CAT 2020 [Slot 1] DILR set 3

Institutes A, B, C, D Vendors W, X, Y, Z

Contracts Awarded are multiyear Contracts (consecutive years) or single Year Contract.

No institute had more than one contract with the single vendor.

Each Institute \( \to \) Two contracts \( \to \) two vendors

Each Vendor \( \to \) two contracts \( \to \) two institutes

V. Exactly 4 multi year contract (A-3years, B-7 years, C-3 years, D-4 years). Exactly 4 single year contracts. In total 8 contracts.

I. Vendor Z had at least one contract in ever year. This is only possible if he had both the contracts which are multi years contract. As 7 + 1 = 8 not possible. Only possibility is (7years + 3 years) or (3 years + 7 years) = 10 years.

II. Vendor X \( \to \) Six years 2010, 2011, 2012, 2013, 2014, 2015. To have contract for theses six years, only possibility is left with multi years contracts (4 years + 3 years or 3 years + 4 years) with 1 year overlapping contract. PI. Note (3years + 3 years) is not possible for vendor X as one 3 years is already awarded to vendor Z{(7years + 3 years ) or (3 years + 7 years) = 10 years}.

So all the 4 multiyear contracts are awarded to Z (3 years, 7 years) & X (3 years, 4 years). So we are left with 4 single year contracts.

III. Vendor Y had contracts in 2010 & 2019. Both of these contracts are single year contracts. Vendor W had contracts (two contracts) only in year 2012. So both of these are single year contracts.

IV. There are 5 contracts in 2012.

VI. Institute C had one or more contracts in 2012, but no contract in 2011.

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

Out of 5 contracts in 2012 {B, D, W, W and C at least one contract). Hence C has exactly one contract in 2012.

For Vendor X, 4 year contract is with D. It Can vary from (2011-2014) or (2012-2015). No contract can be awarded to him after 2015 (point II). Only possibility for 3 year contract is with A only, as C do not have any contract in 2011. Therefore Vendor X has a 3 year contract with institute A from 2010-2012 & a 4 year contract with institute D from 2012 to 2015 (so as to have one or more contract from 2012 to 2015).

Vendor Z can be allotted contracts with only Institute B & C Only. As vendor Z has at least one contract in every year ( point I) , thus the only possibility left is first 7 year contract with institute B and then 3 year contract with institute C ( as institute C do not have any contract in 2011).

In 2012 there are 5 contracts. Three contracts are already assigned. Remaining two are single year contracts of W in 2012. Also Institute C has at least one contract in 2012. {No institute had more than one contract with the same vendor (initial condition)}. Hence both vendor W 1 years contract cannot be with Institute C. Hence Exactly one contract of vendor W is with institute C. Further, Point VII, Institutes B and D each had exactly one contract in 2012 which is already assigned. Hence second 1 year contract of vendor W is with institute A in 2012 (only possibility).

Institute A has allotted two contracts to 2 vendors {X & W}. Institute C had allotted contracts to two vendors {W & Z}. Hence Vendor Y can have a 1 year contract with only Institute B in 2010, (only possibility left). Hence vendor Y had 1 year contract in 2019 with Institute D (only possibility left).

Question 1:

In 2015 there were two contracts with vendor Z and X

Option: 3
Question 2:

D had a contract with Y in 2019

Option: 1
Question 3:

In three years {in 2016 (Z), 2017 (Z), 2018 (Z)} there were only one contract

Option: 3
Question 4:

In 2010 {(A-X), (B-Z), (B-Y)} exactly three contracts.

Option: 3
Question 5:

A \( \to \) (X & W) in 2012, B \( \to \) (Z & Y) in 2010

Option: 4
Question 6:

Institutes { A \( \to \) 2012, B \( \to \) 2010}, Vendors { W \( \to \) 2012 X \( \to \) 2012}

Option: 4