Data Interpretation Discussion

**Common Information**

Many Asian countries including China, Japan, Kazakhstan, India, Singapore, Malaysia and Jordon participated in one or more sporting events held at the 2006 Asian Games. In each sporting event at least three countries participated.

At the end of each sporting event, the country finishing at the first, the second and the third positions were awarded a gold, a silver and a bronze medal respectively. The following bar graph shows distribution of the three types of medals.

In this graph, the parts marked by "Data Not Available" may have belonged to one or more of all the participating countries.

Q. |
Which of the following could not have been the sum of the number of silver and the number of bronze medals won by Malaysia ? |

✖ A. |
142 |

✔ B. |
164 |

✖ C. |
213 |

✖ D. |
284 |

✖ E. |
355 |

**Solution:**

Option(**B**) is correct

At the end of each event exactly one each of gold, silver and bronze medals were awarded hence the total number of gold or silver or bronze medals must be the same.

Let there be $N$ number each of gold, silver and bronze medals.

Sum of the numbers of silver and bronze medals won by Malaysia:

$=\dfrac{71N}{200}$

As this sum must be an integer, it will be a multiple of $71$. Accordingly $142, 213, 284$ and $355$ all are possible values.

Only $164$ is not a multiple of $71$.

**Lakshman**

*()
*

Let there be $N$ number each of gold, silver and bronze medals.

Sum up the percentage of silver and bronze medals won by Malaysia,

$=(20.5\%+15\%) N$

$=(35.5\%)N$

$=\left(\dfrac{35.5}{100}\right)N$

$=\dfrac{71N}{200}$

From where $\dfrac{71N}{200}$ came from, can anyone please explain?