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.

- 2015
- 2017
- 2016
- 2018

- D had a contract with X in 2011
- B had a contract with Y in 2019
- B had a contract with Z in 2017
- D had a contract with Y in 2019

- 3
- 4
- 2
- 5

- at least 4
- at least 3
- exactly 4
- exactly 3

- A and B only
- B and C only
- B only
- A only

- B, D, W, and X
- B, W, X, and Z
- A, B, W, and X
- A, D, W, and Z

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

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 informationâ€™s can be tabulated as below .

Vendors | ||

Institutes | Vendor 1 | Vendor 1 |

A | X â€“ 2010 to 2012 | Y â€“ 2010 |

B | Z â€“ 2010 to 2016 | W â€“2012 |

C | W – 2012 | Z â€“ 2017 to 2019 |

D | X â€“ 2012 to 2015 | Y- 2019 |

Now all questions can be answered.

Option 4) is correct .

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 informationâ€™s can be tabulated as below .

Vendors | ||

Institutes | Vendor 1 | Vendor 1 |

A | X â€“ 2010 to 2012 | Y â€“ 2010 |

B | Z â€“ 2010 to 2016 | W â€“2012 |

C | W – 2012 | Z â€“ 2017 to 2019 |

D | X â€“ 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

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 informationâ€™s can be tabulated as below.

Vendors | ||

Institutes | Vendor 1 | Vendor 1 |

A | X â€“ 2010 to 2012 | Y â€“ 2010 |

B | Z â€“ 2010 to 2016 | W â€“2012 |

C | W – 2012 | Z â€“ 2017 to 2019 |

D | X â€“ 2012 to 2015 | Y- 2019 |

Now all questions can be answered.

There were exactly 3 contract in 2010.

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 informationâ€™s can be tabulated as below.

Vendors | ||

Institutes | Vendor 1 | Vendor 1 |

A | X â€“ 2010 to 2012 | Y â€“ 2010 |

B | Z â€“ 2010 to 2016 | W â€“2012 |

C | W – 2012 | Z â€“ 2017 to 2019 |

D | X â€“ 2012 to 2015 | Y- 2019 |

Now all questions can be answered.

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 informationâ€™s can be tabulated as below .

Vendors | ||

Institutes | Vendor 1 | Vendor 1 |

A | X â€“ 2010 to 2012 | Y â€“ 2010 |

B | Z â€“ 2010 to 2016 | W â€“2012 |

C | W – 2012 | Z â€“ 2017 to 2019 |

D | X â€“ 2012 to 2015 | Y- 2019 |

Now all questions can be answered.

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