Previous CAT Questions - Solved (Logical Reasoning) - Set 3


  • Skadoooosh!!!


    (CAT 2001)
    A King has unflinching loyalty from eight of his ministers M1 to M8, but he has to select only four to make a cabinet committee. He decides to choose these four such that each selected person shares a liking with at least one of the other three selected. The selected persons must also hate at least one of the likings of any of the other three persons selected. M1 likes fishing and smoking, but hates gambling. M2 likes smoking and drinking, but hates fishing. M3 likes gambling, but hates smoking. M4 likes mountaineering, but hates drinking. M5 likes drinking, but hates smoking and mountaineering. M6 likes fishing, but hates smoking and mountaineering. M7 likes gambling and mountaineering, but hates fishing, and M8 likes smoking and gambling, but hates mountaineering. Who are the four people selected by the king?
    (a) M1, M2, M5, M6
    (b) M3, M4, M5, M6
    (c) M4, M5, M6, M8
    (d) M1, M2, M4, M7

    Use tabular method, it will be easy and less time consuming.

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    Now, instead of forming your combination with the table, check with the given options. That will, again, save a lot of time, especially, in problems like this. Here, we observe that option a, b and c will not work out with the condition given. (Person should have 1 common like with any of the other 3, and should hate one thing liked by any other 3).
    Hence the correct option will be d.

    (CAT 2001)
    In a “keep-fit” gymnasium class there are fifteen females enrolled in a weight-loss program. They all have been grouped in any one of the five weight-groups W1, W2, W3, W4, or W5. One instructor is assigned to one weight-group only. Sonali, Shalini, Shubhra, and Shahira belong to the same weight-group. Sonali and Rupa are in one weight-group, Rupali and Renuka are also in one weight-group. Rupa, Radha, Renuka, Ruchika, and Ritu belong to different weight-groups. Somya cannot be with Ritu, and Tara cannot be with Radha. Komal cannot be with Radha, Somya, or Ritu. Shahira is in W1 and Somya is in W4 with Ruchika. Sweta and Jyotika cannot be with Rupali, but are in a weight-group with total membership of four. No weight-group can have more than five or less than one member. Amita, Babita, Chandrika, Deepika, and Elina are instructors of weightgroups with membership sizes 5, 4, 3, 2 and 1, respectively. Who is the instructor of Radha?
    (a) Babita
    (b) Elina
    (c) Chandrika
    (d) Deepika

    Read the question fully, first fill up the given “fixed” details. Then start filling up the rest.
    Sonali, Shalini, Shubhra, Shahira , Rupa - W1 – Amita
    Rupali, Renuka
    Radha
    Ruchika, Somya – W4
    Ritu

    Now, to the confusing “multi” details. Sweta and Jyotika are not with Rupali, but are in a weight group with 4 members. So they are with Ruchika and Somya. So the list becomes:
    Sonali, Shalini, Shubhra, Shahira , Rupa - W1 – Amita
    Rupali, Renuka
    Radha
    Ruchika, Somya, Sweta, Jyotika – W4 - Babita
    Ritu

    Komal cannot be with Radha, Somya or Ritu. So she is with Rupali and Renuka. Tara cannot be with Radha, hence she is with Ritu (since all the other group, maximum number has been reached).
    So the final list we have is:
    Sonali, Shalini, Shubhra, Shahira , Rupa - W1 – Amita
    Rupali, Renuka, Komal - Chandrika
    Radha - Elina
    Ruchika, Somya, Sweta, Jyotika – W4 - Babita
    Ritu, Tara - Deepika

    (CAT 2001)
    A group of three or four has to be selected from seven persons. Among the seven are two women, Fiza and Kavita, and five men: Ram, Shyam, David, Peter and Rahim. Ram would not like to be in the group if Shyam is also selected. Shyam and Rahim want to be selected together in the group. Kavita would like to be in the group only if David is also there. David, if selected, would not like Peter in the group. Ram would like to be in the group only if Peter is also there. David insists that Fiza be selected in case he is there in the group.

    Q1) Which of the following statements is true?
    (a) Kavita and Ram can be part of a group of four.
    (b) A group of four can have two women.
    (c) A group of four can have all four men.
    (d) None of the above.

    Q2) Which of the following is a feasible group of four?
    (a) Ram, Peter, Fiza, Rahim
    (b) Shyam, Rahim, Kavita, David
    (c) Shyam, Rahim, Fiza, David
    (d) Fiza, David, Ram, Peter

    Q3) Which of the following is a feasible group of three?
    (a) David, Ram, Rahim
    (b) Peter, Shyam, Rahim
    (c) Kavita, David, Shyam
    (d) Fiza, David, Ram

    Read all the questions belonging to the category. Here, for instance, the 1st 2 questions are based on a group of 4. So, it will be better to find out the group of 4, as a part of 2nd question, rather than doing the 1st one initially.

    Again, use the “reverse” tracking method for Q2. Check out the options, which will be less time consuming here.
    For the 1st option, Rahim and Shyam need to be together. hence can be ruled out.
    2nd option can be ruled out as David will be there only if Fiza will be there.
    3rd option is fine. (Ideally, you can stop here, and proceed to the next question)
    4th option can be ruled out as David and Peter cannot be together. Hence the group will be Shyam, Rahim, Fiza, David.

    From the above solution, we got the only feasible group.
    Hence for Q1 solution is none of the above.
    For the more curious ones, let us solve it.
    Kavita and Ram cannot be part of group of 4, as Kavita needs David, and David needs Fiza, Ram needs Peter.
    2 women – Kavita and Fiza together. Kavita needs David, David needs Fiza. So 3 are fine. Now who will be the other one? Ram is not possible, as Ram needs Peter. Peter is not possible, as David cannot be with Peter. Shyam and Rahim are always together.
    A group of 4 cannot have all men. David cannot be with Peter, and Ram cannot be with Shyam, and Ram needs to be with Peter. Hence no group of 4 can be formed with all boys.

    Q3 can be solved with reverse tracking again.
    Ram needs Peter, option 1 can be ruled out.
    Option 2 is fine. (Ideally, you can stop here, and proceed to the next question)
    Davind needs Fiza. Option 3 ruled out.
    Ram needs Peter, option 4 can be ruled out.

    (CAT 2001)
    Elle is three times older than Yogesh
    Zaheer is half the age of Wahida
    Yogesh is older than Zaheer.

    Q1) Which of the following information will be sufficient to estimate Elle’s age?
    (a) Zaheer is 10 years old.
    (b) Both Yogesh and Wahida are older than Zaheer by the same number of years.
    (c) Both (a) and (b) above.
    (d) None of the above.

    Q2) Which of the following can be inferred?
    (a) Yogesh is older than Wahida.
    (b) Elle is older than Wahida.
    (c) Elle may be younger than Wahida.
    (d) None of the above.

    Zaheer’s age = z, similarly for others.
    We know, e = 3y, w = 2z, y > z.

    Q1, we check the options.
    From option 1 alone, we know z and we can calculate w, but not y and e.
    From option 2 alone, we know y and w are of same age, but do not know the numeric quantity.
    From option 3, we know z = 10, w = 20, y = 20, e = 60. So, we can calculate Elle’s age.
    From option 3, we can calculate.

    Again for Q2, check the options.
    We cannot know if y > w or not.
    y > w. w = 2z and e = 3y. y is atleast z+1.
    3y is minimum 3 *(z + 1), 3z + 3, which definitely more than 2z.
    Hence e > w. So option b is right.
    Elle cannot be younger than Wahida from option b.
    Option 4 can be ruled out as option 2 is right.

    (CAT 2001)
    At a village mela, the following six nautankis (plays) are schedule as shown in the table below:

    NautankiDurationShow times
    Sati Savitri1 hour9.00 am and 2.00 pm
    Joru ka Gulam1 hour10.30 am and 11.30 am
    Sunder Kand30 minutes10.00 am and 11.00 am
    Veer Abhimanyu1 hour10.00 am and 11.00 am
    Reshma aur Shera1 hour9.30 am, 12.00 noon and 2.00 pm
    Jhansi ki Rani30 minutes11.00 am and 1.30 pm

    You wish to see all the six nautankis.
    Further you wish to ensure that you get a lunch break from 12.30 p.m. to 1.30 p.m.
    Which of the following ways can you do this?
    (a) Sati-Savitri is viewed first; Sunder Kand is viewed third and Jhansi ki Rani is viewed last.
    (b) Sati-Savitri is viewed last; Sunder Kand is viewed third and Jhansi ki Rani is viewed last.
    (c) Sati-Savitri is viewed first; Sunder Kand is viewed third and Joru ka Gulam is viewed fourth.
    (d) Veer Abhimanyu is viewed third; Reshma aur Shera is viewed fourth and Jhansi ki Rani is viewed fifth.

    Sati Savitri is the only programme to start at 9am, hence it shall be viewed first, from 9 – 10.
    There are 2 programmes at 10, VA and SK. If we choose SK, it is till 10:30, and JKG is from 10:30 to 11:30. However, no programmes start at 11:30. Hence 11:30 – 1:30 , there shall be no programs. This cannot cover all the programmes.
    Hence, select VA at 10 – 11. At 11, the option left is S.K. till 11:30, and at 11:30, we have JKG till 12:30. 12:30 – 1:30 will be break. JKR at 1:30 – 2, and RAS from 2 – 3.
    Hence, the order will be SS, VA, SK, JKG, JKR, RAS.


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