Data Interpretation Discussion

**Common Information**

There are eight companies $C1, C2, C3, C4, C5, C6, C7$ and $C8$ in the market that manufacture furniture.

The furniture manufactured by these companies is sold in one or more than one of the five regions namely $R1, R2, R3, R4$ and $R5.$

Two companies are said to be ‘Competitors’ if there is at least one region where both the companies sell their furniture.

The following bar- graph provides information about the number of competitors seven of these eight companies have.

Assume that these are the only eight companies that sell furniture in the mentioned regions.

Q. |
The number of companies selling furniture in one region is at most: |

✖ A. |
4 |

✔ B. |
5 |

✖ C. |
6 |

✖ D. |
7 |

✖ E. |
8 |

**Solution:**

Option(**B**) is correct

Since $C5$ is the competitor of each of the other companies, therefore the only competitor of $C1$ is $C5$.

Let’s consider $C3$: Number of competitors is $6$.

We know for sure that $C1$ is not the competitor of $C3$; therefore the six competitors of $C3$ are $C2, C4, C5, C6, C7$ and $C8.$

Similarly $C8$: Number of competitors is $6$ and the competitors of $C8$ are $C2, C3, C4, C5, C6$ and $C7$.

Therefore competitors of $C7$ are $C5, C3$ and $C8$ and competitors of $C2$ are $C5, C3$ and $C8$.

Since the competitors of $C1, C2, C3, C5, C7$ and $C8$ are known and fixed by us, the third competitor has to be $C6$.

Therefore the competitors of $C6$ are $C5, C3, C8$ and $C4$.

Now consider $C4$: Out of the four competitors it has, three are $C5, C3$ and $C8$.

Since the number of competitors of $C1, C2$ and $C7$ is $1, 3$ and $3$ respectively, therefore the number of competitors who sell furniture in the regions in which either of $C1, C2$ and $C7$ sell furniture can be at most 4.

So the region in which maximum possible numbers of competitors sell furniture is the one that sells $C4$ or $C6$.

So, such a region could possibly have $C5, C4, C6, C3$ and $C8$.

Hence at most **5** competitors can sell furniture in one region.