Directions for questions (5 to 8) : Answer these Questions on the basis of the information given below: The table below presents the revenue (in million rupees) of four firms in three states. These firms, Honest Ltd., Aggressive Ltd., Truthful Ltd. and Profitable Ltd. are disguised in the table as A,B,C and D, in no particular order. In the state of MP, Truthful Ltd. has the highest market share. Aggressive Ltd. 's aggregate revenue differs from Honest Ltd. 's by Rs. 5 million. What can be said regarding the following two statements? Statement 1: Honest Ltd. has the highest share in the UP market. Statement 2: Aggressive Ltd. has the highest share in the Bihar market.

At most one of the statements is true.

At least one of the statements must be true.

What can be said regarding the following two statements? Statement 1 : Aggressive Ltd. 's lowest revenues are from MP. Statement 2 : Honest Ltd. 's lowest revenues are from Bihar.

If Statement I is true then Statement 2 is necessarily true.

If Statement 2 is true then Statement 1 is necessarily false.

If Statement I is false then Statement 2 is necessarily true.

What can be said regarding the following two statements? Statement 1: Profitable Ltd. has the lowest share in MP market. Statement 2 : Honest Ltd. 's total revenue is more than Profitable Ltd.

"If Statement 1 is true then Statement 2 is necessarily false.

If Statement I is true then Statement 2 is necessarily true.

Both Statement 1 and Statement 2 are true.

Neither Statement 1 nor Statement 2 is true.

If Profitable Ltd. 's lowest revenue is from UP, then which of the following is true?

Truthful Ltd. 's lowest revenues are from UP.

Truthful Ltd. 's lowest revenues are from MP.

Truthful Ltd. 's lowest revenues are from Bihar.

No definite conclusion is possible.

Which of the following additional information would enable to find the exact number of volunteers involved in various projects?

Twenty volunteers are involved in FR.

Four volunteers are involved in all the three projects.

Twenty three volunteers are involved in exactly one project.

No need for any additional information.

After some time, the volunteers who were involved in all the three projects were asked to withdraw from one project. As a result, one of the volunteers opted out of the TR project, and one opted out ofthe ER project, while the remaining ones involved in all the three projects opted out of the FR project. Which of the following statements, then, necessarily follows?

More volunteers are now in FR project as compared to ER project.

The lowest number of volunteers is now in TR project.

More volunteers are now in TR project as compared to ER project.

Directions for questions (21 to 24) : Answer these questions on the basis ofthe information given below. Each question is followed by two statements, A and B. Answer each question using the following instructions: In a football match, at the half-time, Mahindra and Mahindra Club was trailing by three goals. Did it win the match? A: In the second-half Mahindra and Mahindra Club scored four goals. B: The opponent scored four goals in the match

if the question cannot be answered on the basis of the two statements.

if the question can be answered by using the statement A alone but not by using the statement B alone.

if the question can be answered by using the statement B alone but not by using the statement A alone.

if the question can be answered by using either of the statements alone.

if the question can be answered by using both the statements together but not by either of the statements alone.

In a particular school, sixty students were athletes. Ten among them were also among the top academic performers. How many top academic performers were in the school? A: Sixty per cent of'the top academic performers were not athletes. B: All the top academic performers were not necessarily athletes.

if the question can be answered by using the statement A alone but not by using the statement B alone.

if the question can be answered by using the statement B alone but not by using the statement A alone.

if the question can be answered by using either of the statements alone.

if the question can be answered by using both the statements together but not by either of the statements alone.

if the question cannot be answered on the basis of the two statements.

Five students Atul, Bala, Chetan, Dev and Ernesto were the only ones who participated in a quiz contest. They were ranked based on their scores in the contest. Dev got a higher rank as compared to Ernesto, while Bala got a higher rank as compared to Chetan. Chetan's rank was lower than the median. Who among the five got the highest rank? A: Atul was the last rank holder. B: Bala was not among the top two rank holders.

if the question can be answered by using both the statements together but not by either of the statements alone.

if the question can be answered by using the statement A alone but not by using the statement B alone.

if the question can be answered by using the statement B alone but not by using the statement A alone.

if the question can be answered by using either of the statements alone.

if the question cannot be answered on the basis of the two statements.

Thirty per cent of the employees ofa call centre are males. Ten per cent of the female employees have an engineering background. What is the percentage of male employees with engineering background? A: Twenty five per cent of the employees have engineering background. B: Number of male employees having an engineering background is 20% more than the number of female employees having an engineering background.

if the question can be answered by using either of the statements alone.

if the question can be answered by using the statement A alone but not by using the statement B alone.

if the question can be answered by using the statement B alone but not by using the statement A alone.

if the question can be answered by using both the statements together but not by either of the statements alone.

if the question cannot be answered on the basis of the two statements.

Data Interpretation And Logical Reasoning Test

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| By Tanmay Shankar

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Quizzes Created: 484 | Total Attempts: 1,789,416

Questions: 70 | Attempts: 2,585 | Updated: Nov 16, 2023

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Data Interpretation And Logical Reasoning Test - Quiz

Are you ready for a data interpretation and logical reasoning test? When interpreting data, an analyst must try to distinguish between association, relationship, and coincidences. The analyst also must consider all the variables involved, which may have led to a result. Data interpretation entails graphs, charts, and tables. Logical thinking is one of the most important skills used in critical thinking. This thought-provoking quiz on data interpretation and logical reasoning will get your mind working.

Questions and Answers

1.

Directions for questions (1 to 4): Answer these Questions on the basis of the information given below: Venkat, a stockbroker, invested a part of his money in the stock of four companies - A, B, C and D. Each of these companies belonged to different industries, viz., Cement, Information Technology (IT), Auto, and Steel, in no particular order. At the-time of investment, the price of each stock was Rs 100. Venkat purchased only one stock of each of these companies. He was expecting returns of 20%, 10%, 30% and 40% from the stock of companies A, B, C and D, respectively. Returns are defined as the change in the value of the stock after one year, expressed as a percentage of the initial value. During the year, two of these companies announced extraordinarily good results. One of these two companies belonged to the Cement or the IT industry, while the other one belonged to either the Steel or the Auto industry. As a result, the returns on the stocks of these two companies were higher than the initially expected returns. For the company belonging to the Cement or the IT industry with extraordinarily good results, the returns were twice that of the initially expected returns. For the company belonging to the Steel or[ the Auto industry, the returns on announcement of extraordinarily good results were only one and a halftimes that of the initially expected returns. For the remaining two companies. Which do not announce extraordinarily good results, the returns realized during the year were the same as initially expected. What is the minimum average return Venkat would have earned during the year?
- A.
  
  30%
- B.
  
  31 Y 4%
- C.
  
  32 1/2%
- D.
  
  Cannot be determined
Correct Answer
A. 30%

Explanation
Venkat invested in four stocks with expected returns of 20%, 10%, 30%, and 40% from companies A, B, C, and D, respectively. It is mentioned that two companies announced extraordinarily good results, one from the Cement or IT industry and the other from the Steel or Auto industry. The returns on these two stocks were higher than initially expected, with the Cement/IT industry stock having returns twice the initial expectation and the Steel/Auto industry stock having returns one and a half times the initial expectation. The remaining two stocks, which did not announce extraordinarily good results, had returns that were the same as initially expected. Since the question asks for the minimum average return Venkat would have earned, it can be concluded that the minimum average return would be the same as the initially expected returns, which is 30%.

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1
0
2.

If Venkat earned a 35% return on average during the year, then which of these statements would necessarily be true? I. Company A belonged either to Auto or to Steel Industry. II. Company B did not announce extraordinarily good results. III. Company A announced extraordinarily good results. Iv. Company D did not announce extraordinarily good results.
- A.
  
  I and II only
- B.
  
  II and III only
- C.
  
  III and IV only
- D.
  
  II and IV only
Correct Answer
B. II and III only

Explanation
If Venkat earned a 35% return on average during the year, it implies that Company A did not necessarily belong to the Auto or Steel Industry (statement I is not necessarily true). However, it does imply that Company B did not announce extraordinarily good results (statement II is true) and that Company A did announce extraordinarily good results (statement III is true). There is no information provided about Company D, so statement IV cannot be determined. Therefore, the correct statements are II and III only.

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3.

If Venkat earned a 38.75% return on average during the year, then which of these statement(s) would necessarily be true? I. Company C belonged either to Auto or to Steel Industry. II. Company D belonged either to Auto or to Steel Industry. III. Company A announced extraordinarily good results. IV. Company B did not announce extraordinarily good results.
- A.
  
  I and II only
- B.
  
  II and III only
- C.
  
  III and IV only
- D.
  
  II and IV only
Correct Answer
C. III and IV only

Explanation
The given question does not provide any information about the industries to which the companies belong or their performance. Therefore, statements I and II cannot be determined based on the given information. However, since Venkat earned a 38.75% return on average during the year, it can be inferred that Company A announced extraordinarily good results (statement III). Additionally, since Company B did not announce extraordinarily good results, statement IV is also true. Therefore, the correct answer is III and IV only.

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4.

If Company C belonged to the Cement or the IT industry and did announce extraordinarily good results, then which of these statement(s) would necessarily be true? I. Venkat earned not more than 36.25% return on average. II. Venkat earned not less than 33.75% return on average. III. If Venkat earned 33.75% return on average, Company A announced extraordinarily good results. Iv. If' Venkat earned 33.75% return on average, Company B belonged either to Auto or to Steel Industry.
- A.
  
  I and II only
- B.
  
  II and IV only
- C.
  
  II and III only
- D.
  
  III and IV only
Correct Answer
B. II and IV only

Explanation
If Company C belonged to the Cement or the IT industry and announced extraordinarily good results, it implies that Venkat earned not less than 33.75% return on average. This is because the question states that the company announced extraordinarily good results, suggesting that Venkat's returns were also good. Additionally, if Venkat earned 33.75% return on average, it implies that Company B belonged either to the Auto or Steel industry. This is because the question states that if Venkat earned a certain return, Company B belonged to one of these two industries. Therefore, the correct answer is II and IV only.

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5.

Directions for questions (5 to 8) : Answer these Questions on the basis of the information given below: The table below presents the revenue (in million rupees) of four firms in three states. These firms, Honest Ltd., Aggressive Ltd., Truthful Ltd. and Profitable Ltd. are disguised in the table as A,B,C and D, in no particular order. In the state of MP, Truthful Ltd. has the highest market share. Aggressive Ltd. 's aggregate revenue differs from Honest Ltd. 's by Rs. 5 million. What can be said regarding the following two statements? Statement 1: Honest Ltd. has the highest share in the UP market. Statement 2: Aggressive Ltd. has the highest share in the Bihar market.
- A.
  
  Both statements could be true.
- B.
  
  At least one of the statements must be true.
- C.
  
  At most one of the statements is true.
- D.
  
  None of the above.
Correct Answer
C. At most one of the statements is true.

Explanation
The table presents the revenue of four firms in three states. It is mentioned that Truthful Ltd. has the highest market share in MP and Aggressive Ltd.'s revenue differs from Honest Ltd.'s by Rs. 5 million. Based on this information, it is possible that Honest Ltd. has the highest share in the UP market, making Statement 1 true. However, it is also possible that Aggressive Ltd. has the highest share in the Bihar market, making Statement 2 true. Therefore, both statements could be true. However, it is also possible that neither statement is true. Therefore, the correct answer is "At most one of the statements is true."

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6.

What can be said regarding the following two statements? Statement 1 : Aggressive Ltd. 's lowest revenues are from MP. Statement 2 : Honest Ltd. 's lowest revenues are from Bihar.
- A.
  
  If Statement 2 is true then Statement 1 is necessarily false.
- B.
  
  If Statement I is false then Statement 2 is necessarily true.
- C.
  
  If Statement I is true then Statement 2 is necessarily true.
- D.
  
  None of the above.
Correct Answer
C. If Statement I is true then Statement 2 is necessarily true.

Explanation
If Statement 1 is true, it means that Aggressive Ltd. has its lowest revenues from MP. If Statement 2 is true, it means that Honest Ltd. has its lowest revenues from Bihar. The answer suggests that if Statement 1 is true, it necessarily implies that Statement 2 is also true. This means that if Aggressive Ltd. has its lowest revenues from MP, then it is necessarily true that Honest Ltd. has its lowest revenues from Bihar.

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7.

What can be said regarding the following two statements? Statement 1: Profitable Ltd. has the lowest share in MP market. Statement 2 : Honest Ltd. 's total revenue is more than Profitable Ltd.
- A.
  
  If Statement I is true then Statement 2 is necessarily true.
- B.
  
  "If Statement 1 is true then Statement 2 is necessarily false.
- C.
  
  Both Statement 1 and Statement 2 are true.
- D.
  
  Neither Statement 1 nor Statement 2 is true.
Correct Answer
B. "If Statement 1 is true then Statement 2 is necessarily false.

Explanation
If Statement 1 is true, it means that Profitable Ltd. has the lowest share in the MP market. However, if Statement 2 is necessarily false, it means that Honest Ltd.'s total revenue is not more than Profitable Ltd. In other words, even if Profitable Ltd. has the lowest share in the market, it does not necessarily mean that Honest Ltd.'s total revenue is more than Profitable Ltd.

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8.

If Profitable Ltd. 's lowest revenue is from UP, then which of the following is true?
- A.
  
  Truthful Ltd. 's lowest revenues are from MP.
- B.
  
  Truthful Ltd. 's lowest revenues are from Bihar.
- C.
  
  Truthful Ltd. 's lowest revenues are from UP.
- D.
  
  No definite conclusion is possible.
Correct Answer
C. Truthful Ltd. 's lowest revenues are from UP.

Explanation
If Profitable Ltd.'s lowest revenue is from UP, it implies that UP is not a profitable market for Profitable Ltd. On the other hand, if Truthful Ltd.'s lowest revenues are also from UP, it suggests that UP is also not a profitable market for Truthful Ltd. Therefore, the statement "Truthful Ltd.'s lowest revenues are from UP" is true based on the given information.

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9.

Directions for questions (9 to 12) : Answer these Questions on the basis ofthe information given below: In the table below is the listing of players, seeded from highest (#1) to lowest (#32), who are due to play in an Association of Tennis Players (ATP) tournament for women. This tournament has four knockout rounds before the final, i.e., first round, second round, quarterfinals, and semi-finals. In the first round, the highest seeded player plays the lowest seeded player (seed # 32) which is designated match No.1 of first round; the 2nd seeded player plays the 31 st seeded player which is designated match No.2 of the first round, and so on. Thus, for instance, match No. 16 of first round is to be played between 16th seeded player and the 17th seeded player. In thesecond round, the winner of match No.1 of first round plays the winner of match No. 16 of first round and is designated match No.1 of second round. Similarly, the winner of match No.2 of first round plays the winner of match No. 15 of first round, and is designated match No.2 of second round. Thus, for instance, match No.8 of the second round is to be played between the winner of match No.8 offirst round and the winner of match No.9 of first round. The same pattern is followed for later rounds as well. If Elena Dementieva and Serena Williams lose in the second round, while Justine Henin and Nadia Petro va make it to the semi-finals, then who would play Maria Sharapova in the quarterfinals, in the event Sharapova reaches quarterfinals?
- A.
  
  Dinara Safina
- B.
  
  Justine Henin
- C.
  
  Nadia Petrova
- D.
  
  Patty Schnyder
Correct Answer
C. Nadia Petrova

Explanation
If Elena Dementieva and Serena Williams lose in the second round, and Justine Henin and Nadia Petrova make it to the semi-finals, then Nadia Petrova would play Maria Sharapova in the quarterfinals, assuming Sharapova also reaches the quarterfinals. This can be determined by following the pattern mentioned in the information given. In the second round, the winner of match No.2 of the first round (which would be Justine Henin) plays the winner of match No.15 of the first round (which would be Nadia Petrova), and is designated match No.2 of the second round. Therefore, if both Henin and Petrova make it to the semi-finals, Petrova would play Sharapova in the quarterfinals.

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10.

If the top eight seeds make it to the quarterfinals, then who, amongst the players listed below, would definitely not play against Maria Sharapova in the final, in case Sharapova reaches the final?
- A.
  
  Amelie Mauresmo
- B.
  
  Elena Dementieva
- C.
  
  Kim Clijsters
- D.
  
  Lindsay Davenport
Correct Answer
C. Kim Clijsters

Explanation
If the top eight seeds make it to the quarterfinals, it means that only those eight players will be left in the tournament. Since Maria Sharapova is one of the top eight seeds, she would have to win her quarterfinal match to reach the final. If Kim Clijsters is listed below as one of the players, it means that she is not one of the top eight seeds. Therefore, if the top eight seeds make it to the quarterfinals, Kim Clijsters would definitely not play against Maria Sharapova in the final.

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11.

If there are no upsets (a lower seeded player beating a higher seeded player) in the first round, and only match Nos. 6, 7, and 8 of the second round result in upsets, then who would meet Lindsay Davenport in quarter finals, in case Davenport reaches quarter finals?
- A.
  
  Justine Henin
- B.
  
  Nadia Petrova
- C.
  
  Patty Schnyder
- D.
  
  Venus Williams
Correct Answer
D. Venus Williams

Explanation
If there are no upsets in the first round, it means that all the higher seeded players have won their matches. In the second round, only match Nos. 6, 7, and 8 result in upsets, which means that the higher seeded players in those matches have been defeated by lower seeded players. Therefore, if Lindsay Davenport reaches the quarter finals, she would meet Venus Williams, as she is the only option left among the given players who has not been mentioned as causing an upset in the second round.

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12.

If, in the first round, all even numbered matches (and none of the odd numbered ones) result in upsets, and there are no upsets in the second round, then who could be the lowest seeded player facing Maria Sharapova in semi-finals?
- A.
  
  Anastasia Myskina
- B.
  
  Flavia Pennetta
- C.
  
  Nadia Petrova
- D.
  
  Svetlana Kuznetsova
Correct Answer
A. Anastasia Myskina

Explanation
In the first round, all even numbered matches resulted in upsets, meaning that the lower seeded players won those matches. This implies that Anastasia Myskina, who is the lowest seeded player among the given options, won her match in the first round. Since there were no upsets in the second round, it can be inferred that all higher seeded players won their matches. Therefore, the lowest seeded player facing Maria Sharapova in the semi-finals could be Anastasia Myskina.

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13.

Directions for questions (13 to 16) : Answer these Questions on the basis of the information given below: Help Distress (HD) is an NGO involved in providing assistance to people suffering from natural disasters. Currently, it has 37 volunteers. They are involved in three projects: Tsunami Relief(TR) in Tamil Nadu, Flood Relief(FR) in Maharashtra, and Earthquake Relief (ER) in Gujarat. Each volunteer working with Help Distress has to be involved in at least one relief work project. A Maximum number of volunteers are involved in the FR project. Among them, the number of volunteers involved in FR project alone is equal to the volunteers having additional involvement in the ER project. The number of volunteers involved in the ER project alone is double the number of volunteers involved in all the three projects. 17 volunteers are involved in the TR project. , The number of volunteers involved in the TR project alone is one less than the number of volunteers involved in ER project alone. Ten volunteers involved in the TR project are also involved in at least one more project. Based on the information given above, the minimum number of volunteers involved in both FR and TR projects, but not in the ER project is:
- A.
  
  1
- B.
  
  3
- C.
  
  4
- D.
  
  5
Correct Answer
C. 4

Explanation
The minimum number of volunteers involved in both FR and TR projects, but not in the ER project is 4. This can be determined by analyzing the given information. We know that 17 volunteers are involved in the TR project alone, and the number of volunteers involved in the TR project alone is one less than the number of volunteers involved in the ER project alone. Therefore, there must be 18 volunteers involved in the ER project alone. Since the number of volunteers involved in the ER project alone is double the number of volunteers involved in all three projects, there must be 9 volunteers involved in all three projects. This leaves us with 37 - 17 - 18 - 9 = 4 volunteers involved in both FR and TR projects, but not in the ER project.

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14.

Which of the following additional information would enable to find the exact number of volunteers involved in various projects?
- A.
  
  Twenty volunteers are involved in FR.
- B.
  
  Four volunteers are involved in all the three projects.
- C.
  
  Twenty three volunteers are involved in exactly one project.
- D.
  
  No need for any additional information.
Correct Answer
A. Twenty volunteers are involved in FR.

Explanation
The information provided states that twenty volunteers are involved in FR. This additional information would enable us to find the exact number of volunteers involved in various projects because it specifies the number of volunteers involved in one specific project. By knowing this number, we can subtract it from the total number of volunteers involved in all three projects to determine the number of volunteers involved in the other two projects.

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15.

After some time, the volunteers who were involved in all the three projects were asked to withdraw from one project. As a result, one of the volunteers opted out of the TR project, and one opted out ofthe ER project, while the remaining ones involved in all the three projects opted out of the FR project. Which of the following statements, then, necessarily follows?
- A.
  
  The lowest number of volunteers is now in TR project.
- B.
  
  More volunteers are now in FR project as compared to ER project.
- C.
  
  More volunteers are now in TR project as compared to ER project.
- D.
  
  None of the above.
Correct Answer
B. More volunteers are now in FR project as compared to ER project.

Explanation
After some volunteers withdrew from different projects, it is clear that one volunteer opted out of the TR project, one opted out of the ER project, and the remaining volunteers involved in all three projects opted out of the FR project. This means that the number of volunteers in the TR project has decreased by one, while the number of volunteers in the ER project has also decreased by one. However, since the remaining volunteers opted out of the FR project, it can be inferred that more volunteers are now in the FR project compared to the ER project. Therefore, the correct answer is "More volunteers are now in FR project as compared to ER project."

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16.

After the withdrawal of volunteers, as indicated in Question 85, some new volunteers joined the NGO. Each one ofthem was allotted only one project in a manner such that, the number of volunteers working in one project alone for each of the three projects became identical. At that point, it was also found that the number of volunteers involved in FR and ER projects was the same as the number of volunteers involved in TR and ER projects. Which of the projects now has the highest number of volunteers?
- A.
  
  ER
- B.
  
  FR
- C.
  
  TR
- D.
  
  Cannot be determined
Correct Answer
A. ER

Explanation
After the withdrawal of volunteers, new volunteers joined the NGO and were allotted one project each. The number of volunteers working in one project for each of the three projects became identical. Additionally, the number of volunteers involved in FR and ER projects was the same as the number of volunteers involved in TR and ER projects. Based on this information, it can be concluded that ER project now has the highest number of volunteers.

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17.

Directions for questions (17 to 20) : Answer these Questions on the basis of the information given below: The year is 2089. Beijing, London, New York, and Paris are in contention to host the 2096 Olympics. The eventual winner is determined through several rounds of voting by members of the lac with each member representing a different city. All the four cities in contention are also represented in lac. In any round of voting; the city receiving the lowest number of votes in that round gets eliminated. The survivor after the last round of voting gets to host the event. A member is allowed to cast votes for at most two different cities in all rounds of voting combined. (Hence, a member becomes ineligible to cast a vote in a given round if both the cities(s) he voted for in earlier rounds are out of contention in that round of voting.) A member is also ineligible to cast a vote in a round if the city(s) he represents is in contention in that round of voting . As long as the member is eligible,(s)he must vote and vote for only one candidate city in any round of voting. The following incomplete table shows the information on cities that received the maximum and minimum votes in different rounds, the number of votes cast in their favour, and the total votes that were cast in those rounds. It is also known that : All those who voted for London and Paris in round 1, continued to vote for the same cities in subsequent rounds as long as these cities were in contention. 75% of those who voted for Beijing in round I, voted for Beijing in round 2 as well. Those who voted for New York in round 1, voted either for Beij ing or Paris in round 2. The difference in votes cast for the two contending cities in the last round was I. 50% of those who voted for Beijing in round I, voted for Paris in round 3. What percentage of members from among those who voted for New York in round 1, voted for Beijing in round 2?
- A.
  
  33.33
- B.
  
  50
- C.
  
  66.67
- D.
  
  75
Correct Answer
D. 75

Explanation
In round 1, those who voted for New York either voted for Beijing or Paris in round 2. We know that 75% of those who voted for Beijing in round 1 voted for Beijing in round 2 as well. Therefore, if the percentage of members from among those who voted for New York in round 1 and voted for Beijing in round 2 is 75%, it means that 75% of those who voted for New York in round 1 voted for Beijing in round 2.

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18.

What is the number of votes cast for Paris in round I?
- A.
  
  16
- B.
  
  18
- C.
  
  22
- D.
  
  24
Correct Answer
D. 24
19.

What percentage of members from among those who voted for Beijing in round 2 and were eligible to vote in round 3, voted for London?
- A.
  
  33.33
- B.
  
  38.10
- C.
  
  50
- D.
  
  66.67
Correct Answer
D. 66.67

Explanation
The correct answer is 66.67. This means that 66.67% of the members who voted for Beijing in round 2 and were eligible to vote in round 3, voted for London.

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20.

Which of the following statements must be true? (a) IOC member from New York must have voted for Paris in round 2. (b) IOC member from Beijing voted for London in round 3.
- A.
  
  Only a
- B.
  
  Only b
- C.
  
  Both a and b
- D.
  
  Neither a nor b
Correct Answer
A. Only a

Explanation
The given question is asking which of the statements must be true. In this case, the correct answer is "Only a." This means that the statement (a) "IOC member from New York must have voted for Paris in round 2" must be true, while statement (b) "IOC member from Beijing voted for London in round 3" may or may not be true.

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21.

Directions for questions (21 to 24) : Answer these questions on the basis ofthe information given below. Each question is followed by two statements, A and B. Answer each question using the following instructions: In a football match, at the half-time, Mahindra and Mahindra Club was trailing by three goals. Did it win the match? A: In the second-half Mahindra and Mahindra Club scored four goals. B: The opponent scored four goals in the match
- A.
  
  If the question can be answered by using the statement A alone but not by using the statement B alone.
- B.
  
  If the question can be answered by using the statement B alone but not by using the statement A alone.
- C.
  
  If the question can be answered by using either of the statements alone.
- D.
  
  If the question can be answered by using both the statements together but not by either of the statements alone.
- E.
  
  If the question cannot be answered on the basis of the two statements.
Correct Answer
E. If the question cannot be answered on the basis of the two statements.

Explanation
The correct answer is if the question cannot be answered on the basis of the two statements.

The question asks whether Mahindra and Mahindra Club won the match after trailing by three goals at half-time. Statement A states that Mahindra and Mahindra Club scored four goals in the second half, but it does not provide information about the goals scored by the opponent or the final result of the match. Statement B states that the opponent scored four goals in the match, but it does not provide information about the goals scored by Mahindra and Mahindra Club or the final result of the match. Therefore, neither statement alone nor both statements together can answer the question.

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22.

In a particular school, sixty students were athletes. Ten among them were also among the top academic performers. How many top academic performers were in the school? A: Sixty per cent of'the top academic performers were not athletes. B: All the top academic performers were not necessarily athletes.
- A.
  
  If the question can be answered by using the statement A alone but not by using the statement B alone.
- B.
  
  If the question can be answered by using the statement B alone but not by using the statement A alone.
- C.
  
  If the question can be answered by using either of the statements alone.
- D.
  
  If the question can be answered by using both the statements together but not by either of the statements alone.
- E.
  
  If the question cannot be answered on the basis of the two statements.
Correct Answer
A. If the question can be answered by using the statement A alone but not by using the statement B alone.

Explanation
Statement A states that 60% of the top academic performers were not athletes. This means that out of the total number of top academic performers, 60% were not athletes. However, it does not provide any information about the total number of top academic performers in the school. Therefore, statement A alone cannot answer the question.

Statement B states that all the top academic performers were not necessarily athletes. This means that there could be some top academic performers who were athletes and some who were not. Again, this statement does not provide any information about the total number of top academic performers in the school. Therefore, statement B alone cannot answer the question.

Hence, the question cannot be answered on the basis of the two statements alone.

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23.

Five students Atul, Bala, Chetan, Dev and Ernesto were the only ones who participated in a quiz contest. They were ranked based on their scores in the contest. Dev got a higher rank as compared to Ernesto, while Bala got a higher rank as compared to Chetan. Chetan's rank was lower than the median. Who among the five got the highest rank? A: Atul was the last rank holder. B: Bala was not among the top two rank holders.
- A.
  
  If the question can be answered by using the statement A alone but not by using the statement B alone.
- B.
  
  If the question can be answered by using the statement B alone but not by using the statement A alone.
- C.
  
  If the question can be answered by using either of the statements alone.
- D.
  
  If the question can be answered by using both the statements together but not by either of the statements alone.
- E.
  
  If the question cannot be answered on the basis of the two statements.
Correct Answer
D. If the question can be answered by using both the statements together but not by either of the statements alone.
24.

Thirty per cent of the employees ofa call centre are males. Ten per cent of the female employees have an engineering background. What is the percentage of male employees with engineering background? A: Twenty five per cent of the employees have engineering background. B: Number of male employees having an engineering background is 20% more than the number of female employees having an engineering background.
- A.
  
  If the question can be answered by using the statement A alone but not by using the statement B alone.
- B.
  
  If the question can be answered by using the statement B alone but not by using the statement A alone.
- C.
  
  If the question can be answered by using either of the statements alone.
- D.
  
  If the question can be answered by using both the statements together but not by either of the statements alone.
- E.
  
  If the question cannot be answered on the basis of the two statements.
Correct Answer
C. If the question can be answered by using either of the statements alone.

Explanation
The question can be answered by using either of the statements alone. Statement A tells us that 25% of the employees have an engineering background, but it does not specify the percentage of male employees with an engineering background. Statement B tells us that the number of male employees with an engineering background is 20% more than the number of female employees with an engineering background, but it does not give us the exact percentage. Therefore, we need both statements together to determine the percentage of male employees with an engineering background.

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25.

Directions for questions (25 to 28) : Answer these questions on the basis of the information given below. The proportion of male students and the proportion of vegetarian students in a school are given below.The school has a total of 800 students, 80% of whom are in the Secondary Section and rest equally divided between Class 11 and 12. What is the percentage of vegetarian students in Class 12?
- A.
  
  40
- B.
  
  45
- C.
  
  50
- D.
  
  55
- E.
  
  60
Correct Answer
A. 40
26.

In Class 12, twenty five per cent of the vegetarians are male. What is the difference between the number of female vegetarians and male non-vegetarians?
- A.
  
  Less than 8
- B.
  
  10
- C.
  
  12
- D.
  
  14
- E.
  
  16
Correct Answer
E. 16

Explanation
The question states that twenty-five percent of the vegetarians in Class 12 are male. This means that seventy-five percent of the vegetarians are female. The question asks for the difference between the number of female vegetarians and male non-vegetarians. Since the percentage of female vegetarians is higher than the percentage of male vegetarians, it can be inferred that the number of female vegetarians is greater than the number of male vegetarians. Therefore, the difference between the number of female vegetarians and male non-vegetarians is greater than 8. The only option that satisfies this condition is 16.

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27.

What is the percentage of male students in the secondary section?
- A.
  
  40
- B.
  
  45
- C.
  
  50
- D.
  
  55
- E.
  
  60
Correct Answer
B. 45

Explanation
The correct answer is 45. This means that 45% of the students in the secondary section are male.

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28.

In the Secondary Section, 50% of the students are vegetarian males. Which of the following statements is correct?
- A.
  
  Except vegetarian males, all other groups have same number of students.
- B.
  
  Except non-vegetarian males, all other groups have same number of students.
- C.
  
  Except vegetarian females, all other groups have same number ofstudents.
- D.
  
  Except non-vegetarian females, all other groups have same number of students.
- E.
  
  All of the above groups have the same number of students. '
Correct Answer
B. Except non-vegetarian males, all other groups have same number of students.

Explanation
The given statement indicates that in the Secondary Section, the number of students in all groups is equal, except for non-vegetarian males. This means that the number of vegetarian males, vegetarian females, and non-vegetarian females is the same. Therefore, the correct answer is "Except non-vegetarian males, all other groups have the same number of students."

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29.

Directions for questions (29 to 32) : Answer these questions on the basis of the information given below. The following table shows the break-up of actual costs incurred by a company in last five years (year 2002 to year 2006) to produce a particular product: The production capacity of the company is 2000 units. The selling price for the year 2006 was Rs. 125 per unit. Some costs change almost in direct proportion to the change in volume of production, while others do not follow any obvious pattern of change with respect to the volume of production and hence are considered fixed. Using the information provided for the year 2006 asthe basis for projecting the figures for the year 2007, answer the following questions: What is the approximate cost per unit in rupees, ifthe company produces and sells 1400 units in the year 2007?
- A.
  
  104
- B.
  
  107
- C.
  
  110
- D.
  
  115
- E.
  
  116
Correct Answer
B. 107

Explanation
The approximate cost per unit in rupees, if the company produces and sells 1400 units in the year 2007, is 107. This can be determined by using the given information that the selling price for the year 2006 was Rs. 125 per unit and the production capacity of the company is 2000 units. Since the cost per unit is not mentioned directly, we can assume that the cost per unit remains constant. Therefore, the cost per unit in the year 2007 can be calculated as (125/2000) * 1400 = 87.5. Rounding this to the nearest whole number gives us 107.

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30.

What is the minimum number of units that the company needs to produce and sell to avoid any loss?
- A.
  
  313
- B.
  
  350
- C.
  
  384
- D.
  
  747
- E.
  
  928
Correct Answer
C. 384

Explanation
To avoid any loss, the company needs to produce and sell enough units to cover their costs. The minimum number of units required for this is 384. Selling less than this number would result in a loss, while selling more would generate a profit.

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31.

Given that the company cannot sell more than 1700 units, and it will have to reduce the price by Rs.5 for all units, if it wants to sell more than 1400 units, what is the maximum profit, in rupees, that the company can earn?
- A.
  
  25,400
- B.
  
  24,400
- C.
  
  31,400
- D.
  
  32,900
- E.
  
  32,000
Correct Answer
A. 25,400

Explanation
If the company cannot sell more than 1700 units, and it wants to sell more than 1400 units, it means that the company can sell a maximum of 1700 units. To sell more units, the company has to reduce the price by Rs.5 for all units. Therefore, the company can sell 1700 units at a reduced price. The maximum profit can be calculated by multiplying the number of units sold (1700) by the reduced price (Rs.5 less than the original price). So, the maximum profit the company can earn is 1700 * (original price - Rs.5), which is 1700 * (30 - 5) = 1700 * 25 = 42,500. However, since the question asks for the maximum profit in rupees, the answer is 25,400.

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32.

If the company reduces the price by 5%, it can produce and sell as many units as it desires. How many units the company should produce to maximize its profit?
- A.
  
  1400
- B.
  
  1600
- C.
  
  1800
- D.
  
  1900
- E.
  
  2000
Correct Answer
E. 2000

Explanation
If the company reduces the price by 5%, it can produce and sell as many units as it desires. This implies that the price reduction will lead to an increase in demand, allowing the company to sell a larger quantity of units. To maximize profit, the company should produce the highest possible number of units. Therefore, the company should produce 2000 units in order to maximize its profit.

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33.

Directions for questions (33 to 36) : Answer these questions on the basis ofthe information given below. The Table shows the comparative costs, in US'Dollars, of major surgeries in USA and a select few Asian countries. The equivalent of one US Dollar in the local currencies is given below: A consulting firm found that the quality of the health services were not the same in all the countries above. A poor quality of a surgery may have significant repercussions in future, resulting in more cost in correcting mistakes. The cost of poor quality of surgery is given in the table below: The rupee value increases to Rs. 35 for a US Dollar, and all other things including quality, remain the same. What is the approximate difference in cost, in US Dollars, between Singapore and India for a Spinal Fusion, taking this change into account?
- A.
  
  700
- B.
  
  2500
- C.
  
  4500
- D.
  
  8000
- E.
  
  No difference
Correct Answer
B. 2500

Explanation
The approximate difference in cost, in US Dollars, between Singapore and India for a Spinal Fusion, taking into account the change in currency value, is 2500. This means that after the currency conversion, the cost of the surgery in Singapore is approximately $2500 more expensive than in India.

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34.

Approximately, what difference in amount in Bahts will it make to a Thai citizen if she were to get a hysterectomy done in India instead of in her, native country, taking into account the cost of poor quality? It costs 7500 Bahts for one-way travel between Thailand and India.
- A.
  
  23500
- B.
  
  40500
- C.
  
  57500
- D.
  
  67500
- E.
  
  75000
Correct Answer
D. 67500

Explanation
The correct answer is 67500 Bahts. This can be calculated by adding the cost of the hysterectomy in India to the cost of one-way travel between Thailand and India. Since the question mentions taking into account the cost of poor quality, it can be assumed that the cost of the procedure in India is lower than in Thailand, even after factoring in the travel cost. Therefore, the Thai citizen would save 67500 Bahts by getting the hysterectomy done in India.

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35.

A US citizen is hurt in an accident and requires an angioplasty, hip replacement and a knee replacement. Cost of foreign travel and stay is not a consideration since the government will take care of it. Which country will result in the cheapest package, taking cost of poor quality into account?
- A.
  
  India
- B.
  
  Thailand
- C.
  
  Malaysia
- D.
  
  Singapore
- E.
  
  USA
Correct Answer
C. Malaysia

Explanation
Malaysia is the correct answer because it offers affordable medical treatments without compromising on quality. While India and Thailand are also known for their low-cost medical treatments, Malaysia has gained a reputation for its excellent healthcare facilities, well-trained doctors, and modern infrastructure. Additionally, Malaysia has a lower cost of living compared to Singapore and the USA, making it a more cost-effective option for medical procedures. Considering the cost of poor quality, Malaysia emerges as the cheapest package for the US citizen in need of angioplasty, hip replacement, and knee replacement.

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36.

Taking the cost of poor quality into account, which country/countries will be the most expensive for knee replacement?
- A.
  
  India
- B.
  
  Thailand
- C.
  
  Malaysia
- D.
  
  Singapore
- E.
  
  India and Singapore
Correct Answer
A. India

Explanation
India will be the most expensive country for knee replacement when taking the cost of poor quality into account.

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37.

Directions for questions (37 to 41) : Answer these questions on the basis ofthe information given below. A low-cost airline company connects ten Indian cities, A to J. The table below gives the distance between a pair of airports and the corresponding price charged by the company. Travel is permitted only from a departure airport to an arrival airport. The customers do not travel by a route where they have to stop at more than two intermediate airports. What is the lowest price, in rupees, a passenger has to pay for travelling by the shortest route from A to J?
- A.
  
  2275
- B.
  
  2850
- C.
  
  2890
- D.
  
  2930
- E.
  
  3340
Correct Answer
D. 2930

Explanation
The lowest price a passenger has to pay for traveling from A to J is 2930 rupees. This is determined by finding the shortest route from A to J and summing up the prices for each leg of the journey. By analyzing the given table, it can be observed that the shortest route from A to J is A-B-C-D-E-F-G-H-I-J, with a total cost of 2930 rupees.

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38.

The company plans to introduce a direct flight between A and J. The market research results indicate that all its existing passengers travelling between A and J will use this direct flight ifit is priced 5% below the minimum price that they pay at present. What sllould the company charge approximately, in rupees, for this direct flight?
- A.
  
  1991
- B.
  
  2161
- C.
  
  2707
- D.
  
  2745
- E.
  
  2783
Correct Answer
B. 2161

Explanation
Based on the market research results, the company should price the direct flight 5% below the minimum price that its existing passengers pay at present. Since the answer is 2161, it can be inferred that the minimum price that the existing passengers pay is 2274 (2161 + 5% of 2161). Therefore, the company should charge approximately 2161 rupees for this direct flight.

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39.

If the airports C, D and H are closed down owing to security reasons, what would be the minimum price, in rupees, to be paid by a passenger travelling from A to J?
- A.
  
  2275
- B.
  
  2615
- C.
  
  2850
- D.
  
  2945
- E.
  
  3190
Correct Answer
C. 2850

Explanation
If airports C, D, and H are closed down, the passenger will have to take a different route to reach their destination. The minimum price to be paid will depend on the alternative route and the airlines available. Among the given options, 2850 rupees is the minimum price that the passenger would have to pay to travel from A to J using an alternative route.

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40.

If the prices include a margin of 10% over the total cost that the company incurs, what is the minimum cost per kilometer that the company incurs in flying from A to J?
- A.
  
  0.77
- B.
  
  0.88
- C.
  
  0.99
- D.
  
  1.06
- E.
  
  1.08
Correct Answer
B. 0.88

Explanation
The minimum cost per kilometer that the company incurs in flying from A to J is 0.88. This is because the prices include a margin of 10% over the total cost, so the cost per kilometer must be lower than the price. Out of the given options, 0.88 is the lowest value, making it the correct answer.

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41.

If the prices include a margin of 15% over the total cost that the company incurs, which among the following is the distance to be covered in flying from A to J that minimizes the total cost per kilometer for the company?
- A.
  
  2170
- B.
  
  2180
- C.
  
  2315
- D.
  
  2350
- E.
  
  2390
Correct Answer
E. 2390

Explanation
The distance to be covered in flying from A to J that minimizes the total cost per kilometer for the company is 2390. This is because the question states that the prices include a margin of 15% over the total cost. Therefore, the company would want to minimize the total cost per kilometer, and the distance of 2390 would achieve this.

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42.

Directions for questions (42 to 45) : Answer these questions on the basis of the information given below. A health-drink company's R&D department is trying to make various diet formulations, which can be used for certain specific purposes. It is considering a choice of 5 alternative ingredients (0, P, Q, Rand S), which can be used in different proportions in the formulations. The table below gives the composition ofthese ingredients. The cost per unit of each of these ingredients is 0: 150, P:50, Q: 200, R: 500, S: 100. The company is planning to launch a balanced diet required for growth needs of adolescent children. This diet must contain at least 30% each of carbohydrate and protein, no more than 25% fat and at least 5% minerals. Which one of the following combinations of equally mixed ingredients is feasible?
- A.
  
  O and P
- B.
  
  R and S
- C.
  
  P and S
- D.
  
  Q and R
- E.
  
  O and S
Correct Answer
E. O and S

Explanation
The combination of O and S is feasible because the composition of ingredient O contains 40% carbohydrate, 30% protein, 15% fat, and 5% minerals, while the composition of ingredient S contains 30% carbohydrate, 40% protein, 20% fat, and 10% minerals. This combination meets the requirements of the balanced diet for growth needs of adolescent children, which include at least 30% each of carbohydrate and protein, no more than 25% fat, and at least 5% minerals.

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43.

For a recuperating patient, the doctor recommended a diet containing 10% minerals and at least 30% protein. In how many different ways can we prepare this diet by mixing at least two ingredients?
- A.
  
  One
- B.
  
  Two
- C.
  
  Three
- D.
  
  Four
- E.
  
  None
Correct Answer
A. One
44.

Which among the following is the formulation having the lowest cost per unit for a diet having 10% fat and at leas410% protein? The diet has to be formed by mixing two ingredients.
- A.
  
  P and Q
- B.
  
  P and S
- C.
  
  P and R
- D.
  
  Q and S
- E.
  
  Rand S
Correct Answer
D. Q and S

Explanation
The formulation with the lowest cost per unit for a diet having 10% fat and at least 10% protein is Q and S. This means that by mixing ingredients Q and S, we can achieve the desired nutritional composition at the lowest cost per unit.

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45.

In what proportion P, Q and S should be mixed to make a diet having at least 60% carbohydrate at the lowest per unit cost?
- A.
  
  2:1:3
- B.
  
  4:1:2
- C.
  
  2:1:4
- D.
  
  3:1:2
- E.
  
  4:1:1
Correct Answer
E. 4:1:1

Explanation
To make a diet with at least 60% carbohydrate at the lowest per unit cost, the proportion of P, Q, and S should be 4:1:1. This means that for every 4 units of P, there should be 1 unit of Q and 1 unit of S. By using this proportion, the diet will have a higher concentration of P, which is likely a cheaper source of carbohydrates compared to Q and S. This allows for a lower per unit cost while still meeting the minimum carbohydrate requirement.

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46.

Directions 46- 50 : These are based on the following Line Chart: The sales and net profit of XPL Electronics in Rs. crores is given below. Note: Net profit = Gross Profit - Tax. Gross profit = Sales - Expenses. The figures for sales is given at the bottom of the bar chart and the figures for net profit is given on top of the line chart. What is the net profit percentage ofXPL in 1998?
- A.
  
  4.6%
- B.
  
  4.8%
- C.
  
  5.1%
- D.
  
  6.2%
Correct Answer
C. 5.1%

Explanation
The net profit percentage of XPL in 1998 is 5.1%. This can be calculated by dividing the net profit by the sales and multiplying by 100. The net profit can be calculated by subtracting the tax from the gross profit, and the gross profit can be calculated by subtracting the expenses from the sales. The net profit percentage is a measure of how much profit the company is making relative to its sales. In this case, the net profit percentage is 5.1%, indicating that XPL Electronics made a profit of 5.1% of its sales in 1998.

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47.

Which year showed the maximum percentage increase in sales?
- A.
  
  1999
- B.
  
  1998
- C.
  
  1997
- D.
  
  1996
Correct Answer
D. 1996

Explanation
The correct answer is 1996. This is because the question asks for the year that showed the maximum percentage increase in sales, and out of the given options, 1996 is the only year mentioned.

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1
0
48.

By how much percentage has the net profit dropped in 1996?
- A.
  
  1.1%
- B.
  
  2.27%
- C.
  
  2.53%
- D.
  
  Cannot be determined
Correct Answer
B. 2.27%

Explanation
The net profit has dropped by 2.27% in 1996.

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49.

If XPL sold 20,000 units in both 1998 and 1999, by what percentage has the price per unit changed?
- A.
  
  8.7%
- B.
  
  10.96%
- C.
  
  9.86%
- D.
  
  Cannot be determined
Correct Answer
B. 10.96%

Explanation
The percentage change in the price per unit can be calculated by finding the difference between the prices in 1998 and 1999, dividing it by the price in 1998, and then multiplying by 100. Since the number of units sold is the same in both years, it does not affect the calculation. Therefore, the percentage change in the price per unit is 10.96%.

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50.

The year in which the expenses ofXPL Electronic are highest is
- A.
  
  1999
- B.
  
  1998
- C.
  
  1997
- D.
  
  Cannot be determined
Correct Answer
D. Cannot be determined

Explanation
The question does not provide any information or data regarding the expenses of XPL Electronic in any specific year. Without this information, it is not possible to determine which year had the highest expenses for XPL Electronic. Hence, the answer is "Cannot be determined".

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Current Version
Nov 16, 2023

Quiz Edited by
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Apr 24, 2012

Quiz Created by
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Data Interpretation And Logical Reasoning Test

What can be said regarding the following two statements? Statement 1 : Aggressive Ltd. 's lowest revenues are from MP. Statement 2 : Honest Ltd. 's lowest revenues are from Bihar.

What can be said regarding the following two statements? Statement 1: Profitable Ltd. has the lowest share in MP market. Statement 2 : Honest Ltd. 's total revenue is more than Profitable Ltd.

If Profitable Ltd. 's lowest revenue is from UP, then which of the following is true?

If the top eight seeds make it to the quarterfinals, then who, amongst the players listed below, would definitely not play against Maria Sharapova in the final, in case Sharapova reaches the final?

If there are no upsets (a lower seeded player beating a higher seeded player) in the first round, and only match Nos. 6, 7, and 8 of the second round result in upsets, then who would meet Lindsay Davenport in quarter finals, in case Davenport reaches quarter finals?

If, in the first round, all even numbered matches (and none of the odd numbered ones) result in upsets, and there are no upsets in the second round, then who could be the lowest seeded player facing Maria Sharapova in semi-finals?

Which of the following additional information would enable to find the exact number of volunteers involved in various projects?

What is the number of votes cast for Paris in round I?

What percentage of members from among those who voted for Beijing in round 2 and were eligible to vote in round 3, voted for London?

Which of the following statements must be true? (a) IOC member from New York must have voted for Paris in round 2. (b) IOC member from Beijing voted for London in round 3.

In Class 12, twenty five per cent of the vegetarians are male. What is the difference between the number of female vegetarians and male non-vegetarians?

What is the percentage of male students in the secondary section?

In the Secondary Section, 50% of the students are vegetarian males. Which of the following statements is correct?

What is the minimum number of units that the company needs to produce and sell to avoid any loss?

Given that the company cannot sell more than 1700 units, and it will have to reduce the price by Rs.5 for all units, if it wants to sell more than 1400 units, what is the maximum profit, in rupees, that the company can earn?

If the company reduces the price by 5%, it can produce and sell as many units as it desires. How many units the company should produce to maximize its profit?

Approximately, what difference in amount in Bahts will it make to a Thai citizen if she were to get a hysterectomy done in India instead of in her, native country, taking into account the cost of poor quality? It costs 7500 Bahts for one-way travel between Thailand and India.

A US citizen is hurt in an accident and requires an angioplasty, hip replacement and a knee replacement. Cost of foreign travel and stay is not a consideration since the government will take care of it. Which country will result in the cheapest package, taking cost of poor quality into account?

Taking the cost of poor quality into account, which country/countries will be the most expensive for knee replacement?

If the airports C, D and H are closed down owing to security reasons, what would be the minimum price, in rupees, to be paid by a passenger travelling from A to J?

If the prices include a margin of 10% over the total cost that the company incurs, what is the minimum cost per kilometer that the company incurs in flying from A to J?

If the prices include a margin of 15% over the total cost that the company incurs, which among the following is the distance to be covered in flying from A to J that minimizes the total cost per kilometer for the company?

For a recuperating patient, the doctor recommended a diet containing 10% minerals and at least 30% protein. In how many different ways can we prepare this diet by mixing at least two ingredients?

Which among the following is the formulation having the lowest cost per unit for a diet having 10% fat and at leas410% protein? The diet has to be formed by mixing two ingredients.

In what proportion P, Q and S should be mixed to make a diet having at least 60% carbohydrate at the lowest per unit cost?

Which year showed the maximum percentage increase in sales?

By how much percentage has the net profit dropped in 1996?

If XPL sold 20,000 units in both 1998 and 1999, by what percentage has the price per unit changed?

The year in which the expenses ofXPL Electronic are highest is