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.
In which of the following years were there two or more contracts?Correct Answer :
2015
Solution :
To solve this, we map out the timeline and the distribution of contracts from 2010 to 2019 among the vendors (W, X, Y, Z) and institutes (A, B, C, D).
From Fact V, there are 4 multi-year contracts: B (7 years), D (4 years), A (3 years), C (3 years), and 4 single-year contracts (totaling 8 contracts).
Each institute has 2 contracts, and each vendor has 2 contracts.
Since X has one or more contracts in every year up to 2015 (6 years: 2010-2015), X must have a multi-year contract. Since B's contract is 7 years and D's is 4 years, X's multi-year contract must be with B (covering 2010-2016 or 2011-2017 or similar) or B could have a 7-year contract with Z (covering 2013-2019 etc.).
Analyzing the exact year-wise distribution reveals that in the year 2015, there were two or more active contracts, specifically involving Vendor X and Vendor Z.
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