# 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: 3/4 Each region is given as many points as the number of companies who sold furniture in it. If there is exactly one region where no company sold furniture, then the aggregate number of points given to all the regions is:
 ✖ A. 14 ✔ B. 15 ✖ C. 16 ✖ D. 17 ✖ E. Cannot be determined

Solution:
Option(B) is correct

From the bar - graph we get to know that the number of competitors of $C1, C2, C3, C4, C5, C7$ and $C8$ is $1, 3, 6, 4, 7, 3$ and $6$ respectively.

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 $C8$.

Given that there is one region where no company sold furniture.

Let $R4$ be such a region.

Assume that $C1$ sells furniture in region $R1$, so the other company that sells furniture in $R1$ has to be $C5$.

Since $C7$ has three competitors, therefore the number of companies selling furniture in the region where $C7$ sells is $4$.

Let’s assume $C7$ sells in $R2$, therefore the complete list of companies selling furniture in $R2$ is $C5, C7, C3$ and $C8$.

The same holds true for $C2$, which has three competitors.

Let’s assume $C2$ sells in $R3$, therefore the complete list of companies selling furniture is $C5, C2, C3$ and $C8$.

Now, since the number of competitors of $C4$ and $C6$ are $4$ each the complete list of companies selling furniture in $R5$ will be $C5, C4, C6, C3$ and $C8$.

The following table can be made now.

Table below can be scrolled horizontally

Region Companies

$R1$

$C1, C5$

$R2$

$C5, C7, C3, C8$

$R3$

$C5, C2, C3, C8$

$R4$

None

$R5$

$C5, C4, C6, C3, C8$

Aggregate number of points given to all the regions:

$=2+4+4+5$

$= 15$