# Difficult Bar Charts Solved QuestionData 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. Common Information Question: 2/4 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.