Previous CAT Questions - Solved (Logical Reasoning) - Set 6

  • (CAT 2002)
    A country has the following types of traffic signals.
    3 red lights = stop;
    2 red lights = turn left;
    1 red light = turn right;
    3 green lights = go at 100 kmph speed;
    2 green lights = go at 40 kmph speed;
    1 green light = go at 20 kmph speed.

    A motorist starts at a point on a road and follows all traffic signals literally. His car is heading towards the north. He encounters the following signals (the time mentioned in each case below is applicable after crossing the previous signal)

    Starting Point – 1 green light;
    After half an hour, 1st signal –2 red & 2 green lights;
    After 15 minutes, 2nd signal –1 red light;
    After half an hour, 3rd signal –1 red & 3 green lights;
    After 24 minutes, 4th signal –2 red & 2 green 1ight
    After 15 minutes, 5th signal –3 red lights;

    Q1) The total distance traveled by the motorist from the starting point till the last signal is:
    a. 90km.
    b. 100km.
    c. 120km.
    d. none of these

    Q2) What is the position (radial distance) of the motorist when he reaches the last signal:
    a. 45km directly north of Starting Point.
    b. 30 km directly to the east of the Starting Point.
    c. 50 km. away to the northeast of the Starting Point.
    d. 45 km away to the northwest of the Starting Point.

    Q3) After the starting point if the 1st signal were 1 red and 2 green lights, what would be the final position of the motorist:
    a. 30 km to the west and 20 km to the south.
    b. 30 km to the west and 40 km to the north.
    c. 50 km to the east and 40 km to the north.
    d. Directly 30 km to the east.

    Q4) If at the starting point, the car was heading towards south, what would be the final position motorist?
    a. 30 km to the east and 40 km to the south.
    b. 50 km to the east and 40 km to the south.
    c. 30 km to the west and 40 km to the south.
    d. 50 km to the west and 20 km to the north.

    Approach such questions, diagrammatically.

    Starting point – 1 green light – 20kmph for half hour – 10km. (Heading north – given)
    2R and 2G – left, 40kmph – 15 mins – 10km total.
    1R – turn right, 40kmph – 30mins = 20km total.
    1R, 3G – turn right, 100kmph – 24mins = 40km total
    2R, 2G – turn left, 40kmph – 15 mins = 10km total.


    So, total 90kms.

    For Q#2,

    Radial distance = hypotenuse of the triangle, = 50


    For Q#3, diagram will look like below: So, 30km west, 20km south


    For Q#4 diagram will look like below: So, 40km South, 30 km west.


    Four families decided to attend the marriage ceremony of one of their colleagues. One family has no kids, while the others have at least one kid each. Each family with kids has at least one kid attending the marriage. Given below is some information about the families, and who reached when to attend the marriage.
    The family with 2 kids came just before the family with no kids.
    Shanthi who does not have any kids reached just before Sridevi's family.
    Sunil and his wife reached last with their only kid.
    Anil is not the husband of Joya.
    Anil and Raj are fathers.
    Sridevi's and Anita's daughters go to the same school.
    Joya came before Shanthi and met Anita when she reached the venue.
    Raman stays the farthest from the venue.
    Raj said his son could not come because of his exams

    Q1) Which women arrived third?
    a. Shanthi
    b. Sridevi
    c. Anita
    d. Joya

    Q2) Name the correct pair of husband and wife?
    a. Raj and Shanthi
    b. Sunil and Sridevi
    c. Anil and Sridevi
    d. Raj and Anita

    Q3) Of the following pairs, whose daughters go to the same school?
    a. Anil and Raman
    b. Sunil and Raman
    c. Sunil and Anil
    d. Raj and Anil

    Q4) Whose family is known to have more than one kid for certain?
    a. Raman's
    b. Raj's
    c. Anil's
    d. Sunil's

    Read the question fully, thoroughly; eliminate details not required, like Raman stays farthest in this question. Take details 1 by 1. i.e. 1st the name, then the time of arrival, then kids etc etc. Don’t do everything together, as it will be confusing, and will take more time. Form a table with the fixed given details first, and then fill up the table later with the “not-so-easy” clues.

    Shanthi arrived before Sridevi, Joya before Shanthi, so they are 3 separate families.

    Sridevi & Anita’s daughters go to same school. Hence Sridevi & Anita are in different families.

    Shanthi has no kids, but Anita has atleast 1, so Shanti and Anita are also from different families.

    Joya met Anita when she came for party. So Joya and Anita are also different families.

    Hence the 4 families are

    Shanthi and spouse / Sridevi and spouse / Anita and spouse / Joya and spouse


    It says: (Time to reach party set of clues)

    Shanthi came before Sridevi (Clue 1)

    Joya before Shanthi (Clue 7)

    Joya met Anita (Clue 7), so Anita came before Joya.

    So Anita came 1st, then Joya, then Shanthi, and then Sridevi.

    It says : (No: of kids clue)

    Shanthi has no kids.

    Family with 2 kids just came before Shanthi. That means Joya has 2 kids.
    It says : (Matching husbands)

    Sunil and his wife reached last. So Sunil is Sridevi’s husband.

    Anil and Raj are fathers, so Raman is Shanthi’s husband.


    Anil is not the husband of Joya, so Anil is husband of Anita.

    All the questions can be answered now.

    (CAT 2003)
    The plan above shows an office block for six officers, A, B, C, D, E, and F. Both Band C occupies officers to the right of the corridor (as one enters the officer block) and A occupies an officer to the left of the corridor. E and F occupy offices on opposite sides of the corridor but their offices do not face each other. The offices of C and D face each other. E does not have a corner office. F’s office is further down the corridor than A’s but on the same side.


    Q1) If E sits in his office and faces the corridor, whose office is to his left?
    a. A
    b. B
    c. C
    d. D

    Q2) Whose office faces A’s office?
    a. B
    b. C
    c. D
    d. E

    Q3) Who is/ are F’s neighbors (s)?
    a. A only
    b. A and D
    c. C only
    d. B and C

    Q4) D was heard telling someone to go further down the corridor to the last office on the right. To whose room was he trying to direct that person?
    a. A
    b. B
    c. C
    d. F

    We will have to find out which all offices are in left and which in the right:

    B&C are in right.

    A in left.

    F on same side of A, so F in left.

    E opposite side of F, so E in right.

    So B, C, E in right, A,F,D in left.

    Now position them:

    E is in middle (as he is not in corner)

    E does not face F, and C faces D. So E has to face A.

    F is further down A, so F is the last left seat, and hence D is the 1st left seat.

    C faces D, hence C is the 1st right seat, and hence B is the last right seat.


    All the questions can be answered now.

    (CAT 2003)
    Seven faculty members at a management institute frequent a lounge for strong coffee and stimulating conversation. On being asked about their visit to the lounge last Friday we got the following responses.

    JC: I came in first, and the next two persons to enter were SS and SM. When I left the lounge, JP and VR were present in the lounge. DG left with me.
    JP: When I entered the lounge with VR, JC was sitting there. There was someone else, but I cannot remember who it was.
    SM: I went to the lounge for a short while, and met JC, SS, and DG in the lounge that day.
    SS: I left immediately after SM left.
    DG: I met JC, SS, SM, JP, and VR during my first visit to the lounge. I went back to my office with JC. When I went to the lounge the second time, JP and VR were there.
    PK: I had some urgent work, so I did not sit in the lounge that day, but just collected my coffee and left, JP and DG were the only people in the lounge while I was there.
    VR: No comments.

    Q1) Based on the responses, which of the two, JP or DG, entered the lounge first?
    a. JP
    b. DG
    c. Both entered together.
    d. Cannot be deduced.

    Q2) Who was sitting with JC when JP entered the lounge?
    a. SS
    b. SM
    c. DG
    d. PK

    Q3) How many of the seven members did VR meet on Friday in the lounge?
    a. 2
    b. 3
    c. 4
    d. 5

    Q4) Who were the last two faculty members to leave the lounge?
    a. JC and DG
    b. PK and DG
    c. JP and PK
    d. JP and DG

    JC came in 1st, then SS and SM.

    SM met JC, SS and DG, and then SM left. So DG came in before SM left.

    SM left, immediately SS left. Now, we have JC and DG in the lounge.

    JP and VR come in now, because they see JC and “someone else”. JP sees JC, and the “unknown” person is DG, along with JC.

    Now, all the people that JC says that he saw are covered, JC and DG goes back.

    When DG comes for 2nd time, he sees JP and VR. So, he comes in next.

    When PK comes in and goes back, he sees JP and DG. That means VR has left before PK comes in. PK goes back immediately.

    So, diagrammatically,

    JC -----comes in------>
    SS, SM -----comes in------>
    DG ----- comes in ------>
    < ----goes out ----- SM
    < ----goes out ----- SS
    JP, VR -----comes in------>
    < ----goes out ----- JC, DG
    DG -----comes in------>
    < ----goes out ----- VR
    PK -----comes in------>
    < ----goes out ----- PK
    < ----goes out ----- JP, DG

    All the questions can be answered now. :smiley:

    (CAT 2003)
    Recently, the answers of a test held nationwide were leaked to a group of unscrupulous people. The investigative agency has arrested the mastermind and nine other people A, B, C, D, E, F, G, H, and I in this matter. Interrogating them, the following facts have been obtained regarding their operation. Initially the mastermind obtains the correct answer-key. All the others create their answer-keys in the following manner. They obtain the answer key from one or two people who already possess the same. These people are called his/her "sources". If the person has two sources, then he/she compares the answer keys obtained from both sources. If the key to a question from both sources is identical, it is copied, otherwise it is left blank. If the person has only one source, he/she copies the source's answers into his/her copy. Finally, each person compulsorily replaces one of the answers (not a blank one) with a wrong answer in his/her answer key. The paper contained 200 questions; so the investigative agency has ruled out the possibility of two or more of them introducing wrong answers to the same question. The investigative agency has a copy of the correct answer key and has tabulated the following data. These data represent question numbers.

    NameWrong AnswersBlank Answers

    Q1) Which one among the following must have two sources?
    a. A
    b. B
    c. C
    d. D

    Q2) How many people (excluding the mastermind) needed to make answer-keys before C could make his answer-key?
    a. 2
    b. 3
    c. 4
    d. 5

    Q3) Both G and H were sources to
    a. F
    b. B
    c. 1
    d. None of the nine

    Q4) Which of the following statements is true?
    a. C introduced the wrong answer to question 27.
    b. E introduced the wrong answer to question 46.
    c. F introduced the wrong answer to question 14.
    d. H introduced the wrong answer to question 46.

    Q5) Which of the following two groups of people had identical sources?
    (1) A, D and G
    (2) E and H
    a. Only (1)
    b. Only (2)
    c. Neither (1) nor (2)
    d. Both (1) and (2)

    Read the question fully, and thoroughly, and understand well, as the question is big and little confusing. Start from the lowest possible “wrong Answer” made, in this case A, D and G, as they have only 1 wrong answer. Then go to the next highest and so on. So,

    A has only 1 wrong answer. So he induced that wrong answer, which is 46.

    D has only 1 wrong answer. So he induced that wrong answer, which is 17.

    G has only 1 wrong answer. So he induced that wrong answer, which is 25.

    E - 2 wrong answers in which one is 46. So A is the source of E. E introduced wrong answer 90.

    H -2 wrong answers in which 1 is 46. So A is the source of H. H introduced wrong answer 92.

    B – 3 blank answers which are 46, 25, and 90. So B has confusion related to these answers. Since he is confused with 46 and 25, obviously he has A and G as sources. A has 46 wrong, and 25 right, and G vice-versa. Additionally he is confused with the answer 90, which was introduced by E. So E is also his source. So B has source A,G and E, and B introduced the wrong answer 96.

    F – 2 blank answers 90 & 92. So he has E & H among his sources. He has got 46 as his wrong answer. Obviously, since E&H both have A as their only source, 46 is wrong in E&H, and also, they have the same wrong answer. Hence, the answer for Q.46 is same in E& H, and this answer is wrong. Hence F also got it wrong. F introduced the wrong answer 14.

    I – 3 blank answers – 17, 46 and 90. So he has sources D (17), E (46, 90).
    I introduced wrong answer 27.

    C – 3 blank answers – 17, 46 and 90. 2 wrong answers 27 & 56. So, I is the source of C. And C introduced the wrong answer 56.

    All the questions can be answered now.

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