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CAT 2020 Slot 1 DILR · Set 2 of 5Logical ReasoningHard DifficultyQ5–Q10 · 6 MCQ

CAT 2020 Slot 1 DILR Set 2: Arrangements (6 Questions) with Solutions

The Arrangements set from the official CAT 2020 Slot 1 DILR paper: the caselet, all 6 questions, the official answer key and a step-by-step solution for each. 100% free, no sign-up.

The Set: Read the Caselet First

CAT 2020 Slot 1 DILR · Questions 5–10
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.
1
Vendor Z had at least one contract in every year.
2
Vendor X had one or more contracts in every year up to 2015, but no contract in any year after that.
3
Vendor Y had contracts in 2010 and 2019. Vendor W had contracts only in 2012.
4
There were five contracts in 2012.
5
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.
6
Institute C had one or more contracts in 2012 but did not have any contract in 2011.
7
Institutes B and D each had exactly one contract in 2012. Institute D did not have any contract in 2010.

In the exam this set competed with 4 others for 40 minutes. Budget about 8 minutes if you attempt it.

Q5. Arrangements

MCQ · +3 / −1
In which of the following years were there two or more contracts?
  1. A) 2015
  2. B) 2017
  3. C) 2018
  4. D) 2016
Correct Answer
A) 2015
Step-by-step solution
📌 Core Concept
Count of contracts = 8 (2 per institute, 2 per vendor). Fix each contract's vendor and years from the clues, then count contracts year by year.
🔢 Step-by-Step Solution
1
Fact 3 makes both W contracts single-year contracts in 2012. The other two single-year contracts are not W's.
2
Z needs a contract in all 10 years using two contracts. Only B's 7-year contract plus a 3- or 4-year contract reach 10 years, so Z = B's 7-year plus one more multi-year contract.
3
X must cover 2010-2015 (6 years). A single-year contract is too short (4+1 = 5), so X holds two multi-year contracts. The two remaining singles therefore go to Y, in 2010 and 2019 (Fact 3).
4
If Z held D's 4-year contract, X would hold A and C in 2010-12 and 2013-15. Clue 6 (C has no 2011 contract) then forces A = 2010-12 and C = 2013-15. That gives only 4 contracts in 2012, against Fact 4. So Z holds a 3-year contract and X holds D plus the other 3-year contract.
5
D has no 2010 contract (Fact 7) and X ends in 2015, so D-X = 2012-15 and the other X contract = 2010-12. Clue 6 rules out C for that one, so A-X = 2010-12 and C-Z is a 3-year contract. B-Z = 2010-16 and C-Z = 2017-19. The alternative B 2013-19 would put C in 2010-12, including 2011.
6
C needs a 2012 contract, so C-W = 2012. D's X contract already covers 2012, so D's other contract is Y in 2019. B's 7-year already covers 2012, so B-Y = 2010 and A-W = 2012.
7
Contracts per year: 2010: 3, 2011: 2, 2012: 5, 2013: 2, 2014: 2, 2015: 2, 2016: 1, 2017: 1, 2018: 1, 2019:
2
### Why Not the Others
2016, 2017 and 2018 each have only one contract (B-Z in 2016, C-Z in 2017 and 2018).
2015 has A-less X... precisely D-X and B-Z, so two contracts.
Correct Answer: A

Q6. Arrangements

MCQ · +3 / −1
Which of the following is true?
  1. A) D had a contract with Y in 2019
  2. B) B had a contract with Z in 2017
  3. C) B had a contract with Y in 2019
  4. D) D had a contract with X in 2011
Correct Answer
A) D had a contract with Y in 2019
Step-by-step solution
📌 Core Concept
The vendor coverage clues fix which contracts are multi-year and where each one sits. Vendor Z is the most constrained, so settle it first, then X, then Y and W.
🔢 Step-by-Step Solution
1
There are 8 contracts (4 institutes × 2). Four are multi-year (B 7 years, D 4 years, A 3 years, C 3 years) and four are single-year. W has contracts only in 2012, so both W contracts are single-year. Each of X, Y and Z holds two contracts, so the four multi-year contracts are shared among X, Y and Z.
2
Z must cover all 10 years with two contracts. One single-year contract adds at most 7+1=87+1=8 years, and 4+3=74+3=7 is also too short. So Z holds B's 7-year contract plus one more multi-year contract: D's, A's or C's.
3
X is active in 2010 to 2015 and nowhere after. B's 7-year contract cannot fit in that window, so X's two contracts come from the other multi-year ones. A single-year contract would give at most 4+1=54+1=5 years, short of the 6 needed, so X holds two multi-year contracts. That leaves Y with both remaining single-year contracts, one in 2010 and one in 2019, as fact 3 requires. W holds the other two single-year contracts.
4
Case Z holds D's contract. D has no 2010 contract, so B's contract must start in 2010 and run to 2016. D's 4-year contract must then reach 2019, which forces 2016 to 2019. X holds A's and C's contracts, split as 2010 to 2012 and 2013 to 2015. C's contract cannot be 2010 to 2012 because C has nothing in 2011 (clue 6), so A's is 2010 to 2012. The 2012 contracts are then W's two, A's 3-year contract and B's 7-year contract, which is 4 and not 5. Rejected.
5
Case Z holds A's contract. X holds D's and C's. D cannot cover 2010, so C's 3-year contract must be 2010 to 2012. That includes 2011, which clue 6 forbids. Rejected.
6
Case Z holds C's contract. X holds A's and D's. X reaches 2015 only if D's contract runs 2012 to 2015, and then A's runs 2010 to 2012. Z's B and C contracts must join exactly. C's cannot be 2010 to 2012 because of 2011, so C's is 2017 to 2019 and B's is 2010 to 2016. The 2012 contracts are then A's (X), D's (X), B's (Z) and W's two, which makes 5 as clue 4 requires.
7
B and D each have exactly one 2012 contract, and their multi-year contracts already cover 2012. So their single-year contracts are not W's. They are Y's, because Y holds both remaining single-year contracts. W's two contracts go to A and C. D has no 2010 contract, so D's Y contract is 2019 and B's Y contract is 2010.
Why Not the Others
B: B's Z contract is 2010 to 2016, so it does not cover 2017.
C: B's Y contract is the 2010 one, not 2019.
D: D's X contract is 2012 to 2015, so it does not cover 2011.
Correct Answer: A

Q7. Arrangements

MCQ · +3 / −1
In how many years during this period was there only one contract?
  1. A) 3
  2. B) 2
  3. C) 5
  4. D) 4
Correct Answer
A) 3
Step-by-step solution
📌 Core Concept
Count of contracts = 8 (2 per institute, 2 per vendor). Fix every contract's vendor and years, then count contracts in each year.
🔢 Step-by-Step Solution
1
Fact 3 makes both W contracts single-year contracts in 2012.
2
Z must cover 2010-2019 with two contracts, so it holds B's 7-year contract plus one 3- or 4-year contract.
3
X must cover 2010-2015 (6 years), which needs two multi-year contracts. The remaining two single-year contracts therefore belong to Y, in 2010 and 2019.
4
If Z held D's 4-year contract, A and C would take X's 2010-12 and 2013-15, which leaves only 4 contracts in 2012 and contradicts Fact 4. So X holds D plus a 3-year contract, and Z holds a 3-year contract.
5
D has no 2010 contract and X stops after 2015, so D-X = 2012-15 and the other X contract is 2010-12. Clue 6 makes it A-X. Then C-Z = 2017-19 and B-Z = 2010-16.
6
C needs a 2012 contract, so C-W = 2012. D-Y = 2019, B-Y = 2010 and A-W = 2012.
7
Contracts per year: 2010: 3, 2011: 2, 2012: 5, 2013: 2, 2014: 2, 2015: 2, 2016: 1, 2017: 1, 2018: 1, 2019:
2
8. Only 2016 (B-Z), 2017 (C-Z) and 2018 (C-Z) have exactly one contract, which gives 3 years.
Quick Check
Total over all years: 3+2+5+2+2+2+1+1+1+2 = 21, which equals the contract-years 7+1+3+1+3+1+4+1 = 21.
Correct Answer: A

Q8. Arrangements

MCQ · +3 / −1
What BEST can be concluded about the number of contracts in 2010?
  1. A) at least 3
  2. B) at least 4
  3. C) exactly 3
  4. D) exactly 4
Correct Answer
C) exactly 3
Step-by-step solution
📌 Core Concept
Count of contracts = 8 (2 per institute, 2 per vendor). Fix every contract's vendor and years, then count the 2010 contracts.
🔢 Step-by-Step Solution
1
Fact 3 makes both W contracts single-year contracts in 2012.
2
Z must cover all 10 years with two contracts, so it holds B's 7-year contract plus a 3- or 4-year one.
3
X must cover 2010-2015 with two multi-year contracts. The two remaining single-year contracts are Y's, in 2010 and 2019.
4
Giving D's 4-year contract to Z would force A = 2010-12 and C = 2013-15 with X (clue 6 bars C from 2011). That leaves only 4 contracts in 2012, contradicting Fact 4. So X holds D and a 3-year contract.
5
D has no 2010 contract (Fact 7) and X ends in 2015, so D-X = 2012-15 and the other X contract is 2010-12. Clue 6 makes it A-X. Then C-Z = 2017-19 and B-Z = 2010-16.
6
C needs a 2012 contract, so C-W = 2012. D-Y = 2019, B-Y = 2010 and A-W = 2012.
7
Contracts running in 2010: B-Z (2010-16), B-Y (2010) and A-X (2010-12). That is exactly 3.
Why Not the Others
"At least 3" is true but weaker than the exact value the data fixes.
"At least 4" and "exactly 4" are false, since D has no 2010 contract and C-Z does not start until 2017.
Correct Answer: C

Q9. Arrangements

MCQ · +3 / −1
Which institutes had multiple contracts during the same year?
  1. A) B only
  2. B) A and B only
  3. C) B and C only
  4. D) A only
Correct Answer
B) A and B only
Step-by-step solution
📌 Core Concept
Count of contracts = 8 (2 per institute, 2 per vendor). Fix every contract's vendor and years, then see which institute has two contracts overlapping in one year.
🔢 Step-by-Step Solution
1
Fact 3 makes both W contracts single-year contracts in 2012.
2
Z must cover all 10 years with two contracts, so it holds B's 7-year contract plus a 3- or 4-year one.
3
X must cover 2010-2015 with two multi-year contracts, so Y gets the two remaining single-year contracts, in 2010 and 2019.
4
Giving D's 4-year contract to Z leaves only 4 contracts in 2012 (Fact 4 fails). So X holds D and a 3-year contract.
5
D has no 2010 contract and X ends in 2015, so D-X = 2012-15 and the other X contract is 2010-12. Clue 6 (C has no 2011 contract) makes it A-X. Then C-Z = 2017-19 and B-Z = 2010-16.
6
C needs a 2012 contract, so C-W = 2012. D-Y = 2019, B-Y = 2010 and A-W = 2012.
7
Check overlaps by institute:
A: A-X (2010-12) and A-W (2012) overlap in 2012.
B: B-Z (2010-16) and B-Y (2010) overlap in 2010.
C: C-W (2012) and C-Z (2017-19) never overlap.
D: D-X (2012-15) and D-Y (2019) never overlap.
Why Not the Others
B only, A only: each leaves out the other institute that overlaps.
B and C: C's contracts do not overlap.
Correct Answer: B

Q10. Arrangements

MCQ · +3 / −1
Which institutes and vendors had more than one contracts in any year?
  1. A) A, B, W, and X
  2. B) A, D, W, and Z
  3. C) B, D, W, and X
  4. D) B, W, X, and Z
Correct Answer
A) A, B, W, and X
Step-by-step solution
📌 Core Concept
Count of contracts = 8 (2 per institute, 2 per vendor). Fix every contract's vendor and years, then find the institutes and vendors that have two contracts running in the same year.
🔢 Step-by-Step Solution
1
Fact 3 makes both W contracts single-year contracts in 2012.
2
Z must cover all 10 years with two contracts, so it holds B's 7-year contract plus a 3- or 4-year one.
3
X must cover 2010-2015 with two multi-year contracts, so Y gets the two remaining single-year contracts, in 2010 and 2019.
4
Giving D's 4-year contract to Z leaves only 4 contracts in 2012 (Fact 4 fails). So X holds D and a 3-year contract.
5
D has no 2010 contract and X ends in 2015, so D-X = 2012-15 and the other X contract is 2010-12. Clue 6 makes it A-X. Then C-Z = 2017-19 and B-Z = 2010-16.
6
C needs a 2012 contract, so C-W = 2012. D-Y = 2019, B-Y = 2010 and A-W = 2012.
7
Final list: B-Z 2010-16, B-Y 2010, C-Z 2017-19, C-W 2012, A-X 2010-12, A-W 2012, D-X 2012-15, D-Y 2019.
8
Institutes with two contracts in one year: A (2012) and B (2010).
9
Vendors with two contracts in one year: W (A and C in 2012) and X (A and D in 2012). Z has one contract in each year, and Y's two contracts are in 2010 and 2019.
Why Not the Others
Options naming D are wrong, since D's contracts (2012-15 and 2019) never overlap.
Options naming Z are wrong, since Z's two contracts (2010-16 and 2017-19) never overlap.
Correct Answer: A
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CAT 2020 Slot 1 DILR at a Glance

Sets in this section5
Questions in this section24
Section time40 minutes
Convenor IIMIIM Indore

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