Question

Which of the given companies has seen the highest year-on-year growth (in percentage) in any single year during this five-year period?

• A. P
• B. There was a tie among multiple companies
• C. R
• D. Q
• E. S
• A. R or S
• B. S only
• C. P or R
• D. P or S
• J. P only
• A. From 2014 to 2015, the increases in revenues of at least two companies were the same
• B. The revenue of Q in 2014 was the same as the revenue of R in 2014
• C. The company that experienced the 50% increase in revenue also experienced the maximum increase in revenue in absolute terms
• D. The 2014 revenues of P and R cannot be determined uniquely
• O. From 2014 to 2015, the revenues of P and R increased by different amounts

Answer 1

The Correct Option is D

To determine which company experienced the highest year-on-year growth percentage in any given year, we will calculate the growth rate for each company between consecutive years from 2015 to 2019. The formula to calculate the percentage growth from one year to the next is:Growth Rate (%) = ((Revenue in Current Year - Revenue in Previous Year) / Revenue in Previous Year) × 100. Using this formula, we will analyze the growth for each company:

• Company P:
  • 2016 Growth: ((175 - 150) / 150) × 100 = 16.67%
  • 2017 Growth: ((200 - 175) / 175) × 100 = 14.29%
  • 2018 Growth: ((250 - 200) / 200) × 100 = 25%
  • 2019 Growth: ((250 - 250) / 250) × 100 = 0%
• Company Q:
  • 2016 Growth: ((140 - 125) / 125) × 100 = 12%
  • 2017 Growth: ((180 - 140) / 140) × 100 = 28.57%
  • 2018 Growth: ((210 - 180) / 180) × 100 = 16.67%
  • 2019 Growth: ((220 - 210) / 210) × 100 = 4.76%
• Company R:
  • 2016 Growth: ((160 - 150) / 150) × 100 = 6.67%
  • 2017 Growth: ((180 - 160) / 160) × 100 = 12.5%
  • 2018 Growth: ((200 - 180) / 180) × 100 = 11.11%
  • 2019 Growth: ((240 - 200) / 200) × 100 = 20%
• Company S:
  • 2016 Growth: ((120 - 100) / 100) × 100 = 20%
  • 2017 Growth: ((140 - 120) / 120) × 100 = 16.67%
  • 2018 Growth: ((170 - 140) / 140) × 100 = 21.43%
  • 2019 Growth: ((180 - 170) / 170) × 100 = 5.88%

Upon analyzing the above calculations, Company Q exhibited the highest year-on-year growth of 28.57% between 2016 and 2017. Thus, the company with the highest growth rate in any single year is Q.

Answer 2

To solve the problem, let's analyze the revenue data for each company to determine which one, if any, is misreporting a revenue such that its revenues would form an arithmetic progression (AP). An arithmetic progression is a sequence of numbers in which the difference between any two consecutive terms is constant.

We have been given:

	Revenue(in Rs. Lakhs )
Year	P	Q	R	S
2015	150	125	150	100
2016	175	140	160	120
2017	200	180	180	140
2018	250	210	200	170
2019	250	220	240	180

We shall assess each company's revenue:

Company P: 150, 175, 200, 250, 250

The differences are: 25, 25, 50, 0. Since the differences aren't equal, it currently does not form an AP.

Company Q: 125, 140, 180, 210, 220

The differences are: 15, 40, 30, 10. Not equal, so not an AP.

Company R: 150, 160, 180, 200, 240

The differences are: 10, 20, 20, 40. Not equal, so not an AP.

Company S: 100, 120, 140, 170, 180

The differences are: 20, 20, 30, 10. Not equal, so not an AP.

To form an AP, for Company P: Adjusting to maintain the AP, changing the fourth or fifth year value could make the differences equal, while for Company S: Adjusting any single year's revenue similarly could achieve AP progression.
This leads us to conclude that either Company P or Company S could potentially be misreporting such that their revenue aligns to form a valid AP, fitting the option P or S.

Answer 3

We have four companies, and during 2014 to 2015, three experienced a 25% revenue increase, while one experienced a 50% increase. The total increase across these companies was Rs. 125 lakhs. Let's solve to find which scenario cannot be true.
Let the revenues of companies P, Q, R, and S in 2014 be represented by \( P_{2014}, Q_{2014}, R_{2014}, \) and \( S_{2014} \). The revenue increases are: 
 

• \(\text{3 companies with 25\% increase: } 0.25P_{2014}, 0.25Q_{2014}, 0.25R_{2014}\)
• \(\text{1 company with 50\% increase: } 0.5S_{2014}\)

The total revenue increase, Rs. 125 lakhs, is the sum of these:
\(0.25P_{2014} + 0.25Q_{2014} + 0.25R_{2014} + 0.5S_{2014} = 125\)
Rearrange to: (1)
\(0.25(P_{2014} + Q_{2014} + R_{2014}) + 0.5S_{2014} = 125\)

Assume \(0.25(P_{2014} + Q_{2014} + R_{2014} + 2S_{2014}) = 125\)
Thus:
\(P_{2014} + Q_{2014} + R_{2014} + 2S_{2014} = 500\)
To solve, let's consider the possible scenarios proposed in the options:

• "From 2014 to 2015, the increases in revenues of at least two companies were the same": With three companies having the same percent increase, the increases are \[0.25a = 0.25b\]; hence, increase equality is possible.
• "The revenue of Q in 2014 was the same as the revenue of R in 2014": This is possible if \(Q_{2014} = R_{2014}\).
• "The company with the 50% increase had the maximum absolute increase": This can be true if the fourth company's revenue was much higher, making its 50\% increase larger.
• "The 2014 revenues of P and R cannot be determined uniquely": With available equations, unique determination is not possible without additional information.
• "From 2014 to 2015, the revenues of P and R increased by different amounts": As either could be one of the companies with equal 25\% increase, differing increases can occur.

The scenario listed as "From 2014 to 2015, the increases in revenues of at least two companies were the same" cannot be ruled out, as these could and are likely to be the same due to equal percentage increases. However, given the problem, observed from equations, and exploring the scenarios, each outcome is possible, and hence, this statement cannot be true that their increases were distinctly different when considering equal percentage increases could impact multiple.