Answer: Option A
Text Explanation :
[1] is eliminated as we cannot state that playing a music instrument is a “unique” experience. The comparison with vocalists is inappropriate as there is no information given about them. Hence, [2] is rejected. [3] is clearly implied in the passage: “Unlike brain-games, playing an instrument is a rich and complex Experience”. [4] is incorrect as the passage only states that integrating the five senses can result in long-lasting changes in the brain which “can be applicable in the business world”. Nothing in the passage suggests that it is a “crucial” element. Hence, [4] is not valid.
Hence, the correct answer is option 1.
Workspace:
Answer the following question based on the information given below.
Lal & Sons, a family business, comprises three different companies in three different industries. Sudarshan Lal was heading this entire business from the inception. Two years ago, he hired three managers, one for each company and Chhaganlal Jha as Chief Executive Officer (CEO) to look after the entire business. These three managers are reporting to the CEO. However, Sudarshan Lal and his family still own the entire business, though they are not involved in day to day operations. Two years after the handing over, Sudarshan was concerned that none of the companies, except one, is profitable.
Which of the following information, if true, will most likely reduce Sudarshan's concerns?
- (a)
A leading financial institution recently advised its investors to purchase the shares of the two loss making companies with a long term outlook.
- (b)
The Corporation's performance was stagnant for three years, before Sudarshan handed it over to professionals.
- (c)
The best performing division belongs to an industry, which is growing in double digits.
- (d)
People holding senior positions have been replaced two years ago by fresh and young talent.
- (e)
The rate at which employees are leaving the best performing division is higher than the industry average.
Answer: Option A
Text Explanation :
Sudarshan Lal is worried that two of his three companies are in the red. However, if a leading financial institution has advised its investors to purchase the shares of these two loss-making companies with a long-term outlook, it is understood that they may overturn their losses and post good profits in the future. Thus [1] is helpful in the given situation. [2] does not address Sudarshan Lal’s concerns at all. Similarly, [3] does not talk about the two loss-making companies. [4] and [5] only talk about employees. They don’t help in providing clarity on the two loss-making companies.
Hence, the correct answer is option 1.
Workspace:
Hari’s family consisted of his younger brother (Chari), younger sister (Gouri), and their father and mother. When Chari was born, the sum of the ages of Hari, his father and mother was 70 years. The sum of the ages of four family members, at the time of Gouri’s birth, was twice the sum of ages of Hari’s father and mother at the time of Hari’s birth. If Chari is 4 years older than Gouri, then find the difference in age between Hari and Chari.
- (a)
5 years
- (b)
6 years
- (c)
7 years
- (d)
8 years
- (e)
9 years
Answer: Option E
Text Explanation :
Let the ages of Father and Mother at the time of Hari’s birth are F and M respectively.
Let Chari be born x years after Hari’s birth.
∴ Ages of Hari, Father and mother will be x , F + x and M + x at the time of Chari’s birth.
∴ x + (F + x) + (M + x) = 70
⇒ 3x + F + M = 70 … (1)
Gouri was born 4 years after Chari’s birth.
∴ Ages of Chari, Hari, Father and mother will be 4, 4 + x , F + x + 4 and M + x + 4 at the time of Gouri’s birth.
∴ (x + 4) + (F + x + 4) + (M + x + 4) + 4 = 2(F + M)
⇒ 3x + 16 = F + M … (2)
From (1) and (2), x = 9
Hence, option (e).
Workspace:
Which of the following options is grammatically correct and meaningful?
- (a)
I want to join an MBA college that is not only the best in the country but also provides the best campus jobs.
- (b)
I want to join an MBA college that is not only the best in the country but also I can get good job.
- (c)
I want to join an MBA college that is not only the best in the country but also best in job.
- (d)
I want to join an MBA college that is not only good but also I can get good job.
- (e)
I want to join an MBA college that I found not only best in the country but also I can get good job.
Answer: Option A
Text Explanation :
Options 2,4 and 5 have parallelism error. So, eliminate option 2. Option 3 is misleading a the author wants to convey that MBA college that provides best jobs.
Hence, the correct answer is option 1.
Workspace:
In 2004, Rohini was thrice as old as her brother Arvind. In 2014, Rohini was only six years older than her brother. In which year was Rohini born?
- (a)
1984
- (b)
1986
- (c)
1995
- (d)
2000
Answer: Option C
Text Explanation :
Let Rohini’s age in the year 2014 is R and Arvind’s age is A.
∴ R – A = 6 … (i)
∴ Rohini’s age in 2004 = R – 10 and Arvind’s age in 2004 = A – 10
∴ (R – 10) = 3(A – 10)
∴ 3A – R = 20 … (ii)
Solving (i) and (ii), we get
R = 19
∴ Rohini was born in year (2014 – 19 =) 1995.
Hence, option (c).
Alternatively,
Rohini’s age in 2004 for the given options:
1. 1984 : 20
2. 1986 : 22
3. 1995 : 9
4. 2000 : 4
As Rohini’s age was thrice as old as her brother, the correct answer should be option 3.
Hence, option (c).
Workspace:
A firm is thinking of buying a printer for its office use for the next one year. The criterion for choosing is based on the least per-page printing cost. It can choose between an inkjet printer which costs Rs. 5000 and a laser printer which costs Rs. 8000. The per-page printing cost for an inkjet is Rs. 1.80 and that for a laser printer is Rs. 1.50. The firm should purchase the laser printer, if the minimum number of a pages to be printed in the year exceeds
- (a)
5000
- (b)
10000
- (c)
15000
- (d)
18000
Answer: Option B
Text Explanation :
Let minimum number of pages to be printed be x.
∴ 5000 + 1.8x = 8000 + 1.5x
Solving, we get x = 10000
Hence, option (b).
Workspace:
Read the following statements and answer the question that follows.
- The two hemispheres of the brain are responsible for learning autonomously.
- Simultaneous activation of circuits can take place in different areas of the brain.
- There are specific regions of the brain associated with sight, touch and smell.
- The brain receives inputs from multiple external sources.
- Learning is not the result of connections between neurons.
Which of the above statements are consistent with ideas expressed in the passage?
- (a)
I, V
- (b)
II, III
- (c)
III, V
- (d)
IV, V
- (e)
I, II, III
Answer: Option B
Text Explanation :
Statement I can be negated on the basis of the information provided in the penultimate sentence of the first paragraph.
Statements II and III can be affirmed on the basis of the data provided in the third paragraph of the passage.
Statements IV and V negate the data given in the passage that “the brain receives inputs amongst itself, through neurons and facilitates learning, which is also termed as neuro chemical communication”.
Thus, only statements II and III follow.
Hence, the correct answer is option 2.
Workspace:
Answer the questions on the basis of information given in the following case.
Bright Engineering College (BEC) has listed 20 elective courses for the next term and students have to choose any 7 of them. Simran, a student of BEC, notices that there are three categories of electives: Job-oriented (J), Quantitative-oriented (Q) and Grade-oriented (G). Among these 20 electives, some electives are both Job and Grade-oriented but are not Quantitative-oriented (JG type). QJ type electives are both job and Quantitative-oriented but are not Grade-oriented and QG type electives are both Quantitative and Grade-oriented but are not Job-oriented. Simran also notes that the total number of QJ type electives is 2 less than QG type electives. Similarly, the total number of QG type electives is 2 less than JG type and there is only 1 common elective (JQG) across three categories. Furthermore, the number of only Quantitative-oriented electives is same as only Job-oriented electives, but less than the number of only Grade-oriented electives. Each elective has at least one registration and there is at least one elective in each category, or combinations of categories.
On her way back Simran met her friend Raj and shared the above information. Raj is preparing for XAT and is only interested in Grade-oriented (G) electives. He wanted to know the number of G-type electives being offered. Simran replied, “You have all the information. Calculate the number of G-type electives yourself. It would help your XAT preparation”. Raj calculates correctly and says that there can be _______ possible answers.
Which of the following options would best fit the blank above?
- (a)
3
- (b)
5
- (c)
8
- (d)
9
- (e)
11
Answer: Option B
Text Explanation :
Let QJ type electives, only Grade-oriented electives and only Quantitative-oriented electives be z, y and x respectively.
Note: y > x
∴ Number of QG type electives = z + 2
∴ Number of JG type electives = z + 4
The given data can be represented in the form of the following Venn diagram,
Thus, the following equation is obtained,
3z + 2x + y = 13
(x, z ≥ 1 and y ≥ 2 )
For z = 1, 2x + y = 10 and possible values of (x, y): (1, 8), (2, 6) and (3, 4).
For z = 2, 2x + y = 7 and possible values of (x, y): (1, 5) and (2, 3).
For z = 3, 2x + y = 4 and possible values of (x, y): (1, 2).
Now, G = 2z + y + 7
If z = 1, G = 17, 15, 13
If z = 2, G = 16, 14
If z = 3, G = 15
Only 5 unique values of G are possible i.e. 13, 14, 15, 16 and 17.
Hence, option (b).
Workspace:
Simran prefers J-type electives and wants to avoid Q-type electives. She noted that the number of only J-type electives is 3. Raj’s preference is G-type electives followed by Q-type electives. However, they want to take as many common electives as possible. What is the maximum number of electives that can be common between them, without compromising their preferences?
- (a)
3
- (b)
4
- (c)
5
- (d)
7
- (e)
Not possible to answer from the above information.
Answer: Option C
Text Explanation :
Electives common between Simran and Raj are JG type electives. i.e., (z + 4)
Referring to the previous solution, as x = 3, 3z + y = 7
As y ≥ 2, the only possible integer solution to 3z + y = 7 is (z, y) ≡ (1, 4)
Thus, a maximum of 5 electives can be common between Simran and Raj, without compromising their preferences.
Hence, option (c).
Workspace:
Vijay and Raj want to avoid each other. Vijay is interested in J-type electives and wants to avoid Q-type electives. Raj’s preference is G-type electives followed by Q-type electives. Raj noted that the number of only G-type electives is 2. Is there a possibility that they would not share any common electives(s)?
- (a)
Yes. There is a possibility
- (b)
No. They would meet in one elective.
- (c)
No. They would not be able to avoid in two electives.
- (d)
No. They meet in five electives.
- (e)
Cannot be solved with the information given.
Answer: Option A
Text Explanation :
As y = 2, x has to be 1.
From the answer to the first question of the set, substituting values of y and x in 3z + 2x + y = 13, we get z = 3.
Vijay prefers J-type and avoids Q-type. Raj prefers G-type followed by Q-type.
If Vijay opts for all 7 JG electives or 6JG electives and 1 J-type elective, and Raj opts for 2 G-type and 5 GQ electives or 2 G-type, 4 GQ electives and 1 Q-type electives, they can completely avoid each other.
Hence, option (a).
Workspace:
Answer the questions on the basis of information given in the following case.
Mr. Dipangshu Barua, a young IT professional, came early to office to assist his boss in the preparation for an important client presentation. When be switched on his computer, he saw an email from Mr. Patel. The email was as follows:
January 2, 2015
Dear Mr. Barua,
This email serves as a follow-up of my conversation with you on December 1, 2014. I have already conveyed need for improvement in your behaviour as desired as desired by your project leader and colleagues. They are yet to notice any visible improvements. I am apprehensive that your failure to act may warrant further action leading to dismissal. I will continue to monitor and assess your performance over the next three months to determine whether improvements meet the expectations. At the same time, I would like to re-affirm that you are very valuable for our organization.
Best Wishes,
Mr. A. Patel
HR Director
Initially, the e-mail distracted Dipangshu but he decided to focus on the job. Which of the following options might best explain his decision to do so?
- (a)
Mr. Patel would soon be transferred to another department.
- (b)
Last week, Mr. Dipangshu has been assigned to a new team in the same project.
- (c)
Three days back, Mr. Dipangshu has been assigned a new project similar to his final year engineering project.
- (d)
His friend has been hospitalized for the last three months.
- (e)
Failing to perform in the client meeting might further complicate things.
Answer: Option E
Text Explanation :
Since the mail says that Dipangshu's performance is under scrutiny, it is imperative for him to conduct himself cautiously in front of his boss. In order to do so, his first step should be to perform well in the tasks assigned to him. Getting demoralized by the letter and performing badly will not help him simplify things.
Hence, option (e) best explains his decision to focus on his job. So, eliminate options 1, 2, 3 and 4.
Hence, the correct answer is option 5.
Workspace:
The scheduled presentation went off smoothly. Back in his cabin, Dipangshu read
Mr. Patel’s e-mail once more and pondered over it. During the last meeting he tried hard to put forward his explanation but Mr. Patel had not allowed him to speak. Dipangshu was thinking of meeting Mr. Patel once again but was doubtful that would help. Incidentally, he had a job offer from a start-up with a comparable salary. If Dipangshu was to join the new job, he had to accept the offer within the next two weeks. However, he cannot think of a life without a job. Dipangshu was confused!
Which of the following options would be the best move for Dipangshu?
- (a)
Talk to Mr. Patel and highlight the initiatives he has taken but at the same time start applying for other jobs.
- (b)
Reject the offer from the start-up. Use the next three months to find a better job, but continue in the present job.
- (c)
Resign from this organization right now.
- (d)
Accept the offer, only if the start-up gives a salary hike, else keep prospecting.
- (e)
Accept the offer with a request to give him a 10% salary hike.
Answer: Option E
Text Explanation :
Option 1 is too risky as he cannot be sure if his position in the company is safe. Hence, he cannot rely on his discussion with Mr. Patel. The passage further mentions that Mr. Patel had not allowed him to even speak. Also, applying simultaneously for other jobs won't ensure the certainty of securing a worthy job. Eliminate option 1.
Option 2 is a poor decision as the offer had opened the door for quitting the current company with a job in hand. Eliminate option 2.
Option 3 is a hasty course of action as the passage mentions that he cannot think of a life without a job. Eliminate option 3.
Option 4 is not a wise approach as demanding a salary hike based on which he would accept the job offer, holds the chance of driving away the only feasible opportunity he had.
Option 5 is a rational move, as accepting the offer with a request for a 10% salary hike will increase his chances of acquiring a worthy job after quitting his current job.
Hence, the correct answer is option 5.
Workspace:
After a couple of weeks, Mr. Patel came to know that Dipangshu’s project leader Mr. John, a very competent senior executive, may have wilfully influenced his team members to file a wrong complaint against Dipangshu. Mr. John may have done it because Dipangshu has refused to tow John’s line. Mr. Patel also came to know that Dipangshu was thinking of quitting this job. He felt regretful about his letter to Dipangshu. He wanted to resolve the complicated situation. He was contemplating following five actions in his mind.
- Talk to Mr. John about Dipangshu and convey to him that losing a bright employee would cost the organization dearly.
- Catch up with Mr. John during coffee break and convey that Dipangshu has a very good track record.
- Chat with Dipangshu during coffee break.
- Catch up with Dipangshu during coffee break and convey that the organization values him.
- Arrange a meeting among Mr. John, Dipangshu and himself to sort out the difference.
Which of the following is the best sequence of actions for resolving the problem?
- (a)
I, III, V
- (b)
II, III, V
- (c)
I, II, IV
- (d)
I, IV, V
- (e)
III, IV, V
Answer: Option D
Text Explanation :
Since there has been a misunderstanding between Mr John and Dipangshu, it is best to straighten out things between the two.
In order to do so, Mr Patel should communicate Dipangshu's plan of quitting the job to Mr John and make him realize his mistake of undermining Dipangshu's spirit which has led the organization on the path of losing a bright employee. Eliminate options 2 and 5.
His next move should be to talk to Dipangshu and explain his worth to the organization with a view to changing his mind. Eliminate options 1 and 3.
Once the two are on the same page, arranging a meeting between Mr. John, Dipangshu and himself would help Mr. Patel reach a solution. This sequence is present in option 4.
Eliminate options 1, 2, 3 and 5.
Hence, the correct answer is option 4.
Workspace:
Answer the questions on the basis of information given in the following case.
A few years back Mr. Arbit and Mr. Boring started an oil refinery business. Their annual earing is currently just 50,000 million rupees. They are now exploring various options to improve the business. Mr. Xanadu, a salesperson from Innovative Technology Solutions (ITS), is trying to sell a new oil refinery technology to Mr. Arbit and Mr. Boring. This technology could potentially enhance their annual earning to 150,000 million rupees within a year. But they have to make one-time investment of 100,000 million rupees to implement the technology. If the technology is not successful, the investment would be lost. Mr. Arbit and Mr. Boring are discussing about possible risks of the investment.
Mr. Arbit is enthusiastic about this investment idea but Mr. Boring is a little sceptical. This impasse makes them approach a consultant. The consultant makes some observations. Which of the following observations, made by the consultant, might reduce Mr. Arbit’s enthusiasm for the new investment idea?
- (a)
Investment is warranted only when benefits outweigh costs.
- (b)
Technology investments give higher earnings in future.
- (c)
Investment in technology leads to reduction of costs in the long run.
- (d)
Technology risks can be controlled.
- (e)
Business is all about taking risky decisions.
Answer: Option A
Text Explanation :
From the options presented, the alternative which casts the biggest shadow of doubt over the technology investment would be an ideal choice.
Option 1 states that investing is only justified if the returns are more than the investment. The passage suggests that the investment if successful will offer an abundant return, but if unsuccessful would cause a substantial loss for the company.
Options 2 and 3 support technology investment and thus, indirectly support Mr. Arbit's enthusiasm.
Similarly option 4 is pro technology investment and can be eliminated.
Option 5 directly supports Mr. Arbit's enthusiasm and invalidates Mr. Boring's scepticism as the technology investment has a certain risk factor.
Hence, the correct answer is option 1.
Workspace:
In order to sell the technology to Mr. Arbit and Mr. Boring, Mr. Xanadu is thinking of five possible sales pitches. Which of the following sales pitches would reduce uncertainties the most for Mr. Arbit and Mr. Boring?
- (a)
All other competitors are aggressively investing in risky technologies.
- (b)
If the technology succeeds, the annual earnings would grow 3 times from the next financial year and they would be able to recover the invested money within 1 year.
- (c)
Preliminary studies indicate that success rate of the technology is 85%.
- (d)
The R&D team of ITS is working to counter any possible downside of the technology.
- (e)
Business is all about taking risky decisions.
Answer: Option C
Text Explanation :
Option 1 cannot be affirmed as it generalises the idea of investing in risky technology. The other competitors mentioned might be better prepared to face the risks involved as compared to Mr. Arbit and Mr. Boring.
Option 2 presents an already mentioned aspect of the technology investment, which is mentioned in the passage.
The data mentioned in option 3 states that the risk of the technology investment becoming unsuccessful is only 15%. Thus, option 3 would most reduce the uncertainties for the partners.
The fact that the R&D team of ITS is working on reducing risks for the technology does not imply the R&D team will be successful in doing so.
Option 5 invalidates the prime purpose presented in the question of reducing uncertainties.
Hence, the correct answer is option 3.
Workspace:
Mr. Arbit and Mr. Boring did not invest in the new technology, but the new technology is a big success. Repentant, they are now estimating the additional amount they would have earned (i.e. forgone earnings) had they invested in the new technology. However, the two owners differed on expected lifespan of the new technology. Mr. Arbit expected lifespan to be 5 years, whereas, Mr. Boring expected it to be 2 years. After the technology gets out-dated, the earnings from the business would drop back to 50,000 million rupees.
What would be the difference between two expected foregone earnings after 5 years of the technology investment, if yearly earnings are deposited in a bank @10%, compounded annually?
Note: Forgone Earnings = (Earnings from business with new technology) – (Earnings from business without new technology)
- (a)
231,200 million rupees
- (b)
331,000 million rupees
- (c)
400,510 million rupees
- (d)
431,000 million rupees
- (e)
464,100 million rupees
Answer: Option B
Text Explanation :
Forgone Earnings (F) = Earnings with new technology – Earnings without new technology
Let X = (Earnings without new technology for 5 years),
Let Y and Z be A’s and B’s respective earnings with new technology.
FA = Y – X
FB = Z – X
FA – FB = Y – Z
Both A and B use the new technology in the first 2 years. For the last 3 years, only A uses the technology.
Y = (Earnings with new technology for first 2 years) + (Earnings with new technology for last 3 years)
Z = (Earnings with new technology for first 2 years) + (Earnings without new technology for last 3 years)
∴ Y – Z = (Earnings with new technology for last 3 years) – (Earnings without new technology for last 3 years)
Earnings of the third year, with (or without) new technology, are placed at compound interest for 2 years. Similarly, earnings of the fourth year are placed at C.I. for 1 year and earnings of the last year do not earn any interest.
∴ Y – Z = [(150 × 1.12 + 150 × 1.1 + 150) – (50 × 1.12 + 50 × 1.1 + 50)] ×1000 million
= [(100) × 1.12 + (100) × 1.1 + 100)] ×1000 million
= 331000 million
Hence, option (b).
Workspace:
Answer the questions on the basis of information given in the following case.
Life saving Pharmaceuticals (LSP) is India-based Pharmaceuticals Company. Their business mostly revolves around a couple of generic drugs and a few patented drugs. LSP operates in 30 odd countries and more than 50% of their sales volume is from outside India.
If more than 50% of their sales volume is from generic drugs, which of the following options is definitely correct? (Note : All percentages figures are with respect to total sales volume)
- (a)
If sales volume of patented drugs in India is 43%, the sales volume of generic drugs in India will be less than 43%.
- (b)
If the sales volume of generic drugs in foreign countries is at least 24%, the sales volume of patented drugs in India will be above 24%.
- (c)
If the sales volume of patented drugs in India is 54%, the sales volume of generic drugs in foreign countries will be above 54%.
- (d)
If the sales volume of patented drugs in India is 29%, the sales volume of generic drugs in foreign countries will be above 29%
- (e)
If the sales volume of generic drugs in India is at least 60%, the sales volume of patented drugs in foreign countries will be above 60%.
Answer: Option D
Text Explanation :
Let the total sales volume be 100. Let the sales volumes from India and outside India be 49 and 51 respectively. Let the sales from generic drugs and patented drugs be 51 and 49 respectively.
These values satisfy all the given conditions.
Solving by options,
Option 1:
If the sales volume of patented drugs in India is 43% of 49, the sales volume of generic drugs in India will be 57% (> 43%) of 49.
Also, (57% of 49) is an acceptable value for sales of generic drugs in India, as it will not exceed the total sales of generic drugs i.e. 51.
Hence, option (a) is eliminated.
Option 2:
If the sales volume of generic drugs in foreign countries is 24% of 51, the sales volume of patented drugs abroad will be 76% of 51 i.e. 38.76. Correspondingly, the sales volumes of patented drugs in India will be (49 – 38.76) i.e. 10.24, which is 20.9% (< 24%) of total sales in India i.e., 49.
Hence, option (b) is eliminated.
Option 3:
If the sales volume of patented drugs in India is 54% of 49, the sales volume of generic drugs in India becomes 46% of 49 i.e. 22.54. Correspondingly, the sales volumes of generic drugs abroad will be (51 – 22.54) i.e. 28.46, which is 55.8% (> 54%) of 51.
Hence, option (c) cannot be eliminated.
Option 4:
If the sales volume of patented drugs in India is 29% of 49, the sales volume of generic drugs in India becomes 71% of 49 i.e. 34.79. Correspondingly, the sales volumes of generic drugs abroad will be (51 – 34.79) i.e. 16.21, which is 31.8% (> 29%) of 51.
Hence, option (d) cannot be eliminated.
Option 5:
If the sales volume of generic drugs in India is 60% of 49, the sales volume of patented drugs in India becomes 40% of 49 i.e. 19.6. Correspondingly, the sales volumes of patented drugs abroad will be (49 – 19.6) i.e. 29.4, which is 57.6% (< 60%) of 51.
Hence, option (e) is eliminated.
Again considering option 3,
Let the sales volumes from India and outside India be 30 and 70 respectively. The rest of the values remain the same.
If the sales volume of patented drugs in India is 54% of 30, the sales volume of generic drugs in India becomes 46% of 30 i.e. 13.8. Correspondingly, the sales volumes of generic drugs abroad will be (51 – 13.8) i.e. 37.2, which is 53.1% (< 54%) of 70.
Hence, option (c) is eliminated.
Hence, option (d).
Workspace:
Mr. Sinha, a senior executive of LSP, observes that their business in India is not vibrant. LSP faces stiff competition from Indian and global players, except in rural areas. Interestingly, most of their sales in the rural area are from cough syrup, used as sedatives by teenagers. Mr. Sinha is planning the following actions to improve business in the long run.
- Invest in development of new drugs.
- Increase sales of cough syrup in the rural markets.
- Try and cut costs.
- Recruit more medical representatives in the rural areas.
Which of the following sequences is best arranged in the descending order of appropriateness?
- (a)
I, III, II
- (b)
II, I, III
- (c)
II, III, I
- (d)
IV, II, III
- (e)
IV, III, I
Answer: Option A
Text Explanation :
The question mentions that the sales of LSP in India are bleak and it faces stiff competition from foreign and local players, except in rural areas where it has high cough syrup sales. In the light of such a background the company intends to improves sales in the long term.
Statement I is the best option from the perspective of the company. Hence, it is the most appropriate course of action.
The next immediate step the company can take to improve business in the long term is to cut operating costs; the process may be time consuming but is an efficient one in the long term aspect of the country's operation.
As the issue of teenagers abusing cough syrups as sedatives is an ethical issue, increase in the sales of cough syrup will be beneficial to the company but not the teenagers. Hence, it can create trouble for the company in the long run. So, statement II is least appropriate.
The motive behind sending more medical representatives to rural areas is unclear from the question. It can either be to create awareness regarding the ill effects of substance abuse or to sell more number of cough syrups. Hence, statement IV is ruled out.
Thus, the correct descending order of the statements is I, III, and II.
Hence, the correct answer is option 1.
Workspace:
Mr. Rastogi, HR head of LSP, is contemplating of transferring MR. Jose, from India to their Luxembourg office. Mr. Jose’s wife is also with the HR department of LSP. The couple is expecting their first child within next four months and hence they want to be together. Mr. Rastogi is wondering whether Mr.Jose would accept the transfer. If he doesn’t, Mr. Rastogi would have to send a less competent person for this job as early as possible. The office in Luxembourg is very important for the company’s future. It is at its nascent stage and does not yet have an HR department. Hence, it is not possible to transfer Mrs. Jose to Luxembourg.
Which of the following options would be most appropriate, from the organization’s perspective, to resolve the issue?
- (a)
Giving a salary hike to Mr. Jose with a promise to transfer Mrs.Jose to Luxembourg in the near future.
- (b)
Giving Mrs. Jose option to work from home while in Luxembourg so that she can be with Mr.Jose.
- (c)
Giving Mr. Jose option to work from India for the time being so that he can be with Mrs. Jose in India.
- (d)
Giving a salary hike to Mr. Jose to compensate for Mrs. Jose’s salary so that she can join Mr. Jose at Luxembourg, even with loss of pay.
- (e)
Asking Mr. Jose to accept the offer right now but give him up to six months to join Luxembourg office.
Answer: Option B
Text Explanation :
Option 1 sidetracks the issue of the couple's desire to be together, considering the fact that they are expecting their first child.
Option 3 does not work in the favour of the organization. Since company needs a more competent person for the job in Luxembourg immediately, it might put the company's future at stake.
Eliminate 3. Same explanation applies to option 5. Hence, eliminate option 5.
Although option 4 looks compelling, it is not reasonable, as pay was never an issue for the couple. It will be unethical on the part of the company to compromise Mrs. Jose's job with a hike in Mr. Jose's salary. Eliminate option 4.
Option 2 comes forth as the most appropriate solution taking into account all the issues.
Hence, the correct answer is option 2.
Workspace:
Mr. Khan used to work as the Vice President of LSP India. However, he had resigned from LSP India for a better job in New York. In the meantime, his wife was promoted to head the HR of LSP India. Mrs. Khan had struggled hard to reach this position and was quite popular and respected within the organization. Mrs. Khan was contemplating whether she should give up her career and join him in New York. Mrs. Khan is considering the following actions:
- Take a break for the time being and focus on personal life. Given her reputation, she can always get back to the same job, if required.
- Go to New York, on leave without pay for two months to help Mr. Khan settle down. After that she can come back and resume her responsibility in LSP India.
- Request Mr. Khan to look for an equivalent job in India.
- Resign form LSP India, join Mr. Khan in New York, and look for a similar job there.
- Request LSP India for a similar position in LSP USA and follow Mr. Khan to New York.
Which of the following sequence of actions can be immediately taken by Mrs. Khan to maintain her work-life balance?
- (a)
I & II
- (b)
I & III
- (c)
I & IV
- (d)
II & V
- (e)
III & V
Answer: Option E
Text Explanation :
Given the reputation and popularity of Mrs Khan, sabotaging her professional life to focus on personal life would be an unwise decision. So, statement I is not a valid course of action. Hence, eliminate options 1, 2 and 3.
Statement II is also not a valid course of action, since it is similar to statement I in that it involves Mrs. Khan sabotaging her professional life. So we can eliminate option 4.
Statement IV is uncertain as there is no guarantee of getting a job in the US. Her career may
be compromised.
Requesting Mr. Khan to find a job in India is an appropriate action as it will save Mrs. Khan's career in India. This way they can both stay together in India. Statement III is justified.
Statement V also makes for an appropriate course of action. Mrs. Khan can also request LSP India for a similar position in LSP USA without disrupting her ongoing career.
Hence, the correct answer is option 5.
Workspace:
Answer the questions on the basis of information given in the following case.
Mohan’s was a popular fast-food joint at Connaught Place, Delhi. Initially Mohan handled his business alone. His sons, Ram and Kishan, joined the business after graduation from college. Ram was entrepreneurial in nature. Subsequently, another branch of Mohan’s was opened in Panipat. Mohan had chosen Ram to head the Panipat branch. Though Ram increased sales in short time, he had stopped using premium quality organic vegetables, the speciality of Mohan’s. Mohan and Kishan were not happy with his way of doing business.
Now, the foremost challenge for Mohan was to sort out this issue with Ram. Mohan knew that replacing Ram with Kishan was difficult as Kishan did not want to leave Delhi. However, giving a freehand to Ram might have long term negative consequences. Mohan was confused about the future of course of actions.
Mohan sought the help of five consultants, who give the following opinions:
- Organic vegetables might be a big success at Connaught place but awareness about organic vegetables is low among Panipat customers.
- The Connaught place model can be implemented in Panipat provided the business is prepared to face the consequences.
- Many high end restaurants in Panipat use organic vegetables. So, using organic vegetables will not be a differentiating factor.
- Selling prices of their dishes in Panipat are significantly lower. Using organic vegetables will bring down profits.
- Premium quality organic vegetables are not easily available in Panipat.
Which of the following set of options would support Ram’s argument of not using organic vegetables?
- (a)
I, III, IV
- (b)
II, IV, V
- (c)
I, III, IV, V
- (d)
II, III, IV, V
- (e)
All of the above
Answer: Option C
Text Explanation :
The question stem asks for the set of options that would support Ram's argument of “not” using organic vegetables.
All the options except II strongly support Ram's argument stating the drawbacks of using organic vegetables in Panipat.
Statement II does not support Ram's argument as it says “provided the business is prepared to face the consequences”; from this, one cannot ascertain whether the consequences will turn out bad and in favour of not using organic vegetables.
So, eliminate options 1, 2, 4 and 5.
Hence, the correct answer is option 3.
Workspace:
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