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CAT 2024 Question Paper Slot 2 | All Questions

Previous Year Questions

    21.

    The coordinates of the three vertices of a triangle are: (1, 2), (7, 2), and (1, 10). Then the radius of the
    incircle of the triangle is

    Answer : 2

    Video Explanation

    Explanatory Answer

    In-radius of the triangle= (a+b-h)/2, where a and b are the lengths of two legs of the triangle and h is the hypotenuse.
    In-radius= (8+6-10)/2= 4/2= 2 units


    The question is "The coordinates of the three vertices of a triangle are: (1, 2), (7, 2), and (1, 10). Then the radius of the incircle of the triangle is"

    Hence, the answer is '2'
    22.

    Bina incurs 19% loss when she sells a product at Rs. 4860 to Shyam, who in turn sells this product to Hari.
    If Bina would have sold this product to Shyam at the purchase price of Hari, she would have obtained 17%
    profit. Then, the profit, in rupees, made by Shyam is

    Answer : 2160

    Video Explanation

    Explanatory Answer

    Let the cost price of the item be C
    We are given that Bina sells this at 19% loss or at (1 - 0.19)C = 0.81C at 4860
    This gives us the value of C at Rs. 6000
    If Bina had sold this at 17% profit, the selling price would have been
    So Shyam bought the product at 4860 and sold it to Hari at 7020
    Giving the profit made by Shyam to be 7020-4860=2160
    Therefore, 2160 is the correct answer.

    23.

    Eight gymnastics players numbered 1 through 8 underwent a training camp where they were coached by three
    coaches - Xena, Yuki, and Zara. Each coach trained at least two players. Yuki trained only even numbered
    players, while Zara trained only odd numbered players. After the camp, the coaches evaluated the players and
    gave integer ratings to the respective players trained by them on a scale of 1 to 7, with 1 being the lowest rating
    and 7 the highest.
    The following additional information is known.
    1. Xena trained more players than Yuki.
    2. Player-1 and Player-4 were trained by the same coach, while the coaches who trained Player-2, Player-3 and
        Player-5 were all different.
    3. Player-5 and Player-7 were trained by the same coach and got the same rating. All other players got a unique
        rating.
    4. The average of the ratings of all the players was 4.
    5. Player-2 got the highest rating.
    6. The average of the ratings of the players trained by Yuki was twice that of the players trained by Xena and
        two more than that of the players trained by Zara.
    7. Player-4's rating was double of Player-8's and less than Player-5's.

    21.

    What best can be concluded about the number of players coached by Zara?

    Option B is the correct answer.

    Video Explanation

    Explanatory Answer

    We are told that each coach had at least two players. Clue 1 says that Xena trained more people than Yuki.
    It must be the case that Yuki trained only two people. If Yuki had trained three, then Xena would have trained at
    least four players, leaving only one for Zara.
    Hence, Yuki trained two people.
    Coming to the scores given to the players themselves:
    We are given that only 5 and 7 received a sam rating; everyone else received a distinct rating.
    We are also given their average to be 4 (clue 4), giving the sum of all the scores they got to be 32
    The sum of all numbers from 1 to 7 would be , hence the repeated score must be 32-28 = 4
    Thus, the score of 5 and 7 was 4
    Clue 5 says that player 2 got the highest score, which is 7
    Clue 7 says that player 4 got a score double that of player 8 but less than player 5; the only possibility is player 4
    getting 2 and player 8 getting 1.
    Now, considering clues 2, 3 and 6:
    We are given the same coach trained in 5 and 7. And 2, 3, and 5 were trained by different coaches, with 1 and 4
    being trained by the same coach.
    Cheer 6 informs us about the average number of players the coaches train.
    We know that Yuki trained only two players.
    Let's take the average score of Yuki's players to be x
    The average of Xena's players would be x/2, and that of Zara's players would be x-2
    The total score of Yuki's players would be 2x.
    The total score of Xena's players would be 3x/2 or 2x.
    The total score of Zara's players would be 3x-6 or 2x-4
    We have two cases to consider:
    Let's say Xena and Zara had three players each.
    The total score of Yuki's players would be 2x.
    The total score of Xena's players would be 3x/2.
    The total score of Zara's players would be 3x-6.
    2 ×
    8 7 = 28

    The sum of all these scores would be which should be equal to 32
    This would give us the value of x as
    Which would give a non-integral value of 2s, that is, the sum of Yuki's player's score.
    Hence, this must not be the case.
    The other possibility:
    The total score of Yuki's players would be 2x.
    The total score of Xena's players would be 2x.
    The total score of Zara's players would be 2x-4.
    The sum of all these scores would be 6x-4, which should be equal to 32
    This would give the value of x as 6
    Hence, the sum of all of Yuki's players would be 12
    The sum of all of Xena's players would be 12
    The sum of all of Zara's players would be 8
    Yuki has only two players whose scores add up to 12; the only combination possible is scores 7+5, where seven
    were scored by player 2. Hence, player two must be under Yuki.
    Zara got a total of 8 scores, with 7 and 5 gone. The combinations that could get this score are 2+6 and 4+4
    The score of 2 is obtained by player 4, which must come with player 1
    It is possible that 1 could have gotten a score 6
    But then we run into a contradiction: players 3 and 5 would end up under the same coach.
    Hence, Zara must have gotten 8 through 4+4 with players 5 and 7.
    All the remaining scores must be with Xena, adding up to 12, which is the case.
    4 and 1 must be present together, and 3 must be present in Xena as well, giving us the arrangement.

    22.

    What was the rating of Player-7?

    Answer : 4

    Video Explanation

    Explanatory Answer

    Score of player 7 was 4

    23.

    What was the rating of Player-6?

    Answer : 5

    Video Explanation

    Explanatory Answer

    The rating of player 6 was 5
    Therefore, 5 is the correct answer.

    24.

     For how many players the ratings can be determined with certainty?

    Answer : 6

    Video Explanation

    Explanatory Answer

    We can determine the ratings of all the players except 1 and 3
    Therefore, 6 is the correct answer

    25.

    Who all were the players trained by Xena?

    Option B is the correct answer.

    Video Explanation

    Explanatory Answer

    Xena coached players numbered 1, 3, 4 and 8
    Therefore, Option B is the correct answer

    24.

    The two plots below give the following information about six firms A, B, C, D, E, and F for 2019 and 2023.

    PAT: The firm's profits after taxes in Rs. crores,

    ES: The firm's employee strength, that is the number of employees in the firm, and

    PRD: The percentage of the firm's PAT that they spend on Research and Development (R&D).

    In the plots, the horizontal and vertical coordinates of point representing each firm gives their ES and PAT values respectively. The PRD values of each firm are proportional to the areas around the points representing each firm. The areas are comparable between the two plots, i.e., equal areas in the two plots represent the same PRD values for the two years.

    a1.png

    21.

    Assume that the annual rate of growth in PAT over the previous year (ARG) remained constant over the
    years for each of the six firms. Which among the firms A, B, C, and E had the highest ARG?

    Option C is the correct answer.

    Video Explanation

    Explanatory Answer

    The question is "Assume that the annual rate of growth in PAT over the previous year (ARG) remained constant over the years for each of the six firms. Which among the firms A, B, C, and E had the highest ARG? "

    Answer:

    Since the annual growth rate in PAT is constant, we can compare the ratio changes in the firm’s PAT in 2019 and 2023 and then compare them.

    Firm A: 3900 / 3000 = 1.3

    Firm B: 3800 / 2800 = 1.35

    Firm C: 3000 / 2400 = 1.25

    Firm E: 3500 / 2400 = 1.45

    Therefore, the highest among these will be for E.

    Hence, the answer is 'Firm E'
    22.

    The ratio of the amount of money spent by Firm C on R&D in 2019 to that in 2023 is closest to

    Option D is the correct answer.

    Video Explanation

    Explanatory Answer

    The question is "The ratio of the amount of money spent by Firm C on R&D in 2019 to that in 2023 is closest to"

    Answer:

    Amount of money spent by any firm is proportional to areas on the firm’s PAT.

    The amount of money spent by Firm C on R&D in 2019 = 2400 * π * 1.5 * 1.5.

    The amount of money spent by Firm C on R&D in 2023 = 3000 * π * 1 * 1.

    Ratio = (2400 * 1.5 * 1.5) / (3000 * 1 * 1) = 9 / 5.

    Hence, the answer is '9 : 5'
    23.

    Which among the firms A, C, E, and F had the maximum PAT per employee in 2023?

    Option D is the correct answer.

    Video Explanation

    Explanatory Answer

    The question is "Which among the firms A, C, E, and F had the maximum PAT per employee in 2023?"

    Answer:

    PAT per Employee for firm C in 2023 = 3000 / 800 = 3.75

    PAT per Employee for firm A in 2023 = 3900 / 1300 = 3

    PAT per Employee for firm E in 2023 = 3500 / 1400 = 2.5

    PAT per Employee for firm F in 2023 = 3200 / 1000 = 3.2

    The value is maximum for firm C.

    Hence, the answer is 'Firm C'
    24.

    Which among the firms C, D, E, and F had the least amount of R&D spending per employee in 2023?

    Option B is the correct answer.

    Video Explanation

    Explanatory Answer

    The question is "Which among the firms C, D, E, and F had the least amount of R&D spending per employee in 2023?"

    Answer:

    R&D spending per employee for firm D in 2023 = (2400 × 2 × 2800) = 12

    R&D spending per employee for firm E in 2023 = (3500 × 3 × 31400) = 22.5

    R&D spending per employee for firm C in 2023 = (3000 × 2 × 2800) = 15

    R&D spending per employee for firm F in 2023 = (3200 × 2 × 21000) = 12.8

    Firm D has the least amount of R&D spending per employee in 2023.

    Hence, the answer is 'Firm D'
    25.

    An online e-commerce firm receives daily integer product ratings from 1 through 5 given by buyers. The daily
    average is the average of the ratings given on that day. The cumulative average is the average of all ratings
    given on or before that day. The rating system began on Day 1, and the cumulative averages were 3 and 3.1 at
    the end of Day 1 and Day 2, respectively. The distribution of ratings on Day 2 is given in the figure below.

    a1.png

    The following information is known about ratings on Day 3.
    1. 100 buyers gave product ratings on Day 3.
    2. The modes of the product ratings were 4 and 5.
    3. The numbers of buyers giving each product rating are non-zero multiples of 10.
    4. The same number of buyers gave product ratings of 1 and 2, and that number is half the number of buyers
        who gave a rating of 3.

    21.

    How many buyers gave ratings on Day 1?

    Answer : 150

    Video Explanation

    Explanatory Answer

    Day 2

    Ratings Number of Buyers
    1 5
    2 10
    3 5
    4 20
    5 10

    Total number of Buyers in Day 2 = 50.

    Daily Average on Day 2 =
    (1×5 + 2×10 + 3×5 + 4×20 + 5×10) / 50 = 170 / 50 = 3.4

    DAY 1:

    Cumulative averages on Day 1 and Day 2 were 3 and 3.1 respectively.

    Let the number of Buyers in Day 1 = x.

    (3x + 170) / (x + 50) = 3.1

    Solving, 3x + 170 = 3.1(x + 50);
    3x + 170 = 3.1x + 155;
    0.1x = 15;
    x = 150.

    Therefore, the number of Buyers in Day 1 = 150.

    DAY 3:

    Total number of Buyers in Day 3 = 100.

    The numbers of buyers giving each product rating are non-zero multiples of 10.
    Number of buyers giving rating 1 = Number of buyers giving rating 2 = Half of number of buyers giving rating 3.
    The modes of the product ratings were 4 and 5.

    DAY 3
    Ratings Number of Buyers
    1 A
    2 A
    3 2A
    4 B (Mode)
    5 B (Mode)

    Sum of the number of buyers = 4A + 2B = 100.

    The only possible solution for the equation and B value being the mode is A = 10 and B = 30.

    DAY 3
    Ratings Number of Buyers
    1 10
    2 10
    3 20
    4 30
    5 30

    Product rating on Day 3 = (1×10 + 2×10 + 3×20 + 4×30 + 5×30) / 100 = 360 / 100 = 3.6

    Cumulative rating on Day 3 = (3×150 + 3.4×50 + 3.6×100) / (150 + 50 + 100) = 980 / 300 = 3.266

    DAY NUMBER OF PASSENGERS DAILY AVERAGE CUMULATIVE AVERAGE
    1 150 3 3
    2 50 3.4 3.1
    3 100 3.6 3.266
    22.

    What is the daily average rating of Day 3?

    Option A is the correct answer.

    Video Explanation

    Explanatory Answer

    Day 2

    Ratings Number of Buyers
    1 5
    2 10
    3 5
    4 20
    5 10

    Total number of Buyers in Day 2 = 50.

    Daily Average on Day 2 =
    (1×5 + 2×10 + 3×5 + 4×20 + 5×10) / 50 = 170 / 50 = 3.4

    DAY 1:

    Cumulative averages on Day 1 and Day 2 were 3 and 3.1 respectively.

    Let the number of Buyers in Day 1 = x.

    (3x + 170) / (x + 50) = 3.1

    Solving, 3x + 170 = 3.1(x + 50);
    3x + 170 = 3.1x + 155;
    0.1x = 15;
    x = 150.

    Therefore, the number of Buyers in Day 1 = 150.

    DAY 3:

    Total number of Buyers in Day 3 = 100.

    The numbers of buyers giving each product rating are non-zero multiples of 10.
    Number of buyers giving rating 1 = Number of buyers giving rating 2 = Half of number of buyers giving rating 3.
    The modes of the product ratings were 4 and 5.

    DAY 3
    Ratings Number of Buyers
    1 A
    2 A
    3 2A
    4 B (Mode)
    5 B (Mode)

    Sum of the number of buyers = 4A + 2B = 100.

    The only possible solution for the equation and B value being the mode is A = 10 and B = 30.

    DAY 3
    Ratings Number of Buyers
    1 10
    2 10
    3 20
    4 30
    5 30

    Product rating on Day 3 = (1×10 + 2×10 + 3×20 + 4×30 + 5×30) / 100 = 360 / 100 = 3.6

    Cumulative rating on Day 3 = (3×150 + 3.4×50 + 3.6×100) / (150 + 50 + 100) = 980 / 300 = 3.266

    DAY NUMBER OF PASSENGERS DAILY AVERAGE CUMULATIVE AVERAGE
    1 150 3 3
    2 50 3.4 3.1
    3 100 3.6 3.266

     


    The question is "What is the daily average rating of Day 3?"

    Hence, the answer is '3.6'
    23.

    What is the median of all ratings given on Day 3?

    Answer : 4

    Video Explanation

    Explanatory Answer

    Day 2

    Ratings Number of Buyers
    1 5
    2 10
    3 5
    4 20
    5 10

    Total number of Buyers in Day 2 = 50.

    Daily Average on Day 2 =
    (1×5 + 2×10 + 3×5 + 4×20 + 5×10) / 50 = 170 / 50 = 3.4

    DAY 1:

    Cumulative averages on Day 1 and Day 2 were 3 and 3.1 respectively.

    Let the number of Buyers in Day 1 = x.

    (3x + 170) / (x + 50) = 3.1

    Solving, 3x + 170 = 3.1(x + 50);
    3x + 170 = 3.1x + 155;
    0.1x = 15;
    x = 150.

    Therefore, the number of Buyers in Day 1 = 150.

    DAY 3:

    Total number of Buyers in Day 3 = 100.

    The numbers of buyers giving each product rating are non-zero multiples of 10.
    Number of buyers giving rating 1 = Number of buyers giving rating 2 = Half of number of buyers giving rating 3.
    The modes of the product ratings were 4 and 5.

    DAY 3
    Ratings Number of Buyers
    1 A
    2 A
    3 2A
    4 B (Mode)
    5 B (Mode)

    Sum of the number of buyers = 4A + 2B = 100.

    The only possible solution for the equation and B value being the mode is A = 10 and B = 30.

    DAY 3
    Ratings Number of Buyers
    1 10
    2 10
    3 20
    4 30
    5 30

    Product rating on Day 3 = (1×10 + 2×10 + 3×20 + 4×30 + 5×30) / 100 = 360 / 100 = 3.6

    Cumulative rating on Day 3 = (3×150 + 3.4×50 + 3.6×100) / (150 + 50 + 100) = 980 / 300 = 3.266

    DAY NUMBER OF PASSENGERS DAILY AVERAGE CUMULATIVE AVERAGE
    1 150 3 3
    2 50 3.4 3.1
    3 100 3.6 3.266

     


    The question is "What is the median of all ratings given on Day 3?"

    Answer: No of 1s’= 10; No of 2’s= 10; No of 3’s= 20; No of 4’s= 30; No of 5’s= 30.
    Therefore, the median will be average of 50th and 51st term which is (4+4)/2 = 4.

    Hence, the answer is '4'
    24.

    Which of the following is true about the cumulative average ratings of Day 2 and Day 3?

    Option C is the correct answer.

    Video Explanation

    Explanatory Answer

    Day 2

    Ratings Number of Buyers
    1 5
    2 10
    3 5
    4 20
    5 10

    Total number of Buyers in Day 2 = 50.

    Daily Average on Day 2 =
    (1×5 + 2×10 + 3×5 + 4×20 + 5×10) / 50 = 170 / 50 = 3.4

    DAY 1:

    Cumulative averages on Day 1 and Day 2 were 3 and 3.1 respectively.

    Let the number of Buyers in Day 1 = x.

    (3x + 170) / (x + 50) = 3.1

    Solving, 3x + 170 = 3.1(x + 50);
    3x + 170 = 3.1x + 155;
    0.1x = 15;
    x = 150.

    Therefore, the number of Buyers in Day 1 = 150.

    DAY 3:

    Total number of Buyers in Day 3 = 100.

    The numbers of buyers giving each product rating are non-zero multiples of 10.
    Number of buyers giving rating 1 = Number of buyers giving rating 2 = Half of number of buyers giving rating 3.
    The modes of the product ratings were 4 and 5.

    DAY 3
    Ratings Number of Buyers
    1 A
    2 A
    3 2A
    4 B (Mode)
    5 B (Mode)

    Sum of the number of buyers = 4A + 2B = 100.

    The only possible solution for the equation and B value being the mode is A = 10 and B = 30.

    DAY 3
    Ratings Number of Buyers
    1 10
    2 10
    3 20
    4 30
    5 30

    Product rating on Day 3 = (1×10 + 2×10 + 3×20 + 4×30 + 5×30) / 100 = 360 / 100 = 3.6

    Cumulative rating on Day 3 = (3×150 + 3.4×50 + 3.6×100) / (150 + 50 + 100) = 980 / 300 = 3.266

    DAY NUMBER OF PASSENGERS DAILY AVERAGE CUMULATIVE AVERAGE
    1 150 3 3
    2 50 3.4 3.1
    3 100 3.6 3.266

     


    The question is "Which of the following is true about the cumulative average ratings of Day 2 and Day 3?"

    Answer: Percentage increase from Day 2 to Day 3= ((3.266-3.1))/3.1 *100= 5.37%

    Hence, the answer is 'The cumulative average of Day 3 increased by a percentage between 5% and 8% from Day 2.'
    26.

    a1.png

    The above is a schematic diagram of walkways (indicated by all the straight-lines) and lakes (3 of them, each in
    the shape of rectangles - shaded in the diagram) of a gated area. Different points on the walkway are indicated
    by letters (A through P) with distances being OP = 150 m, ON = MN = 300 m, ML = 400 m, EL = 200 m, DE = 400m.
    The following additional information about the facilities in the area is known.
    1. The only entry/exit point is at C.
    2. There are many residences within the gated area; all of them are located on the path AH and ML with four of
        them being at A, H, M, and L.
    3. The post office is located at P and the bank is located at B

    21.

    One resident whose house is located at L, needs to visit the post office as well as the bank. What is the
    minimum distance (in m) he has to walk starting from his residence and returning to his residence after
    visiting both the post office and the bank?

    Option B is the correct answer.

    Video Explanation

    Explanatory Answer

    The first thing to realise here is the lengths of the paths.
    KN should be equal to LM, giving the length of KO using Pythagoras theorem as 500m
    Similarly, the length of HJ=OP=150m and length of GJ=EL=200m, giving the length of HG as 250 m
    The shortest path from L to B and then to P (or the other way around would involve) using these hypotenuses
    as much as possible instead of the two adjacent sides. The shortest can be visualised as shown below or
    multitude of others variations, as there are multiple ways that would make one travel the shortest distance)

    22.

    One person enters the gated area and decides to walk as much as possible before leaving the area without
    walking along any path more than once and always walking next to one of the lakes. Note that he may
    cross a point multiple times. How much distance (in m) will he walk within the gated area?

    Option C is the correct answer.

    Video Explanation

    Explanatory Answer

    Since we can only walk along the side of lakes, that drastically reduces the paths we can take.
    The diagram below shows the path with the maximum distance travelled.

    The path is CD-DE-EF-FK-KL-LM-MN-NK-KJ-JG-GF-FC
    (the reverse of this path is also valid)
    We can either manually add the lengths or use shorter methods to note that in the path we travel walkways of
    length 400 m 4 times (DE, LM, KN, EF), walkways of length 300m 6 times (CD, EF, KL, MN, KJ, GF) and walkways
    of length 200 m 2 times (FK, JG)
    Giving the total length to be 1600+1800+400 = 3800
    Therefore, Option C is the correct answer.

    23.

    One resident takes a walk within the gated area starting from A and returning to A without going through
    any point (other than A) more than once. What is the maximum distance (in m) she can walk in this way?

    Answer : 5100

    Video Explanation

    Explanatory Answer

    Counter to the first question, we should minimize the use of those hypotenuse walkways as they reduce the
    distance we travel.
    The longest possible route would include then travelling through the edges of the rectangles and sqaures, and
    not touch any point more than once.
    Best case scenario would be us touching each point exactly once.
    This can be visualized as:

    24.

    Visitors coming for morning walks are allowed to enter as long as they do not pass by any of the
    residences and do not cross any point (except C) more than once. What is the maximum distance (in m)
    that such a visitor can walk within the gated area?

    Answer : 3500

    Video Explanation

    Explanatory Answer

    3500
    Similar to the previous question, we should try to avoid the hypotenuse

    The total path distance would be 300(CD) + 400(DE) + 300(EF) + 200(FK) + 400(KN) + 300(NO) + 150(OP) +
    400(PI) + 150(IJ) + 200(JG) + 400(GB) + 300(BC)
    Adding up to 3,500 meters
    Therefore, 3500 is the correct answer

    27.

    The numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 are placed in ten slots of the following grid based on the conditions
    below.

    a1.png

    1. Numbers in any row appear in an increasing order from left to right.
    2. Numbers in any column appear in a decreasing order from top to bottom.
    3. 1 is placed either in the same row or in the same column as 10.
    4. Neither 2 nor 3 is placed in the same row or in the same column as 10.
    5. Neither 7 nor 8 is placed in the same row or in the same column as 9.
    6. 4 and 6 are placed in the same row.

    21.

    What is the row number which has the least sum of numbers placed in that row?

    Answer : 4

    Video Explanation

    Explanatory Answer

    We are given that the numbers keep increasing from left to right (clue 1), and the number keeps decreasing
    from top to bottom (clue 2)
    The key takeaway from this is that 10 must be placed in Row 1, column 4, as placing it anywhere else would
    mean that the number above it, or right to it, must be greater than 10, which is not an option.
    Clue 3 says that one is either in the same row or the same column as 10.
    The same logic that we used for 10 applies for 1; it must be either in Row 1, column 1, or Row 4, column 4; we
    don't know which one yet.
    We are given that 2 and 3 are not in the same column or row as 10, meaning that they must occupy two spots
    from (Row 2, Col. 2), (Row 2, Col. 3), and (Row 3, Col. 3)
    2 and 3 must be present in Row 2, column 2 or Row 3, column 3, as there is no number smaller than it to be in
    the cell left to it.
    Clue 6 says that 4 and 6 are in the same row; this can be rows 1, 2, or 3.
    Clue 5 is a good starting point.
    Once we found the position of 10, the only positions possible for 9 are R1C3 or R2C4

    If 9 is placed in R2C4, 7 and 8 must be placed in row 1.
    Clue 6 says that 4 and 6 are in the same row, but with 7 and 8 in row 1, no rows are left with two spaces. Hence,
    9 can not be in R2C4, and the arrangement must be:
    7 and 8 must be in column 4, occupying R3C4 and R2C4, respectively.
    Hence, 4, 6 must be in row 1:

    22.

    Which of the following statements MUST be true?
    I. 10 is placed in a slot in Row 1.
    II. 1 is placed in a slot in Row 4.

    Option A is the correct answer.

    Video Explanation

    Explanatory Answer

    We are given that the numbers keep increasing from left to right (clue 1), and the number keeps decreasing
    from top to bottom (clue 2)
    The key takeaway from this is that 10 must be placed in Row 1, column 4, as placing it anywhere else would
    mean that the number above it, or right to it, must be greater than 10, which is not an option.
    Clue 3 says that one is either in the same row or the same column as 10.
    The same logic that we used for 10 applies for 1; it must be either in Row 1, column 1, or Row 4, column 4; we
    don't know which one yet.
    We are given that 2 and 3 are not in the same column or row as 10, meaning that they must occupy two spots
    from (Row 2, Col. 2), (Row 2, Col. 3), and (Row 3, Col. 3)
    2 and 3 must be present in Row 2, column 2 or Row 3, column 3, as there is no number smaller than it to be in
    the cell left to it.
    Clue 6 says that 4 and 6 are in the same row; this can be rows 1, 2, or 3.
    Clue 5 is a good starting point.
    Once we found the position of 10, the only positions possible for 9 are R1C3 or R2C4

    If 9 is placed in R2C4, 7 and 8 must be placed in row 1.
    Clue 6 says that 4 and 6 are in the same row, but with 7 and 8 in row 1, no rows are left with two spaces. Hence,
    9 can not be in R2C4, and the arrangement must be:
    7 and 8 must be in column 4, occupying R3C4 and R2C4, respectively.
    Hence, 4, 6 must be in row 1:

    23.

    Which of the following statements MUST be true?
    I. 2 is placed in a slot in Column 2.
    II. 3 is placed in a slot in Column 3.

    Option C is the correct answer.

    Video Explanation

    Explanatory Answer

    We are given that the numbers keep increasing from left to right (clue 1), and the number keeps decreasing
    from top to bottom (clue 2)
    The key takeaway from this is that 10 must be placed in Row 1, column 4, as placing it anywhere else would
    mean that the number above it, or right to it, must be greater than 10, which is not an option.
    Clue 3 says that one is either in the same row or the same column as 10.
    The same logic that we used for 10 applies for 1; it must be either in Row 1, column 1, or Row 4, column 4; we
    don't know which one yet.
    We are given that 2 and 3 are not in the same column or row as 10, meaning that they must occupy two spots
    from (Row 2, Col. 2), (Row 2, Col. 3), and (Row 3, Col. 3)
    2 and 3 must be present in Row 2, column 2 or Row 3, column 3, as there is no number smaller than it to be in
    the cell left to it.
    Clue 6 says that 4 and 6 are in the same row; this can be rows 1, 2, or 3.
    Clue 5 is a good starting point.
    Once we found the position of 10, the only positions possible for 9 are R1C3 or R2C4

    If 9 is placed in R2C4, 7 and 8 must be placed in row 1.
    Clue 6 says that 4 and 6 are in the same row, but with 7 and 8 in row 1, no rows are left with two spaces. Hence,
    9 can not be in R2C4, and the arrangement must be:
    7 and 8 must be in column 4, occupying R3C4 and R2C4, respectively.
    Hence, 4, 6 must be in row 1:

    24.

     For how many slots in the grid, placement of numbers CANNOT be determined with certainty?

    Answer : 2

    Video Explanation

    Explanatory Answer

    We are given that the numbers keep increasing from left to right (clue 1), and the number keeps decreasing
    from top to bottom (clue 2)
    The key takeaway from this is that 10 must be placed in Row 1, column 4, as placing it anywhere else would
    mean that the number above it, or right to it, must be greater than 10, which is not an option.
    Clue 3 says that one is either in the same row or the same column as 10.
    The same logic that we used for 10 applies for 1; it must be either in Row 1, column 1, or Row 4, column 4; we
    don't know which one yet.
    We are given that 2 and 3 are not in the same column or row as 10, meaning that they must occupy two spots
    from (Row 2, Col. 2), (Row 2, Col. 3), and (Row 3, Col. 3)
    2 and 3 must be present in Row 2, column 2 or Row 3, column 3, as there is no number smaller than it to be in
    the cell left to it.
    Clue 6 says that 4 and 6 are in the same row; this can be rows 1, 2, or 3.
    Clue 5 is a good starting point.
    Once we found the position of 10, the only positions possible for 9 are R1C3 or R2C4

    If 9 is placed in R2C4, 7 and 8 must be placed in row 1.
    Clue 6 says that 4 and 6 are in the same row, but with 7 and 8 in row 1, no rows are left with two spaces. Hence,
    9 can not be in R2C4, and the arrangement must be:
    7 and 8 must be in column 4, occupying R3C4 and R2C4, respectively.
    Hence, 4, 6 must be in row 1:

    Placements of all the numbers except 2 and 3 can be determined.
    Therefore, 2 is the correct answer

    25.

    What is the sum of the numbers placed in Column 4?

    Answer : 26

    Video Explanation

    Explanatory Answer

    The sum of numbers in the 4th column is 10+8+7+1 = 26
    Therefore, 26 is the correct answer.

    28.

    The passage below is accompanied by four questions. Based on the passage, choose the best answer for
    each question.
    (. . .) There are three other common drivers for carnivore-human attacks, some of which are more preventable
    than others. Natural aggression-based conflicts - such as those involving females protecting their young or
    animals protecting a food source - can often be avoided as long as people stay away from those animals and
    their food.
    Carnivores that recognise humans as a means to get food, are a different story. As they become more reliant on
    human food they might find at campsites or in rubbish bins, they become less avoidant of humans. Losing that
    instinctive fear response puts them into more situations where they could get into an altercation with a human,
    which often results in that bear being put down by humans. “A fed bear is a dead bear,” says Servheen, referring
    to a common saying among biologists and conservationists. Predatory or predation-related attacks are quite
    rare, only accounting for 17% of attacks in North America since 1955. They occur when a carnivore views a
    human as prey and hunts it like it would any other animal it uses for food. (. . .)
    Then there are animal attacks provoked by people taking pictures with them or feeding them in natural settings
    such as national parks which often end with animals being euthanised out of precaution. “Eventually, that
    animal becomes habituated to people, and [then] bad things happen to the animal. And the folks who initially
    wanted to make that connection don’t necessarily realise that,” says Christine Wilkinson, a postdoctoral
    researcher at UC Berkeley, California, who’s been studying coyote-human conflicts.
    After conducting countless postmortems on all types of carnivore-human attacks spanning 75 years,
    Penteriani’s team believes 50% could have been avoided if humans reacted differently. A 2017 study coauthored by Penteriani found that engaging in risky behaviour around large carnivores increases the likelihood
    of an attack.
    Two of the most common risky behaviours are parents leaving their children to play outside unattended and
    walking an unleashed dog, according to the study. Wilkinson says 66% of coyote attacks involve a dog.
    “[People] end up in a situation where their dog is being chased, or their dog chases a coyote, or maybe they’re
    walking their dog near a den that’s marked, and the coyote wants to escort them away,” says Wilkinson.
    Experts believe climate change also plays a part in the escalation of human-carnivore conflicts, but the
    correlation still needs to be ironed out. “As finite resources become scarcer, carnivores and people are coming
    into more frequent contact, which means that more conflict could occur,” says Jen Miller, international
    programme specialist for the US Fish & Wildlife Service. For example, she says, there was an uptick in lion
    attacks in western India during a drought when lions and people were relying on the same water sources.
    (. . .) The likelihood of human-carnivore conflicts appears to be higher in areas of low-income countries
    dominated by vast rural landscapes and farmland, according to Penteriani’s research. “There are a lot of
    working landscapes in the Global South that are really heterogeneous, that are interspersed with carnivore
    habitats, forests and savannahs, which creates a lot more opportunity for these encounters, just statistically,”
    says Wilkinson.

    21.

    According to the passage, what is a significant factor that contributes to the habituation of carnivores to
    human presence?

    Option D is the correct answer.

    Video Explanation

    Explanatory Answer

    Option D is the correct answer.
    The passage states that: “As they become more reliant on human food they might find at campsites or in
    rubbish bins, they become less avoidant of humans. Losing that instinctive fear response puts them into more
    situations where they could get into an altercation with a human, which often results in that bear being put
    down by humans."
    This means that the factor contributing most to carnivores' habituation to human presence is the reduction in
    instinctive fear response and reliance on human food sources, which is evident in option D.
    Option A: The passage does not mention their natural aggression. It focuses more on losing fear due to food
    reliance on human food.
    Option B: The passage mentions climate change as a possible reason for increased conflict, but it doesn't
    suggest it directly contributes to loss of fear or habituation.
    Option C: The passage does not mention about the predatory perception of humans as potential prey, hence
    eliminated.

    22.

    Given the insights provided by Penteriani’s research and Wilkinson’s statement, which of the following
    conclusions can be drawn about the relationship between landscape heterogeneity and human-carnivore
    conflicts?

    Option D is the correct answer.

    Video Explanation

    Explanatory Answer

    Option D is the correct answer. The passage mentions that landscape heterogeneity (a mix of farmland, forests,
    and carnivore habitats ) in rural areas of low-income countries creates more opportunities for human-carnivore
    encounters.
    As Penteriani’s research shows, such landscapes increase the statistical probability of these conflicts because
    the areas are interspersed with human and carnivore habitats. This aligns with option D.
    Option A: This is inconsistent with the passage. The passage states, "The likelihood of human-carnivore
    conflicts appears to be higher in areas of low-income countries dominated by vast rural landscapes and
    farmland". Therefore, it is not less prone, rather more prone as per the passage.

    Option B: The passage does not claim that landscape heterogeneity inherently decreases the chances of
    human-carnivore conflict. Instead, it states that diversity increases the likelihood of encounters rather than
    reducing it.
    Option C: The passage does not state that homogeneous landscapes cause high rates of conflict due to
    predictability. Instead, it suggests that landscape heterogeneity increases encounters.

    23.

    Which of the following statements, if false, would be inconsistent with the concerns raised in the passage
    regarding the drivers of carnivore-human conflicts?

    Option A is the correct answer.

    Video Explanation

    Explanatory Answer


    Option A: Climate change has had negligible effects on the frequency of carnivore-human interactions in
    affected regions.
    False version 1: Climate change has had no effect on the frequency of carnivore-human interactions in affected
    regions. - Inconsistent with the passage
    False version 2: Climate change has had a lot of effect on the frequency of carnivore-human interactions in
    affected regions. - Consistent
    As one of the versions contradicts the passage, we can say that the statement if false is inconsistent.
    Option B:
    Predatory attacks by carnivores are a common occurrence and have steadily increased over the past few
    decades.
    False Version: Predatory attacks by carnivores are a rare occurrence and have steadily increased over the past
    few decades.
    This is consistent with the passage.
    Option C: Carnivores lose their instinctive fear of humans, when consistently exposed to human food sources.
    False Version: Carnivores do not lose their instinctive fear of humans, when consistently exposed to human
    food sources. -- irrelevant to the passage as the author speaks on reliance on human food and not exposure to
    human food "sources".
    Option D: Human efforts to avoid risky behaviours around large carnivores have proven effective in reducing
    conflict incidents.
    False version: Human efforts to avoid risky behaviours around large carnivores have not proven effective in
    reducing conflict incidents. -- beyond the scope of the passage.

    24.

    According to the passage, which of the following scenarios would MOST likely exacerbate the frequency of
    carnivore-human conflicts?

    Option D is the correct answer.

    Video Explanation

    Explanatory Answer

    Option D is the correct answer.
    The passage mentions that 66% of coyote attacks involve a dog, which can either provoke a carnivore or
    escalate a dangerous situation when the dog chases a carnivore or vice versa. In areas with large carnivores,
    unleashing dogs can increase the likelihood of encounters and conflicts. Therefore, option D is the most likely
    scenario to exacerbate carnivore-human conflicts.
    Why the other options are less likely to exacerbate the conflicts:
    Option A: Preventing wild animals from being attracted to human food sources would actually reduce carnivorehuman conflicts by keeping animals from becoming habituated to humans. This would prevent potential issues,

    Option B: The passage suggests that climate change could increase the frequency of human-carnivore
    encounters due to scarcity of resources. Therefore, addressing climate change would likely help prevent the
    issue rather than exacerbate it.
    Option C: According to the passage, photographing wild animals in secured viewing areas is not a major driver
    of carnivore-human conflicts. Conflicts typically arise from behaviours that encourage animals to approach
    humans or interact in risky ways, not from observation in protected zones. Therefore, this is unlikely to
    exacerbate conflicts.

    29.

    The passage below is accompanied by four questions. Based on the passage, choose the best answer for
     

    [S]pices were a global commodity centuries before European voyages. There was a complex chain of relations,
    yet consumers had little knowledge of producers and vice versa. Desire for spices helped fuel European
    colonial empires to create political, military and commercial networks under a single power.
    Historians know a fair amount about the supply of spices in Europe during the medieval period - the origins,
    methods of transportation, the prices - but less about demand. Why go to such extraordinary efforts to procure
    expensive products from exotic lands? Still, demand was great enough to inspire the voyages of Christopher
    Columbus and Vasco Da Gama, launching the first fateful wave of European colonialism. . . .
    So, why were spices so highly prized in Europe in the centuries from about 1000 to 1500? One widely
    disseminated explanation for medieval demand for spices was that they covered the taste of spoiled meat. . . .
    Medieval purchasers consumed meat much fresher than what the average city-dweller in the developed world
    of today has at hand. However, refrigeration was not available, and some hot spices have been shown to serve
    as an anti-bacterial agent. Salting, smoking or drying meat were other means of preservation. Most spices used
    in cooking began as medical ingredients, and throughout the Middle Ages spices were used as both medicines
    and condiments. Above all, medieval recipes involve the combination of medical and culinary lore in order to
    balance food's humeral properties and prevent disease. Most spices were hot and dry and so appropriate in
    sauces to counteract the moist and wet properties supposedly possessed by most meat and fish. . . .
    Where spices came from was known in a vague sense centuries before the voyages of Columbus. Just how
    vague may be judged by looking at medieval world maps . . . To the medieval European imagination, the East
    was exotic and alluring. Medieval maps often placed India close to the so-called Earthly Paradise, the Garden of
    Eden described in the Bible.
    Geographical knowledge has a lot to do with the perceptions of spices’ relative scarcity and the reasons for
    their high prices. An example of the varying notions of scarcity is the conflicting information about how pepper
    is harvested. As far back as the 7th century Europeans thought that pepper in India grew on trees "guarded" by
    serpents that would bite and poison anyone who attempted to gather the fruit. The only way to harvest pepper
    was to burn the trees, which would drive the snakes underground. Of course, this bit of lore would explain the
    shriveled black peppercorns, but not white, pink or other colors.
    Spices never had the enduring allure or power of gold and silver or the commercial potential of new products
    such as tobacco, indigo or sugar. But the taste for spices did continue for a while beyond the Middle Ages. As
    late as the 17th century, the English and the Dutch were struggling for control of the Spice Islands: Dutch New
    Amsterdam, or New York, was exchanged by the British for one of the Moluccan Islands where nutmeg was
    grown

    21.

     It can be inferred that all of the following contributed to a decline in the allure of spices, EXCEPT:

    Option B is the correct answer.

    Video Explanation

    Explanatory Answer

    Option B is the correct answer.
    The demand for spices was not necessarily tied to their availability. The passage states that medieval
    Europeans had limited geographical knowledge of where spices came from and were highly prized despite their
    relative scarcity. Spices were used for culinary and medicinal purposes, and the demand was driven by cultural
    and medical factors rather than availability.
    Option A: The passage states that spices were used partly due to the unavailability of refrigeration, and some
    spices served as antibacterial agents. With the development of refrigeration techniques, the necessity for
    spices to preserve or enhance food properties would diminish, leading to a decline in their appeal.
    Option C: The passage mentions how spices were used for medicinal properties in medieval times as part of
    humeral balancing. As medical science evolved, such practices would likely fall out of favour, reducing their
    significance.
    Option D: The passage states that spices played a significant role in medieval cooking, balancing humeral
    properties in food. Changes in European tastes or culinary practices would have contributed to a decline in the
    demand for spices

    22.

    In the context of the passage, the people who heard the story of pepper trees being guarded by snakes
    would be least likely to arrive at the conclusion that

    Option A is the correct answer.

    Video Explanation

    Explanatory Answer

    Option A is the correct answer.
    This is a wrong conclusion because it confuses the physical heat from the harvesting process with the pepper's
    actual spiciness. The process of using fire for harvesting could not be related to the spiciness (being hot) of the
    pepper.
    Option B: The story of snakes and burning trees implies that pepper was difficult and dangerous to harvest,
    which could explain why it was costly. This is a reasonable conclusion based on the story.
    Option C: Given the danger described in the myth (snakes and burning trees), it's logical that people would
    conclude it's not advisable to go to India to harvest pepper themselves. This could be a conclusion from the
    story.
    Option D: The story suggests that harvesting pepper is difficult and dangerous, which might lead people to think
    that the supply is limited. Based on the information provided in the myth, this is a reasonable conclusion.

    23.

     In the context of the passage, which one of the following conclusions CANNOT be reached?

    Option B is the correct answer.

    Video Explanation

    Explanatory Answer

    Option B is the correct answer.
    While spices were a major part of European trade with the East, the passage does claim that gold was a
    motivation for colonizing India. The main focus of the passage is on spices, not gold. Hence, the conclusion
    that India was colonized for both spices and gold cannot be definitively drawn from the passage.
    Option A: The passage hints that the desire for spices played a significant role in driving European colonial
    expansion. Therefore, this conclusion can be reached from the passage.
    Option C: The passage briefly mentions that spices never had the same enduring allure or commercial potential
    as gold, silver, tobacco, indigo, or sugar. From this, we can infer that tobacco was more marketable than spices
    at certain points in history.
    Option D: In the passage, the desire for spices is described as one of the major factors that led to European
    colonialism. Therefore, this conclusion could be reached.

    24.

     If a trader brought white peppercorns from India to medieval Europe, all of the following are unlikely to
    happen, EXCEPT:

    Option B is the correct answer.

    Video Explanation

    Explanatory Answer

    Option B is the correct answer.
    If white peppercorns were brought to Europe, Europeans would likely doubt the myth of harvesting pepper by
    burning trees, as white peppercorns would not be burnt like the black peppercorns described in the story. This
    inconsistency would make them question the accuracy of the myth.
    Option A: Medieval maps were mentioned as symbolic and inaccurate, making them impractical for navigation.
    Traders did not rely on these maps for precise geographical guidance.
    Option C: This outcome is unlikely. The passage explains that spices were scarce and expensive; thus, bringing
    white pepper would not significantly affect its price, since it remained a rare and highly valued commodity.
    Option D: Even if a trader brought white peppercorns, pepper would still be viewed as exotic by Europeans due
    to its rarity and the long journey it took to reach Europe. So, this outcome is also unlikely.

    30.

    The passage below is accompanied by four questions. Based on the passage, choose the best answer for
    each question.
    The job of a peer reviewer is thankless. Collectively, academics spend around 70 million hours every year
    evaluating each other’s manuscripts on the behalf of scholarly journals — and they usually receive no monetary
    compensation and little if any recognition for their effort. Some do it as a way to keep abreast with
    developments in their field; some simply see it as a duty to the discipline. Either way, academic publishing
    would likely crumble without them.
    In recent years, some scientists have begun posting their reviews online, mainly to claim credit for their work.
    Sites like Publons allow researchers to either share entire referee reports or simply list the journals for whom
    they’ve carried out a review…. The rise of Publons suggests that academics are increasingly placing value on
    the work of peer review and asking others, such as grant funders, to do the same. While that’s vital in the
    publish-or-perish culture of academia, there’s also immense value in the data underlying peer review. Sharing
    peer review data could help journals stamp out fraud, inefficiency, and systemic bias in academic publishing.….
    Peer review data could also help root out bias. Last year, a study based on peer review data for nearly 24,000
    submissions to the biomedical journal eLife found that women and non- Westerners were vastly
    underrepresented among peer reviewers. Only around one in every five reviewers was female, and less than two
    percent of reviewers were based in developing countries…. Openly publishing peer review data could perhaps
    also help journals address another problem in academic publishing: fraudulent peer reviews. For instance, a
    minority of authors have been known to use phony email addresses to pose as an outside expert and review
    their own manuscripts.…
    Opponents of open peer review commonly argue that confidentiality is vital to the integrity of the review
    process; referees may be less critical of manuscripts if their reports are published, especially if they are
    revealing their identities by signing them. Some also hold concerns that open reviewing may deter referees
    from agreeing to judge manuscripts in the first place, or that they’ll take longer to do so out of fear of scrutiny….
    Even when the content of reviews and the identity of reviewers can’t be shared publicly, perhaps journals could
    share the data with outside researchers for study. Or they could release other figures that wouldn’t compromise
    the anonymity of reviews but that might answer important questions about how long the reviewing process
    takes, how many researchers editors have to reach out to on average to find one who will carry out the work,
    and the geographic distribution of peer reviewers.
    Of course, opening up data underlying the reviewing process will not fix peer review entirely, and there may be
    instances in which there are valid reasons to keep the content of peer reviews hidden and the identity of the
    referees confidential. But the norm should shift from opacity in all cases to opacity only when necessary.

    21.

    According to the passage, which of the following is the only reason NOT given in favour of making peer
    review data public?

    Option D is the correct answer.

    Video Explanation

    Explanatory Answer

    Option D is the correct answer.
    The passage provides several arguments in favour of making peer review data public, but it does not mention
    that making this data public would help in selecting appropriately qualified reviewers for academic writing.
    Option A: The passage mentions that openly publishing peer review data could help journals address fraudulent
    peer reviews, such as authors using fake email addresses to review their own manuscripts. Therefore, this is a
    reason given in favour of making the data public.
    Option B: The passage discusses a study showing that women and non-Westerners are underrepresented
    among peer reviewers. Publishing peer review data could help highlight these gender and race biases, which is
    one of the reasons for making the data public.
    Option C: The passage suggests that sharing peer-review data could help journals tackle issues like fraud,
    inefficiency, and systemic bias in the publishing process, which is another reason given in favour of making the
    data public.

    22.

     All of the following are listed as reasons why academics choose to review other scholars’ work EXCEPT:

    Option D is the correct answer.

    Video Explanation

    Explanatory Answer

    Option D is the correct answer.
    This is not mentioned as a reason in the passage. The focus is on staying informed, contributing to the field,
    and publicizing their own work, not on expanding influence. Therefore, option D is the correct answer as it is the
    only reason not mentioned in the passage.

    Option A: The passage mentions that some academics review work to "keep abreast with developments in their
    field," which aligns with the idea that reviewing helps them stay updated with cutting-edge ideas. This is a valid
    reason.
    Option B: The passage also mentions that some scientists post their reviews online "mainly to claim credit for
    their work," which indicates that some view reviewing as an opportunity to publicize their contributions. This is
    a valid reason
    Option C: The passage states that some view reviewing as "a duty to the discipline," which is a form of service
    to the academic community. Therefore, option C is also a valid reason.

    23.

    Based on the passage we can infer that the author would most probably support

    Option D is the correct answer.

    Video Explanation

    Explanatory Answer

    Option D is the correct answer.
    The passage discusses the value of making peer-reviewed data public to help address various issues in
    academic publishing, such as bias, inefficiency, and fraud. The author advocates for a shift"from opacity in all
    cases to opacity only when necessary," implying support for greater transparency in peer review.
    Option A: The passage mentions concerns about reviewer selection, such as gender and geographic
    imbalances, but it does not suggest that careful screening of content-familiar reviewers is a priority.
    Option B: The passage mentioned about maintaining confidentiality, but it does not strongly argue in favour of
    preserving anonymity.
    Option C: The author does not fully endorse the publication of actual reviews or reviewer identities in every
    situation. While the author advocates for sharing peer review data, they also acknowledge that, in some cases,
    the content of reviews and reviewers' identities may need to remain confidential.

    24.

    According to the passage, some are opposed to making peer reviews public for all the following reasons
    EXCEPT that it

    Option B is the correct answer.

    Video Explanation

    Explanatory Answer

    Let's evaluate the options:
    Option A: The passage mentions this concern: "referees may be less critical of manuscripts if their reports are
    published, especially if they are revealing their identities by signing them."
    Option B: The passage does not mention that one of the reasons to oppose open peer review is to protect
    reviewers from unwarranted and unjustified criticism. Instead, the passage discusses the concern that
    reviewers may avoid giving critical feedback if their identities and reports are made public, not because they
    want to avoid unjust criticism. The key concern is the fear of justified criticism rather than avoiding unjust or
    unwarranted criticism.
    Option C: The passage mentions that reviewers may be less critical in their reports if they fear their reviews will
    be published. This might prevent reviewers from being honest and offering critical assessments, which are
    crucial for the integrity of the publishing process.
    Option D: Another concern raised in the passage is that reviewers might take longer to submit their reviews if
    they know they will be publicly scrutinized. This delay in the review process is seen as a disadvantage of open
    peer review.
    Therefore, option B is the correct answer because the passage does not mention concerns about leaving
    reviewers unexposed to unwarranted criticism.