Logical Reasoning – Four institutes, A, B, C, and D, had contracts with four


Slot – 1 – LR – Four institutes, A, B, C,

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.

Q.1 In which of the following years were there two or more contracts?

  1. 2015
  2. 2017
  3. 2016
  4. 2018
Answer: 1

Q.2 Which of the following is true?

  1. D had a contract with X in 2011
  2. B had a contract with Y in 2019
  3. B had a contract with Z in 2017
  4. D had a contract with Y in 2019
Answer: 4

Q.3 In how many years during this period was there only one contract?

  1. 3
  2. 4
  3. 2
  4. 5
Answer: 1

Q.4 What BEST can be concluded about the number of contracts in 2010?

  1. at least 4
  2. at least 3
  3. exactly 4
  4. exactly 3
Answer: 4

Q.5 Which institutes had multiple contracts during the same year?

  1. A and B only
  2. B and C only
  3. B only
  4. A only
Answer: 1

Q.6 Which institutes and vendors had more than one contracts in any year?

  1. B, D, W, and X
  2. B, W, X, and Z
  3. A, B, W, and X
  4. A, D, W, and Z
Answer: 3
Solutions:
Q.1 From statement 1, 2, 3 and 4 it is clear that W and X doesn’t had any contract after the year 2015. Y had contract only in 2010 and 2019. Z had contract in all the years.
From the given option , only year 2015 will have 2 or more contracts ( at least 1 for Z and at least 1 for X)
Correct option 4) 2015

Q.2 From point V) Institute B had a 7-year contract so it should be with Z as no other vendor worked for more than 5 years. From this statement it can also be concluded that Z had one more contract of either 4 years or 3 years and X will have one contract of 3 years and other can be of 4 years or 3 years . Each of W and Y will have 2 contracts each of 1 years.
From point IV)There were 5 contracts in 2012 and we also know that W had both of its contract in 2012, and Y do not have any contract in 2012 so either X or Z must have exactly 2 contract in 2012 which is not possible for Z . it mean X will have 2 contracts in 2012.
If X had contracts of 3 years and 4 years , Z will have contracts of 7 years and 3 years.
As X has 2 contract in 2012 so he should start his 2nd contract of 4 years in 2012 and first in 2010. Now D had a contract in 2012 so it should be with X and B must have a 7 year contract in 2012 which starts in 2010 with Z. Which also means the three year contract of Z will start in 2017.
Now from point VI) Institute C had one or more contracts in 2012 but did not have any contract in 2011 , It mean the three year contract of X starts with A. It means 3 year contract of Z will be with C.
Also C will have a one year contract with W in 2012.
Now all these given information’s can be tabulated as below .
  Vendors
Institutes Vendor 1 Vendor 1
A X – 2010 to 2012 Y – 2010
B Z – 2010 to 2016 W –2012
C W – 2012 Z – 2017 to 2019
D X – 2012 to 2015 Y- 2019

Now all questions can be answered.
Option 4) is correct .

Q.3 From point V) Institute B had a 7-year contract so it should be with Z as no other vendor worked for more than 5 years. From this statement it can also be concluded that Z had one more contract of either 4 years or 3 years and X will have one contract of 3 years and other can be of 4 years or 3 years . Each of W and Y will have 2 contracts each of 1 years.
From point IV)There were 5 contracts in 2012 and we also know that W had both of its contract in 2012, and Y do not have any contract in 2012 so either X or Z must have exactly 2 contract in 2012 which is not possible for Z . it mean X will have 2 contracts in 2012.
If X had contracts of 3 years and 4 years , Z will have contracts of 7 years and 3 years.
As X has 2 contract in 2012 so he should start his 2nd contract of 4 years in 2012 and first in 2010. Now D had a contract in 2012 so it should be with X and B must have a 7 year contract in 2012 which starts in 2010 with Z. Which also means the three year contract of Z will start in 2017.
Now from point VI) Institute C had one or more contracts in 2012 but did not have any contract in 2011 , It mean the three year contract of X starts with A. It means 3 year contract of Z will be with C.
Also C will have a one year contract with W in 2012.
Now all these given information’s can be tabulated as below .
  Vendors
Institutes Vendor 1 Vendor 1
A X – 2010 to 2012 Y – 2010
B Z – 2010 to 2016 W –2012
C W – 2012 Z – 2017 to 2019
D X – 2012 to 2015 Y- 2019

Now all questions can be answered.
There was only one contract in the years years 2016, 2017 and 2018 .
Option 1) 3

Q.4 From point V) Institute B had a 7-year contract so it should be with Z as no other vendor worked for more than 5 years. From this statement it can also be concluded that Z had one more contract of either 4 years or 3 years and X will have one contract of 3 years and other can be of 4 years or 3 years . Each of W and Y will have 2 contracts each of 1 years.
From point IV)There were 5 contracts in 2012 and we also know that W had both of its contract in 2012, and Y do not have any contract in 2012 so either X or Z must have exactly 2 contract in 2012 which is not possible for Z . it mean X will have 2 contracts in 2012.
If X had contracts of 3 years and 4 years , Z will have contracts of 7 years and 3 years.
As X has 2 contract in 2012 so he should start his 2nd contract of 4 years in 2012 and first in 2010. Now D had a contract in 2012 so it should be with X and B must have a 7 year contract in 2012 which starts in 2010 with Z. Which also means the three year contract of Z will start in 2017.
Now from point VI) Institute C had one or more contracts in 2012 but did not have any contract in 2011 , It mean the three year contract of X starts with A. It means 3 year contract of Z will be with C.
Also C will have a one year contract with W in 2012.
Now all these given information’s can be tabulated as below.
  Vendors
Institutes Vendor 1 Vendor 1
A X – 2010 to 2012 Y – 2010
B Z – 2010 to 2016 W –2012
C W – 2012 Z – 2017 to 2019
D X – 2012 to 2015 Y- 2019

Now all questions can be answered.
There were exactly 3 contract in 2010.

Q.5 From point V) Institute B had a 7-year contract so it should be with Z as no other vendor worked for more than 5 years. From this statement it can also be concluded that Z had one more contract of either 4 years or 3 years and X will have one contract of 3 years and other can be of 4 years or 3 years . Each of W and Y will have 2 contracts each of 1 years.
From point IV)There were 5 contracts in 2012 and we also know that W had both of its contract in 2012, and Y do not have any contract in 2012 so either X or Z must have exactly 2 contract in 2012 which is not possible for Z . it mean X will have 2 contracts in 2012.
If X had contracts of 3 years and 4 years , Z will have contracts of 7 years and 3 years.
As X has 2 contract in 2012 so he should start his 2nd contract of 4 years in 2012 and first in 2010. Now D had a contract in 2012 so it should be with X and B must have a 7 year contract in 2012 which starts in 2010 with Z. Which also means the three year contract of Z will start in 2017.
Now from point VI) Institute C had one or more contracts in 2012 but did not have any contract in 2011 , It mean the three year contract of X starts with A. It means 3 year contract of Z will be with C.
Also C will have a one year contract with W in 2012.
Now all these given information’s can be tabulated as below.
  Vendors
Institutes Vendor 1 Vendor 1
A X – 2010 to 2012 Y – 2010
B Z – 2010 to 2016 W –2012
C W – 2012 Z – 2017 to 2019
D X – 2012 to 2015 Y- 2019

Now all questions can be answered.

Q.6 From point V) Institute B had a 7-year contract so it should be with Z as no other vendor worked for more than 5 years. From this statement it can also be concluded that Z had one more contract of either 4 years or 3 years and X will have one contract of 3 years and other can be of 4 years or 3 years . Each of W and Y will have 2 contracts each of 1 years.
From point IV)There were 5 contracts in 2012 and we also know that W had both of its contract in 2012, and Y do not have any contract in 2012 so either X or Z must have exactly 2 contract in 2012 which is not possible for Z . it mean X will have 2 contracts in 2012.
If X had contracts of 3 years and 4 years , Z will have contracts of 7 years and 3 years.
As X has 2 contract in 2012 so he should start his 2nd contract of 4 years in 2012 and first in 2010. Now D had a contract in 2012 so it should be with X and B must have a 7 year contract in 2012 which starts in 2010 with Z. Which also means the three year contract of Z will start in 2017.
Now from point VI) Institute C had one or more contracts in 2012 but did not have any contract in 2011 , It mean the three year contract of X starts with A. It means 3 year contract of Z will be with C.
Also C will have a one year contract with W in 2012.
Now all these given information’s can be tabulated as below .
  Vendors
Institutes Vendor 1 Vendor 1
A X – 2010 to 2012 Y – 2010
B Z – 2010 to 2016 W –2012
C W – 2012 Z – 2017 to 2019
D X – 2012 to 2015 Y- 2019

Now all questions can be answered.

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