Logical Reasoning Discussion

**Common Information**

Five millionaires – Mr. Lim, Mr. Peters, Mr. Yao, Mr. Kumar and Mr. Cartwright – are the owners of five paintings, one each by the artists Cezanne, Picasso, Gauguin, Vermeer and Rembrandt. Each millionaire owns one of the above paintings. The costs of the paintings (in million USD) are, in some order, 4, 6, 12, 13 and 21.

All five millionaires bought their respective painting from one of the following cities: Reykjavik, London, Delhi, Paris and Johannesburg. No two millionaires bought their painting from the same city or of the same price.

The following information is known.

- Neither Mr. Lim nor Mr. Kumar bought their paintings from Reykjavik. They bought their paintings from Paris and Johannesburg, in any order.
- Mr. Yao bought the painting by Picasso.
- Mr. Peters bought the painting worth 12 million USD from Delhi.
- The sum of the costs of the paintings bought by Mr. Lim and Mr. Yao is less than the cost of the painting bought by Mr. Kumar. Mr. Kumar does not own the most expensive painting.
- The most expensive painting is by Gauguin, and was bought from London.
- The second most expensive painting is by Cezanne, and was bought from Johannesburg.

Q. |
What is the total cost (in million USD) of the paintings owned by Mr. Lim, Mr. Yao and Mr. Cartwright? |

✖ A. |
22 |

✖ B. |
23 |

✔ C. |
31 |

✖ D. |
40 |

✖ E. |
Cannot be determined |

**Solution:**

Option(**C**) is correct

*Let us analyze the information and prepare matrix.*

We use the following short forms:

Reykjavik, Delhi, Johannesburg, Paris and London: REY, DEL, JBG, PAR and LON

Cezanne, Picasso, Gauguin, Vermeer and Rembrandt: C, P, G, V and R

**1. **Neither Mr. Lim nor Mr. Kumar bought his painting from Reykjavik: We put a cross in the REY column for both Mr. Lim and Mr. Kumar. Since they bought their paintings from PAR and JBG, we rule out DEL and LON options for both of them. We also rule out PAR and JBG options for all the other millionaires.

**2. **Mr. Yao bought the painting by Picasso: We put a tick in the corresponding box and a cross in all other boxes in the same row and column for the ‘painters’ attribute.

**3. **Mr. Peters bought the painting worth 12 million USD from Delhi: We put ticks in the corresponding boxes, and crosses in the same row and column in the attribute of price.

**4. **The sum of the costs of the paintings bought by Mr. Lim and Mr. Yao is less than the cost of the painting bought by Mr. Kumar. Mr. Kumar does not own the most expensive painting: Since Mr Kumar did not buy the painting worth 21 or 12 million USD, the cost of painting bought by him must be 4, 6 or 13 million USD. But, the cost of the painting bought by Mr. Kumar is more than that of Mr. Lim and Mr. Yao. So Mr. Kumar definitely owns the painting worth 13 million USD. We place ticks and crosses appropriately.

Since we have also derived that Mr. Lim and Yao own paintings worth 4 and 6 million USD (in some order), we put crosses against the paintings of other costs for them.At this point, we observe that the column headed by 21 million USD has 4 crosses. So, we put a tick in the fifth. This tells us that Mr. Cartwright owns the painting worth 21 million USD.Also, all the options for REY except Mr. Yao have been eliminated. So, Mr. Yao bought his painting from Rey.

**5. **The most expensive painting is by Gauguin, and was bought from London: We concluded that the most expensive painting belongs to Mr. Cartwright. We fill in the details given against his name.

**6. **The second most expensive painting is by Cezanne, and was bought from Johannesburg: We know by now that the second most expensive painting costs 13 million USD and belongs to Mr. Kumar. Hence, Mr. Kumar owns the painting C, and bought it from JBG. We enter these details in our matrix.

The matrix at this point looks like this:

The matrix tells us that the costs of the paintings owned by Mr. Lim and Mr. Yao are 4 and 6 million USD in any order, while that of the painting owned by Mr. Cartwright is 21 million USD. So, the total cost is $4 + 6 + 21 = 31$ million USD.

Hence, **option C** is the correct choice.