All 20 DILR questions from the CAT 2021 · Slot 3 paper, with the correct answer for each.
Each bottle holds 50 ml of liquid that is either 100% pure content (P) or has some impurity (I). A test device flags impurity only when the impurity is at least 10% of the content tested; pooling bottles dilutes each impurity. (Worked examples: 10 ml pure + 20 ml of an 80/20 bottle -> 4/30 = 13.3% flags; 10 ml pure + 5 ml of the same bottle -> 1/15 = 6.7% stays clean.)
5 ml of content from bottle A is mixed with 5 ml of content from bottle B. The resultant mixture, when tested, detects the
presence of I. If it is known that bottle A contains only P, what BEST can be concluded about the volume of I in bottle B?
Correct answer: D · 10 ml or more
There are four bottles. Each bottle is known to contain only P or only I. They will be considered to be “collectively ready for
despatch” if all of them contain only P. In minimum how many tests, is it possible to ascertain whether these four bottles are
“collectively ready for despatch”? (in numerical value)
Correct answer: 1
There are four bottles. It is known that three of these bottles contain only P, while the remaining one contains 80% P and 20% I.
What is the minimum number of tests required to definitely identify the bottle containing some amount of I? (in numerical
value)
Correct answer: 2
There are four bottles. It is known that either one or two of these bottles contain(s)only P, while the remaining ones contain
85% P and 15% I. What is the minimum number of tests required to ascertain the exact number of bottles containing only P?
Correct answer: D · 1
The figure above shows the schedule of four employees – Abani, Bahni, Danni and Tinni –whom Dhoni supervised in 2020.
Altogether there were five projects which started and concluded in 2020 in which they were involved. For each of these projects
and for each employee, the starting day was at the beginning of a month and the concluding day was the end of a month, and
these are indicated by the left and right end points of the corresponding horizontal bars. The number within each bar indicates
the percentage of assigned work completed by the employee for that project, as assessed by Dhoni.
For each employee, his/her total project-month (in 2020) is the sum of the number of months(s)he worked across the five
project, while his/her annual completion index is the weight age average of the completion percentage assigned from the
different projects, with the weights being the corresponding number of months (s)he worked in these projects. For each project,
the total employee-month is the sum of the number of months four employees worked in this project, while its completion
index is the weight age average of the completion percentage assigned for the employees who worked in this project, with the
weights being the corresponding number of months they worked in this project.
Which of the following statements is/are true?
I: The total project-month was the same for the four employees.
II: The total employee-month was the same for the five projects.
Correct answer: D · Only I
Which employees did not work in multiple projects for any of the months in 2020?
Correct answer: A · Only Abani, Bahni and Danni
The project duration, measured in terms of the number of months, is the time duringwhich at least one employee worked in the
project. Which of the following pairs of theprojects had the same duration?
Correct answer: D · Project 3, Project 4
The list of employees in decreasing order of annual completion index is:
Correct answer: C · Danni, Tinni, Abani, Bahni
10 players - P1, P2, ... , P10 - competed in an international javelin throw event. The number (after P) of a player reflects his rank at the beginning of the event, with rank 1 going to the topmost player. There were two phases in the event with the first phase consisting of rounds 1, 2, and 3, and the second phase consisting of rounds 4, 5, and 6. A throw is measured in terms of the distance it covers (in meters, up to one decimal point accuracy), only if the throw is a 'valid' one. For an invalid throw, the distance is taken as zero. A player's score at the end of a round is the maximum distance of all his throws up to that round. Players are re-ranked after every round based on their current scores. In case of a tie in scores, the player with a prevailing higher rank retains the higher rank. This ranking determines the order in which the players go for their throws in the next round.
In each of the rounds in the first phase, the players throw in increasing order of their latest rank, i.e. the player ranked 1 at that point throws first, followed by the player ranked 2 at that point and so on. The top six players at the end of the first phase qualify for the second phase. In each of the rounds in the second phase, the players throw in decreasing order of their latest rank i.e. the player ranked 6 at that point throws first, followed by the player ranked 5 at that point and so on. The players ranked 1, 2, and 3 at the end of the sixth round receive gold, silver, and bronze medals respectively.
All the valid throws of the event were of distinct distances (as per stated measurement accuracy). The tables below show distances (in meters) covered by all valid throws in the first and the third round in the event.
The following facts are also known.
i. Among the throws in the second round, only the last two were valid. Both the throws enabled these players to qualify for the second phase, with one of them qualifying with the least score. None of these players won any medal.
ii. If a player throws first in a round AND he was also the last (among the players in the current round) to throw in the previous round, then the player is said to get a double. Two players got a double.
iii. In each round of the second phase, exactly one player improved his score. Each of these improvements was by the same amount.
iv. The gold and bronze medalists improved their scores in the fifth and the sixth rounds respectively. One medal winner improved his score in the fourth round.
v. The difference between the final scores of the gold medalist and the silver medalist, as well as the difference between the final scores of the silver medalist and the bronze medalist was 1.0 m.
Which two players got the double?
Correct answer: C · P8, P10
Who won the silver medal?
Correct answer: D · P1
Who threw the last javelin in the event?
Correct answer: A · P7
What was the final score (in m) of the silver-medalist?
Correct answer: C · 88.6
Which of the following can be the final score (in m) of P8?
Correct answer: C · 82.7
By how much did the gold medalist improve his score (in m) in the second phase?
Correct answer: C · 2.4
13 questions (Q01-Q13) are created by SMEs or by reviewers Amal, Bimal, Komal, each of whom approves or disapproves. An SME question is seen by Amal then Bimal (both approve -> accept; both disapprove -> reject; split -> Komal decides). A reviewer's own question is judged by the other two in a fixed order (Amal's by Bimal then Komal; Bimal's by Komal then Amal; Komal's by Amal then Bimal), accepted iff the deciding reviewer approves. Rejected: Q02, Q06, Q09, Q11, Q12. Amal reviewed Q02,03,04,06,08,10,11,13; Bimal Q02,04,06,07,08,09,12,13; Komal Q01,02,03,04,05,07,08,09,11,12.
How many questions were DEFINITELY created by Amal? (in numerical value)
Correct answer: 3
How many questions were DEFINITELY created by Komal? (in numerical value)
Correct answer: 1
How many questions were DEFINITELY created by the SMEs? (in numerical value)
Correct answer: 3
How many questions were DEFINITELY disapproved by Bimal? (in numerical value)
Correct answer: 4
The approval ratio of a reviewer is the ratio of the number of questions (s)he approved to the number of questions (s)he
reviewed. Which option best describes Amal’s approval ratio?
Correct answer: D · lies between 0.25 and 0.75
How many questions created by Amal or Bimal were disapproved by at least one of the other reviewers?
Correct answer: C · 5