The following graphs show the revenue (in $ million) of three companies in their initial six years of operations, in an economy which is characterized by a persistent inflation.
In 2010, which could be a valid statement about the revenues (adjusted for inflation) of these three companies?
Show Hint
- “Adjusted for inflation” requires an inflation rate; if not given, precise 2010-comparisons are indeterminate.
- Revenues of all three companies were equal.
- Revenues of all three companies could be equal.
- Revenue of Yahoo was definitely less than Facebook which was definitely less than Google.
- Total of Yahoo and Facebook was definitely higher than that of Google.
- None of the above.
The Correct Option is
Solution and Explanation
Step 2: Revenues are to be viewed in 2010 dollars (adjusted for persistent inflation), but without the firms’ starting years and the exact inflation path, no specific equality/inequality among the three can be concluded or even guaranteed as possible.
Step 3: Hence none of the statements (A)–(D) can be asserted as valid.
\[ \boxed{\text{None of the above}} \]
The difference in the average percentage increase in revenues, from 4th to 6th year, of Yahoo and Facebook is:
Show Hint
- Keep fractions to avoid rounding drift; round only at the end.
- 35%
- 40%
- 45%
- 50%
- 55%
The Correct Option is B
Solution and Explanation
Yahoo (Y): \(Y_4=250,\; Y_5=600,\; Y_6=1200\).
Facebook (F): \(F_4=300,\; F_5=750,\; F_6=2000\).
Step 2: Compute percentage increases.
Yahoo: \( \frac{600-250}{250}=140%, \frac{1200-600}{600}=100%\).
Average for Yahoo \(=\frac{140%+100%}{2}=120%\).
Facebook: \( \frac{750-300}{300}=150%, \frac{2000-750}{750}=166.\overline{6}%\).
Average for Facebook \(=\frac{150%+166.\overline{6}%}{2}=158.\overline{3}%\).
Step 3: Difference \(=158.\overline{3}%-120%=38.\overline{3}%\approx 40%\).
\[ \boxed{40%} \]
What would have been Facebook’s revenue (in \$ million) in its sixth year of operation if the company had matched Google’s percentage growth in revenues from the fifth to the sixth year? Choose the option that is nearest to the answer.
Show Hint
- When options are spaced widely, rounding to the nearest sensible figure is safe.
- 1600
- 1700
- 1900
- 2100
- None of the above
The Correct Option is A
Solution and Explanation
Percentage growth \(=\dfrac{3200-1500}{1500}=\dfrac{1700}{1500}=1.133\overline{3}=113.33%\).
Step 2: Apply this growth to Facebook’s 5th year revenue \(F_5=750\).
\[ F_6^{\text{(if matched)}}=750\,(1+1.133\overline{3})=750\times 2.133\overline{3}\approx 1600. \]
Thus the nearest option is \(\boxed{1600}\).
Top Questions on Bar Graph
- Over the top (OTT) subscribers of a platform are segregated into three categories: i) Kid, ii) Elder, and iii) Others. Some of the subscribers used one app and the others used multiple apps to access the platform. The figure below shows the percentage of the total number of subscribers in 2023 and 2024 who belong to the 'Kid' and 'Elder' categories.
The following additional facts are known about the numbers of subscribers.
The total number of subscribers increased by 10% from 2023 to 2024.
In 2024, 1/2 of the subscribers from the 'Kid' category and 2/3 of the subscribers from the 'Elder' category subscribers use one app.
In 2023, the number of subscribers from the 'Kid' category who used multiple apps was the same as the number of subscribers from the 'Elder' category who used one app.
10,000 subscribers from the 'Kid' category used one app and 15,000 subscribers from the 'Elder' category used multiple apps in 2023. - An online e-commerce firm receives daily integer product ratings from 1 through 5 given by buyers. The daily average is the average of the ratings given on that day. The cumulative average is the average of all ratings given on or before that day. The rating system began on Day 1, and the cumulative averages were 3 and 3.1 at the end of Day 1 and Day 2, respectively. The distribution of ratings on Day 2 is given in the figure below
The following information is known about ratings on Day 3.
1. 100 buyers gave product ratings on Day 3.
2. The modes of the product ratings were 4 and 5.
3. The numbers of buyers giving each product rating are non-zero multiples of 10.
4. The same number of buyers gave product ratings of 1 and 2, and that number is half the number of buyers who gave a rating of 3. - Six web surfers M, N, O, P, X, and Y each had 30 stars which they distributed among four bloggers A, B, C, and D. The number of stars received by A and B from the six web surfers is shown in the figure below
The following additional facts are known regarding the number of stars received by the bloggers from the surfers.
1. The numbers of stars received by the bloggers from the surfers were all multiples of 5 (including 0).
2. The total numbers of stars received by the bloggers were the same.
3. Each blogger received a different number of stars from M.
4. Two surfers gave all their stars to a single blogger.
5. D received more stars than C from Y - The chart below provides complete information about the number of countries visited by Dheeraj, Samantha and Nitesh, in Asia, Europe and the rest of the world (ROW).
The following additional facts are known about the countries visited by them.
1. 32 countries were visited by at least one of them.
2. USA (in ROW) is the only country that was visited by all three of them.
3. China (in Asia) is the only country that was visited by both Dheeraj and Nitesh, but not by Samantha.
4. France (in Europe) is the only country outside Asia, which was visited by both Dheeraj and Samantha, but not by Nitesh.
5. Half of the countries visited by both Samantha and Nitesh are in Europe. - Analyse the bar graph carefully and answer the following questions.
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