Logical Reasoning previous years questions (CAT) - Set 0009


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    Previous years`s CAT questions: Logical Reasoning

    Post your solutions as reply to respective questions below.


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    Question 1

    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 IOC with each member representing a different city. All the four cities in contention are also represented in IOC.

    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 favor, and the total votes that were cast in those rounds.  

     

    Round

    Total votes cast

    Maximum votes cast

    Eliminated

     

     

    City

    No: of votes

    City

    No: of votes

    1

     

    London

    30

    New York

            12

    2

    83

    Paris

    32

    Beijing

            21

    3

    75

     

     

     

     

     

    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 1, voted for Beijing in round 2 as well.

    Those who voted for New York in round 1, voted either for Beijing or Paris in round 2.

    The difference in votes cast for the two contending cities in the last round was 1.

    50% of those who voted for Beijing in round 1, voted for Paris in round 3.

    1) What  %  of members from among those who voted for New York in round I, voted for Beijing in round 2?

    (1) 33.33    (2) 50     (3) 66.67     (4) 75              

    2) What is the number of votes cast for Paris in round 1?

    (1) 16     (2) 18     (3) 22     (4) 24              

    3) 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?

    (1) 33.33     (2) 38.10       (3) 50        (4) 66.67         

    4) 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.

    (1) Only a
    (2) Only b

    (3) Both a and b
    (4) Neither a nor b          (CAT 2005)


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    Question 2

    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.

    States

    Firm A

    Firm B

    Firm C

    Firm D

    UP

    49

    82

    80

    55

    Bihar

    69

    72

    70

    65

    MP

    72

    63

    72

    65

    Further, it is known that:

    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.

    1) 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.

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

    (3) Both Statement 1 and Statement 2 are true.
    (4) Neither Statement 1 nor Statement 2 is true.          

    2) 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.

    (1) If Statement 2 is true then Statement 1 is necessarily false.
    (2) If Statement 1 is false then Statement 2 is necessarily true.
    (3) If Statement 1 is true then Statement 2 is necessarily true.
    (4) None of the above.           

    3) 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.

    (1) Both statements could be true.
    (2) At least one of the statements must be true.
    (3) At most one of the statements is true.
    (4) None of the above            

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

    (1) Truthful Ltd.’s lowest revenues are from MP.
    (2) Truthful Ltd.’s lowest revenues are from Bihar.
    (3) Truthful Ltd.’s lowest revenues are from UP.
    (4) No definite conclusion is possible.          (CAT 2005)


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    Question 3

    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.

    1) 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:

    (1) 1                (2) 3               (3) 4               (4) 5                

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

    (1) Twenty volunteers are involved in FR.
    (2) Four volunteers are involved in all the three projects.

    (3) Twenty three volunteers are involved in exactly one project.
    (4) No need for any additional information.         

    3) 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 of the 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?

    (1) The lowest number of volunteers is now in TR project.
    (2) More volunteers are now in FR project as compared to ER project.
    (3) More volunteers are now in TR project as compared to ER project.
    (4) None of the above            

    4) After the withdrawal of volunteers, as indicated in Question 3, some new volunteers joined the NGO. Each one of them 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?

    (1) ER       (2) FR        (3) TR        (4) Cannot be determined       (CAT 2005)


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    Question 4

    Mathematicians are assigned a number called Erdös number, (named after the famous mathematician, Paul Erdös). Only Paul Erdös himself has an Erdös number of zero. Any mathematician who has written a research paper with Erdös has an Erdös number of 1. For other mathematicians, the calculation of his/her Erdös number is illustrated below: Suppose that a mathematician X has co-authored papers with several other mathematicians. From among them, mathematician Y has the smallest Erdös number. Let the Erdös number of Y be y. Then X has an Erdös number of y + 1. Hence any mathematician with no co-authorship chain connected to Erdös has an Erdös number of infinity.    

    In a seven day long mini-conference organized in memory of Paul Erdös, a close group of eight mathematicians, call them A, B, C, D, E, F, G and H, discussed some research problems. At the beginning of the conference, A was the only participant who had an infinite Erdös number. Nobody had an Erdös number less than that of F.

    On the third day of the conference F co-authored a paper jointly with A and C. This reduced the average Erdös number of the group of eight mathematicians to 3. The Erdös numbers of B, D, E, G and H remained unchanged with the writing of this paper. Further, no other co-authorship among any three members would have reduced the average Erdös number of the group of eight to as low as 3.

    At the end of the third day, five members of this group had identical Erdös numbers while the other three had Erdös numbers distinct from each other.

    On the fifth day, E co-authored a paper with F which reduced the group‘s average Erdös number by 0.5. The Erdös numbers of the remaining six were unchanged with the writing of this paper.

    No other paper was written during the conference.          

    1) The person having the largest Erdös number at the end of the conference must have had Erdös number (at that time):

    (1) 5                (2) 7                (3) 9                (4) 14              (5) 15              

    2) How many participants in the conference did not change their Erdös number during the conference?

    (1) 2                (2) 3                (3) 4                (4) 5              (5) Cannot be determined                

    3) The Erdös number of C at the end of the conference was:

    (1) 1                (2) 2               (3) 3                 (4) 4                      (5) 5                

    4) The Erdös number of E at the beginning of the conference was:

    (1) 2                (2) 5                 (3) 6                 (4) 7                         (5) 8                

    5) How many participants had the same Erdös number at the beginning of the conference?

    (1) 2                (2) 3                 (3) 4                 (4) 5                 (5) Cannot be determined        

    (CAT 2006)


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    Question 5

    Two traders, Chetan and Michael, were involved in the buying and selling of MCS shares over five trading days. At the beginning of the first day, the MCS share was priced at Rs 100, while at the end of the fifth day it was priced at Rs 110. At the end of each day, the MCS share price either went up by Rs 10, or else, it came down by Rs 10. Both Chetan and Michael took buying and selling decisions at the end of each trading day. The beginning price of MCS share on a given day was the same as the ending price of the previous day. Chetan and Michael started with the same number of shares and amount of cash, and had enough of both. Below are some additional facts about how Chetan and Michael traded over the five trading days.       

    Each day if the price went up, Chetan sold 10 shares of MCS at the closing price. On the other hand, each day if the price went down, he bought 10 shares at the closing price.

    If on any day, the closing price was above Rs 110, then Michael sold 10 shares of MCS, while if it was below Rs 90, he bought 10 shares, all at the closing price. 

    1) If Chetan sold 10 shares of MCS on three consecutive days, while Michael sold 10 shares only once during the five days, what was the price of MCS at the end of day 3?

    (1) Rs 90     (2) Rs 100      (3) Rs 110       (4) Rs 120       (5) Rs 130               

    2) If Michael ended up with Rs 100 less cash than Chetan at the end of day 5, what was the difference in the number of shares possessed by Michael and Chetan (at the end of day 5)?

    (1) Michael had 10 less shares than Chetan.
    (2) Michael had10 more shares than Chetan.

    (3) Chetan had 10 more shares than Michael.
    (4) Chetan had 20 more shares than Michael.
    (5) Both had the same number of shares.           

    3) If Chetan ended up with Rs 1300 more cash than Michael at the end of day 5, what was the price of MCS share at the end of day 4?

    (1) Rs 90      (2) Rs 100      (3) Rs 110      (4) Rs 120    (5) Not uniquely determinable

    4) What could have been the maximum possible increase in combined cash balance of Chetan and Michael at the end of the fifth day?

    (1) Rs 3700    (2) Rs 4000    (3) Rs 4700    (4) Rs 5000     (5) Rs 6000             

    5) If Michael ended up with 20 more shares than Chetan at the end of day 5, what was the price of the share at the end of day 3?

    (1) Rs 90    (2) Rs 100     (3) Rs 110     (4) Rs 120       (5) Rs 130    (CAT 2006)          


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