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Distribution Questions for CAT

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Verified questions540
Worked solutions in practice mode76 from CAT papers
126 easy108 medium306 hard

20 free Distribution questions

1EasyPassage, 4 questions

Three departments share a budget of 90 (in lakhs). Each department gets at least 20 and at most 40.

Question 1

Is the budget of 90 feasible under the bounds?

  1. A

    Yes - 60 <= 90 <= 120

  2. B

    No - too low

  3. C

    No - too high

  4. D

    It cannot be determined

Question 2

Can one department receive exactly 40?

  1. A

    Yes - the remaining 50 can be split between the other two within bounds

  2. B

    No - 40 exceeds the cap

  3. C

    No - the others cannot absorb the rest

  4. D

    Only if another gets exactly 20

Question 3

What is the maximum any single department can receive?

  1. A

    40

  2. B

    50

  3. C

    60

  4. D

    90

Question 4

'Each department gets at least 20' - does this mean each gets exactly 20?

  1. A

    Yes, exactly 20

  2. B

    No - 'at least 20' means 20 or more

  3. C

    Only the smallest gets 20

  4. D

    It cannot be determined

Show solution
2EasyPassage, 4 questions

Four friends each contribute an amount (a whole number) to a fund. Each contribution is at least 10 and at most 50, and the total collected is 120.

Question 1

Check feasibility: with N = 4, lower bound 10, upper bound 50, is a total of 120 achievable?

  1. A

    Yes - 40 <= 120 <= 200

  2. B

    No - 120 is below the minimum

  3. C

    No - 120 is above the maximum

  4. D

    It cannot be determined

Question 2

What is the maximum possible contribution by a single friend?

  1. A

    30

  2. B

    50

  3. C

    90

  4. D

    120

Question 3

What is the minimum possible contribution by a single friend?

  1. A

    0

  2. B

    10

  3. C

    20

  4. D

    30

Question 4

To make one friend's contribution as large as possible, what should the other three contribute?

  1. A

    Their minimum (10 each)

  2. B

    Their maximum (50 each)

  3. C

    The average (30 each)

  4. D

    It does not matter

Show solution
3MediumPassage, 5 questions

Before the 2014 Lok Sabha elections, a poll was conducted in five major states in the country to estimate the importance of various parameters in the minds of the people. Five parameters, Infrastructure (I), Judicial Reforms (J), Growth (G), Communal Harmony (C), and Youth Oriented Government (Y) were asked to be given positions from 1 to 5 based on their importance. The survey results from each individual state are given in the table provided. The diversity index between two states equals the maximum difference between the positions of any of the five parameters. image

Question 1

Which of the following pairs of states have the least diversity index?

  1. A

    Arunachal and Kerala

  2. B

    Arunachal and Manipur

  3. C

    Manipur and Andhra

  4. D

    Andhra and Tamil Nadu

Question 2

Three of the four pairs given below have the same diversity index. Find the odd pair out.

  1. A

    Arunachal and Manipur

  2. B

    Andhra and Kerala

  3. C

    Tamil Nadu and Andhra

  4. D

    Tamil Nadu and Arunachal

Question 3

Which of the following states has the least diversity index with respect to Arunachal?

  1. A

    Andhra

  2. B

    Kerala

  3. C

    Manipur

  4. D

    Tamil Nadu

Question 4

Which of the following states has the highest diversity index with respect to Kerala?

  1. A

    Arunachal

  2. B

    Andhra

  3. C

    Manipur

  4. D

    Tamil Nadu

Question 5

Which of the following pairs of states has the highest diversity index?

  1. A

    Andhra and Arunachal

  2. B

    Andhra and Kerala

  3. C

    Tamil Nadu and Andhra

  4. D

    Arunachal and Kerala

Show solution
4MediumPassage, 3 questions

Questions are based on a  set of conditions. In answering some of the questions, it may  be useful to draw a rough diagram. Choose the response that  most accurately and completely answers each question.

In a local pet store, seven puppies wait to be introduced to their new owners. The puppies, named Ashlen, Blakely, Custard, Daffy, Earl, Fala and Gabino, are all kept in two  available pens. Pen 1 holds three puppies, and pen 2 holds four puppies.

If Gabino is kept in pen 1, then Daffy is not kept in pen 2.

If Daffy is not kept in pen 2, then Gabino is kept in pen 1.

If Ashlen is kept in pen 2, then Blakely is not kept in pen 2.

If Blakely is kept in pen 1, then Ashlen is not kept in pen 1.

Question 1

Which of the following groups of puppies could be in pen 2?

  1. A

    Gabino, Daffy, Custard, Earl.

  2. B

    Blakely, Gabino, Ashlen, Daffy.

  3. C

    Ashlen, Gabino, Earl, Custard.

  4. D

    Blakely, Custard, Earl, Fala.

  5. E

    Gabino, Ashlen, Fala, Earl.

Question 2

If Earl shares a pen with Fala, then which of the following MUST be true?

  1. A

    Gabino is in pen 1 with Daffy.

  2. B

    Custard is in pen 2.

  3. C

    Blakely is in pen 2 and Fala is in pen 1.

  4. D

    Earl is in pen 1.

  5. E

    Gabino shares a pen with Blakely.

Question 3

If Earl and Fala are in different pens, then which of the following must NOT be true?

  1. A

    Fala shares a pen with Custard.

  2. B

    Gabino shares a pen with Ashlen.

  3. C

    Earl is in a higher-numbered pen than Blakely.

  4. D

    Custard is in a higher numbered pen than Fala.

Show solution
5HardPassage, 4 questions

A high security research lab requires the researchers to set a pass key sequence based on the scan of the five fingers of their left hands. When an employee first joins the lab, her fingers are scanned in an order of her choice, and then when she wants to re-enter the facility, she has to scan the five fingers in the same sequence.

The lab authorities are considering some relaxations of the scan order requirements, since it is observed that some employees often get locked-out because they forget the sequence.

Question 1

The lab has decided to allow a variation in the sequence of scans of the five fingers so that at most two scans (out of five) are out of place. For example, if the original sequence is Thumb (T), index finger (I), middle finger (M), ring finger (R) and little finger (L) then TLMRI is also allowed, but TMRLI is not. How many different sequences of scans are allowed for any given person's original scan?

  1. A

    9

  2. B

    10

  3. C

    11

  4. D

    12

Question 2

The lab has decided to allow variations of the original sequence so that input of the scanned sequence of five fingers is allowed to vary from the original sequence by one place for any of the fingers. Thus, for example, if TIMRL is the original sequence, then ITRML is also allowed, but LIMRT is not. How many different sequences are allowed for any given person's original scan?

  1. A

    7

  2. B

    5

  3. C

    8

  4. D

    13

Question 3

The lab has now decided to require six scans in the pass key sequence, where exactly one finger is scanned twice, and the other fingers are scanned exactly once, which can be done in any order. For example, a possible sequence is TIMTRL. Suppose the lab allows a variation of the original sequence (of six inputs) where at most two scans (out of six) are out of place, as long as the finger originally scanned twice is scanned twice and other fingers are scanned once. How many different sequences of scans are allowed for any given person's original scan?

  1. A

    12

  2. B

    13

  3. C

    14

  4. D

    15

Question 4

The lab has now decided to require six scans in the pass key sequence, where exactly one finger is scanned twice, and the other fingers are scanned exactly once, which can be done in any order. For example, a possible sequence is TIMTRL. Suppose the lab allows a variation of the original sequence (of six inputs) so that input in the form of scanned sequence of six fingers is allowed to vary from the original sequence by one place for any of the fingers, as long as the finger originally scanned twice is scanned twice and other fingers are scanned once. How many different sequences of scans are allowed if the original scan sequence is LRLTIM?

  1. A

    8

  2. B

    11

  3. C

    13

  4. D

    14

Show solution
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See the 76 CAT PYQs on DistributionActual papers, 2017–2025, organised by year and slot

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