Previous CAT Questions - Solved (Logical Reasoning) - Set 7

  • (CAT 2003)
    Seventy percent of the employees in a multinational corporation have VCD players, 75 percent have microwave ovens, 80 percent have ACs and 85 percent have washing machines. At least what percentage of employees has all four gadgets?
    a. 15
    b. 5
    c. 10
    d. Cannot be determined

    To find the minimum percent of employees who have all gadgets, we should assign the gadgets to different employees, so that the ones who do not have A, ones who do not have B, and likewise are all different people. This maximizes the people who do not possess at least 1 of the item, thereby minimizing the number who possesses all the items.

    For that,

    70% has VCD, 30% do not have.

    75% have MO. 35% have. Let this 25% be completely different from the 30% that do not have VCD. So we have maximized people who do not have either of them.

    Similarly, 20% do not have AC and 15% do not have WM. Let all these people be different.

    The people who do not have at least one of these items are 30% + 25% + 20% + 15% = 90%.

    So, the people who have all these items will be minimum 10% (100 – 90).

    (CAT 2003)
    Shown below is the layout of major streets in a city.


    Two days (Thursday and Friday) are left for campaigning before a major election, and the city administration has received requests from five political parties for taking out their processions along the following routes
    Congress: A–C–D–E
    BJP: A–B–D–E
    SP: A–B–C–E
    BSP: B–C–E
    CPM: A–C–D

    Street B - D cannot be used for a political procession on Thursday due to a religious procession. The district administration has a policy of not allowing more than one procession to pass along the same street on the same day. However, the administration must allow all parties to take out their processions during these two days.

    Q1) Congress procession can be allowed
    a. Only on Thursday
    b. Only on Friday.
    c. On either day.
    d. Only if the religious procession is cancelled.

    Q2) Which of the following is NOT true?
    a. Congress and SP can take out their processions on the same day.
    b. The CPM procession cannot be allowed on Thursday.
    c. The BJP procession can only take place on Friday.
    d. Congress and BSP can take out their processions on the same day.

    Read the question fully, find out the streets involved, and associate the parties with it. Form a table.


    So we see that,

    Congress, SP can do on a single day, or Congress and BSP.

    BJP, BSP,CPM can do on a single day.

    BSP and SP cannot do on a single day. So Congress and SP on 1 day. BJP, BSP, CPM on the other day.

    Also, BD cannot be used on Thursday, which BJP uses. So BJP has to do on Friday.
    Hence BSP, CPM also on Friday. Congress and SP on Thursday.

    All the questions can be answered now.

    (CAT 2004)
    The Dean’s office recently scanned student results into the central computer system. When their character reading software cannot read something, it leaves that space blank. The scanner output reads as follows: In the grading system, A, B, C, D, and F grades fetch 6, 4, 3, 2, and 0 grade points respectively. The Grade Point Average (GPA) is the arithmetic mean of the grade points obtained in the five subjects.
    For example Nisha’s GPA is (6 + 2 + 4 + 6 + 0)/5 = 3.6.

    Some additional facts are
    Vipu obtained the same grade in Marketing as Aparna obtained in Finance and Strategy.
    Fazal obtained the same grade in Strategy as Utkarsh did in Marketing.
    Tara received the same grade in exactly three courses


    Q1) What grade did P… obtain in Statistics?
    a. A
    b. B
    c. C
    d. D

    Q2) In Operations, T… could have received the same grade as
    a. I…
    b. H…
    c. J…
    d. M…

    Q3) What grade did U obtain in Finance?
    a. B
    b. C
    c. D
    d. F

    Q4) In Strategy, G…’s grade point was higher than that obtained by
    a. F…
    b. H…
    c. N…
    d. R…

    Read the question fully and thoroughly, and fill the table with the “fixed” given details first. Do not find all the details/all tabular content unnecessarily, read the questions, and find out only the required details.

    F’s GPA is given and 4 subject’s marks are given.
    So we can find out F’s Strategy mark.

    GPA is 2.4. So total is 2.4 * 5 = 12.

    D,F,B,D are 4 subjects’ grade. Total = 8. So 5th subject = 4 marks = B.

    So F’s Strategy = U’s marketing = B. (According to clue 2)

    Now, the clue of T.

    T has same mark in exactly 3 courses. Her GPA is 2.4, hence total marks = 12.

    One subject mark is given as 4.

    We cannot have A grade in the rest of 3 subjects as total will be 18.

    We can have B grade in total of 3 subjects (incl. the give one of Finance), and rest F’s.

    We cannot have 3 C grades as total will be 9, with one existing B grade, total shoots up to 13, which is more than 12.

    We cannot have D grade in 3 subjects, because B + 3D = 10, which means the next subject should also have D grade. So there will be 4 D grades, which mismatch the “exactly” 3 grades statement.

    We cannot have 3 F grades, because total is 12. 3F + 1B = 4 marks. Remaining 1 subject and 8 marks to reach 12, which is not possible, as the maximum mark that can be obtained is 6.

    So Tara, has 3 B’s and 3 F’s.

    Now to the questions :

    Q# 1– P has total marks of 3.2 * 5 = 16.She has now 2D + 1 F = 4. So rest 12 marks, which is possible only with 2 A’s.

    Q# 2 – T has 3 B and 3 F. So she could have obtained the same grade as M in operations which is B.

    Q#3 - U’s marketing is B. So, he has B,F,C,A, i.e. 13 marks. His total is 3.0 * 5 = 15.So he has 2 marks or D grade.

    Q# 4 - G’s total is 3.8 * 5 = 19. She already has C, C, A, B = 16 marks. So she has 3 marks, i.e. C grade in Strategy.

    F, has 4 marks in Strategy (total 12 – already existing 8 marks)

    H has 2 marks together in Strategy + Finance. (Total 14 – already existing 12).
    So, he could have maximum 2 marks in strategy.
    Hence, G’s strategy > H’s strategy.


    (CAT 2004)
    Prof. Singh has been tracking the number of visitors to his homepage. His service provider has provided him with the following data on the country of origin of the visitors and the university they belong to:


    Q1) To which country does University 5 belong?
    a. India or Netherlands but not USA
    b. India or USA but not Netherlands
    c. Netherlands or USA but not India
    d. India or USA but not UK

    Q2) University 1 can belong to
    a. UK
    b. Canada
    c. Netherlands
    d. USA

    Q3) Visitors from how many universities from UK visited Prof. Singh’s homepage in the three days?
    a. 1
    b. 2
    c. 3
    d. 4

    Q4) Which among the listed countries can possibly host three of the eight listed universities?
    a. None
    b. Only UK
    c. Only India
    d. Both India and UK

    From the table for countries, it is difficult to figure out from Day1’s visitors, as Day 1 has visitors from all countries. So, let us start with day 2:

    Netherlands has 1 visitor and India has 2 visitors on day 2.

    Only Univ3 and Univ8 has visitors on day 2, with 1 and 2 visitors respectively.

    So Univ3 is in Netherlands, and Univ8 is in India.

    Now to day 3:

    UK has 2 visitors and USA 1 visitor in day 3.

    Univ 4 has 2 visitors and Univ 6 has 1 visitor in day 3.

    So Univ 4 is in UK, and Univ 6 in USA.

    Day 1, we now have 2 countries with 2 visitors and 3 countries with 1 visitor

    We know Univ 6 is in USA, so the visitor on day 1 from USA is taken care of.

    This means, Univ 2 & 7 belong either to Canada or UK.
    Similarly, Univ 1 and Univ 5 belong either to India or Netherlands.

    We cannot have Univ 1 + Univ 5 to Canada/UK, as this means India/Netherlands will not get their “exact” number.

    All the questions can be answered based on this.

    (CAT 2004)
    A study was conducted to ascertain the relative importance that employees in five different countries assigned to five different traits in their Chief Executive Officers. The traits were compassion (C), decisiveness (D), negotiation skills (N), public visibility (P), and vision (V). The level of dissimilarity between two countries is the maximum difference in the ranks allotted by the two countries to any of the five traits. The following table indicates the rank order of the five traits for each country.


    Q1) Which of the following countries is least dissimilar to India?
    a. China
    b. Japan
    c. Malaysia
    d. Thailand

    Q2) Which amongst the following countries is most dissimilar to India?
    a. China
    b. Japan
    c. Malaysia
    d. Thailand

    Q3) Which of the following pairs of countries are most dissimilar?
    a. China & Japan
    b. India & China
    c. Malaysia & Japan
    d. Thailand & Japan

    Q4) Three of the following four pairs of countries have identical levels of dissimilarity. Which pair is the odd one out?
    a. Malaysia & China
    b. China & Thailand
    c. Thailand & Japan
    d. Japan & Malaysia

    From the question, The level of dissimilarity between two countries is the maximum difference in the ranks allotted by the two countries to any of the five traits.

    Let's construct the below table from the given table.


    From the above table
    Q1) China is least dissimilar to India (max level of dissimilarity is 2 for the trait N (3 - 1 = 2))
    Q2) Japan is most dissimilar to India (For trait D Level of dissimilarity is 5 - 1 = 4 for India & Japan)
    Q3) Thailand & Japan (For trait D Level of dissimilarity is 5 - 1 = 4 for Thailand & Japan)
    Q4) Except for Japan & Malaysia all other pairs have the Level of dissimilarity as 4.

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