CAT 2020 Slot 1 DILR Paper with Solutions

Set 1CAT 2020 · Slot 1 · DILR Q1–Q66 questionsTables & Missing Data

Board exam marks for missed papers

In a certain board examination, students were to appear for examination in five subjects:

English, Hindi, Mathematics, Science and Social Science. Due to a certain emergency situation, a few of the examinations could not be conducted for some students. Hence, some students missed one examination and some others missed two examinations. Nobody missed more than two examinations.

The board adopted the following policy for awarding marks to students. If a student appeared in all five examinations, then the marks awarded in each of the examinations were on the basis of the scores obtained by them in those examinations.

If a student missed only one examination, then the marks awarded in that examination was the average of the best three among the four scores in the examinations they appeared for. If a student missed two examinations, then the marks awarded in each of these examinations was the average of the best two among the three scores in the examinations they appeared for. The marks obtained by six students in the examination are given in the table below. Each of them missed either one or two examinations.

Data for this set (chart, table or figure)

The following facts are also known.

I. Four of these students appeared in each of the English, Hindi, Science, and Social Science examinations.

II. The student who missed the Mathematics examination did not miss any other examination.

III. One of the students who missed the Hindi examination did not miss any other examination. The other student who missed the Hindi examination also missed the Science examination.

Set solution: how to crack this set

A missed paper's mark equals the average of the best three of four scores (one missed) or of the best two of three (two missed). Testing each student:

Student	Possible missed papers
Alva	Hindi; Science; or both (75 $=$ avg of 80, 70, 75 or 80, 70)
Bithi	Science; Social Sc.; or both (85)
Carl	Maths; Social Sc.; or both (90)
Deep	Hindi; Science; or both (90)
Esha	English only (80)
Foni	English; Social Sc.; or both (83)

Fact I: exactly two students missed each of English, Hindi, Science and Social Science.

English: Esha and one more, which can only be Foni. Fact II: the Maths absentee missed nothing else, so Carl missed only Maths and Social Science's two absentees are Bithi and Foni.

Fact III: Hindi was missed by Alva and Deep, one alone and the other with Science. Science's two absentees: Bithi and that one.

Student	Missed
Alva / Deep	Hindi only, and Hindi + Science (either way round)
Bithi	Science, Social Science
Carl	Mathematics
Esha	English
Foni	English, Social Science

Q1CAT 2020 · Slot 1 · DILR Q1MCQ

Who among the following did not appear for the Mathematics examination?

Q2CAT 2020 · Slot 1 · DILR Q2MCQ

Which students did not appear for the English examination?

Q3CAT 2020 · Slot 1 · DILR Q3MCQ

What BEST can be concluded about the students who did not appear for the Hindi examination?

Q4CAT 2020 · Slot 1 · DILR Q4MCQ

What BEST can be concluded about the students who missed the Science examination?

Q5CAT 2020 · Slot 1 · DILR Q5TITA

How many out of these six students missed exactly one examination?

Q6CAT 2020 · Slot 1 · DILR Q6TITA

For how many students can we be definite about which examinations they missed?

Set 2CAT 2020 · Slot 1 · DILR Q7–Q104 questionsSets & Venn Diagrams

Musicians and percussion instruments

Ten musicians (A, B, C, D, E, F, G, H, I and J) are experts in at least one of the following three percussion instruments: tabla, mridangam, and ghatam. Among them, three are experts in tabla but not in mridangam or ghatam, another three are experts in mridangam but not in tabla or ghatam, and one is an expert in ghatam but not in tabla or mridangam. Further, two are experts in tabla and mridangam but not in ghatam, and one is an expert in tabla and ghatam but not in mridangam.

The following facts are known about these ten musicians.

1. Both A and B are experts in mridangam, but only one of them is also an expert in tabla.

2. D is an expert in both tabla and ghatam.

3. Both F and G are experts in tabla, but only one of them is also an expert in mridangam.

4. Neither I nor J is an expert in tabla.

5. Neither H nor I is an expert in mridangam, but only one of them is an expert in ghatam.

Set solution: how to crack this set

Categories: T only 3, M only 3, G only 1, T + M 2, T + G 1.

D is the T + G expert. One of A, B is T + M and the other M only. One of F, G is T + M and the other T only. That uses both T + M places.

I is neither T nor M, so I is G only. Then H (not M, not G) is T only. J (not T) must be M only.

T only: H, one of F/G, and one of C/E. M only: J, one of A/B, and the other of C/E.

Q7CAT 2020 · Slot 1 · DILR Q7MCQ

Who among the following is DEFINITELY an expert in tabla but not in either mridangam or ghatam?

Q8CAT 2020 · Slot 1 · DILR Q8MCQ

Who among the following is DEFINITELY an expert in mridangam but not in either tabla or ghatam?

Q9CAT 2020 · Slot 1 · DILR Q9MCQ

Which of the following pairs CANNOT have any musician who is an expert in both tabla and mridangam but not in ghatam?

Q10CAT 2020 · Slot 1 · DILR Q10MCQ

If C is an expert in mridangam and F is not, then which are the three musicians who are experts in tabla but not in either mridangam or ghatam?

Set 3CAT 2020 · Slot 1 · DILR Q11–Q144 questionsQuant-based Sets

Cab driver ratings and bonus

The local office of the APP-CAB company evaluates the performance of five cab drivers, Arun, Barun, Chandan, Damodaran, and Eman for their monthly payment based on ratings in five different parameters (P1 to P5) as given below:

P1: timely arrival

P2: behaviour

P3: comfortable ride

P4: driver's familiarity with the route

P5: value for money

Based on feedback from the customers, the office assigns a rating from 1 to 5 in each of these parameters. Each rating is an integer from a low value of 1 to a high value of 5. The final rating of a driver is the average of his ratings in these five parameters. The monthly payment of the drivers has two parts - a fixed payment and final rating-based bonus. If a driver gets a rating of 1 in any of the parameters, he is not eligible to get bonus. To be eligible for bonus a driver also needs to get a rating of five in at least one of the parameters. The partial information related to the ratings of the drivers in different parameters and the monthly payment structure (in rupees) is given in the table below:

The following additional facts are known.

1. Arun and Barun have got a rating of 5 in exactly one of the parameters. Chandan has got a rating of 5 in exactly two parameters.

2. None of drivers has got the same rating in three parameters.

Set solution: how to crack this set

Bonus needs no 1 and at least one 5. No rating may appear in three parameters (so at most twice).

Known: Arun P4 $= 4$ (one 5), Barun P1 $= 3$ (one 5), Chandan P3 $= 2$ (two 5s), Damodaran P2 $= 3$ , Eman P5 $= 2$ .

Payment $=$ fixed $+$ multiplier $\times$ final rating.

Q11CAT 2020 · Slot 1 · DILR Q11MCQ

If Damodaran does not get a bonus, what is the maximum possible value of his final rating?

Q12CAT 2020 · Slot 1 · DILR Q12MCQ

If Eman gets a bonus, what is the minimum possible value of his final rating?

Q13CAT 2020 · Slot 1 · DILR Q13MCQ

If all five drivers get bonus, what is the minimum possible value of the monthly payment (in rupees) that a driver gets?

Q14CAT 2020 · Slot 1 · DILR Q14MCQ

If all five drivers get bonus, what is the maximum possible value of the monthly payment (in rupees) that a driver gets?

Set 4CAT 2020 · Slot 1 · DILR Q15–Q184 questionsSets & Venn Diagrams

Patients treated with four medicines

1000 patients currently suffering from a disease were selected to study the effectiveness of treatment of four types of medicines — A, B, C and D. These patients were first randomly assigned into two groups of equal size, called treatment group and control group. The patients in the control group were not treated with any of these medicines; instead they were given a dummy medicine, called placebo, containing only sugar and starch. The following information is known about the patients in the treatment group.

a. A total of 250 patients were treated with type A medicine and a total of 210 patients were treated with type C medicine.

b. 25 patients were treated with type A medicine only. 20 patients were treated with type C medicine only. 10 patients were treated with type D medicine only.

c. 35 patients were treated with type A and type D medicines only. 20 patients were treated with type A and type B medicines only. 30 patients were treated with type A and type C medicines only. 20 patients were treated with type C and type D medicines only.

d. 100 patients were treated with exactly three types of medicines.

e. 40 patients were treated with medicines of types A, B and C, but not with medicines of type D. 20 patients were treated with medicines of types A, C and D, but not with medicines of type B.

f. 50 patients were given all the four types of medicines. 75 patients were treated with exactly one type of medicine.

Set solution: how to crack this set

Treatment group: 500 patients.

Exactly one type: A 25, C 20, D 10, so B only $= 75 - 55 = 20$ .

Exactly two: AD 35, AB 20, AC 30, CD 20, BC $= x$ , BD $= y$ . Exactly three: ABC 40, ACD 20, ABD $= p$ , BCD $= q$ , with $p + q = 40$ . All four: 50.

A: $25 + 35 + 20 + 30 + 40 + 20 + p + 50 = 250 \Rightarrow p = 30$ , $q = 10$ .

C: $20 + 30 + 20 + x + 40 + 20 + 10 + 50 = 210 \Rightarrow x = 20$ .

Total: $75 + (125 + y) + 100 + 50 = 500 \Rightarrow y = 150$ .

Q15CAT 2020 · Slot 1 · DILR Q15TITA

How many patients were treated with medicine type B?

Q16CAT 2020 · Slot 1 · DILR Q16TITA

The number of patients who were treated with medicine types B, C and D, but not type A was:

Q17CAT 2020 · Slot 1 · DILR Q17TITA

How many patients were treated with medicine types B and D only?

Q18CAT 2020 · Slot 1 · DILR Q18TITA

The number of patients who were treated with medicine type D was:

Set 5CAT 2020 · Slot 1 · DILR Q19–Q246 questionsScheduling & Timelines

Institute–vendor contracts, 2010–2019

Four institutes, A, B, C, and D, had contracts with four vendors W, X, Y, and Z during the ten calendar years from 2010 to 2019. The contracts were either multi-year contracts running for several consecutive years or single-year contracts. No institute had more than one contract with the same vendor. However, in a calendar year, an institute may have had contracts with multiple vendors, and a vendor may have had contracts with multiple institutes. It is known that over the decade, the institutes each got into two contracts with two of these vendors, and each vendor got into two contracts with two of these institutes.

The following facts are also known about these contracts.

I. Vendor Z had at least one contract in every year.

II. Vendor X had one or more contracts in every year up to 2015, but no contract in any year after that.

III. Vendor Y had contracts in 2010 and 2019. Vendor W had contracts only in 2012.

IV. There were five contracts in 2012.

V. There were exactly four multi-year contracts. Institute B had a 7-year contract, D had a 4-year contract, and A and C had one 3-year contract each. The other four contracts were single-year contracts.

VI. Institute C had one or more contracts in 2012 but did not have any contract in 2011.

VII. Institutes B and D each had exactly one contract in 2012. Institute D did not have any contract in 2010.

Set solution: how to crack this set

8 contracts: 4 multi-year (B 7, D 4, A 3, C 3) and 4 single-year. W's two contracts are 2012 singles.

Z must cover 10 years with two contracts, so it holds B's 7-year contract plus a 3- or 4-year one. X must cover 2010–2015 with the other two multi-year contracts. Y gets the two remaining singles (2010 and 2019). Each institute has exactly one single.

If Z were B 7 + D 4 and X were A 3 + C 3, the 2012 count would only reach 4. So Z $=$ B 7 + a 3-year, and X $=$ D 4 + the other 3-year.

D had nothing in 2010, so X is 2010–2012 (3-year) and D 2012–2015. C had nothing in 2011, so the X 3-year is A's and C holds Z 2017–2019, with B's Z 2010–2016.

B and D already have one 2012 contract each, so their singles are Y: D 2019 (none in 2010), B 2010. A and C take W in 2012.

Institute	Contracts
A	X 2010–2012, W 2012
B	Z 2010–2016, Y 2010
C	Z 2017–2019, W 2012
D	X 2012–2015, Y 2019

Contracts per year: 2010: 3, 2011: 2, 2012: 5, 2013–2015: 2, 2016–2018: 1, 2019: 2.

Q19CAT 2020 · Slot 1 · DILR Q19MCQ

In which of the following years were there two or more contracts?

Q20CAT 2020 · Slot 1 · DILR Q20MCQ

Which of the following is true?

Q21CAT 2020 · Slot 1 · DILR Q21MCQ

In how many years during this period was there only one contract?

Q22CAT 2020 · Slot 1 · DILR Q22MCQ

What BEST can be concluded about the number of contracts in 2010?

Q23CAT 2020 · Slot 1 · DILR Q23MCQ

Which institutes had multiple contracts during the same year?

Q24CAT 2020 · Slot 1 · DILR Q24MCQ

Which institutes and vendors had more than one contracts in any year?

CAT 2020 Slot 1 DILR paper with solutions

Board exam marks for missed papers

Solution

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Solution

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Musicians and percussion instruments

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Cab driver ratings and bonus

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Patients treated with four medicines

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Institute–vendor contracts, 2010–2019

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