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 regions in which the company $C1$ sold furniture is at most: |

✖ A. |
1 |

✔ B. |
2 |

✖ C. |
3 |

✖ D. |
4 |

✖ E. |
5 |

**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 $C8$.

Referring to the table made in the previous question, for maximizing the number of regions in which $C1$ sells furniture, it is possible that $C1$ sells furniture in $R4$ as well.

Hence, the number of regions in which $C1$ sells furniture is at most $2$

**Jane**

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**Jane**

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Note that C1, C2 , C4 and C4 are not competitors.

Thus they have no area in common

Let R1 be the area exclusive to C1(only C1 sells here)

similarly,

Let R2 be the area exclusive to C2

Let R4 be the area exclusive to C4

and Let R3 be the area exclusive to C7

Then there is only one area left now which is R5

in R5 only one among C1, C2 , C4 or C4 can sell (else they become competitors)

Hence to maximize the number of areas in which C1 can sell lets say its C1 which sells in R5

Therefore , maximum areas in which C1 can possibly sell are 2 ( R1 and R5)

Cheers!!

**Ken Adams**

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How can we base the answer on presumptions/conclusions drawn from the previous questions?

Would you please explain the solution in context of the general conditions?

In Line 1 and Line 8 of the solution explanation its C4 and C7 ; C4 or C7 respectively

(not C4 and C4)

Typos:/