# Difficult Bar Charts Solved QuestionData 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. Common Information Question: 4/4 It is given that the parts of the graph marked as "Data Not Available" belonged to exactly one of the seven countries that are mentioned above but was not included in the respective bar in the graph. When arranged in an ascending order of the total number of medals won, which of the following will never be a possible case?
 ✖ A. Jordon, Japan, Kazakhstan ✖ B. Malaysia, India, Singapore ✖ C. Japan, China, Singapore ✔ D. Japan, Singapore, Jordon ✖ E. Malaysia, India, Kazakhstan

Solution:
Option(D) is correct

Gold Medals: The number of gold medals whose data is not available is:

$= \dfrac{21N}{200}$

and all of them may have belonged either to Malaysia or to Jordon.

Silver Medals: The number of silver medals whose data is not available is:

$= \dfrac{46N}{200}$

and all of them may have belonged either to China or to Japan.

Bronze Medals: The number of bronze medals whose data is not available is:

$=\dfrac{62N}{200}$

and all of them may have belonged either to Kazakhstan or to Singapore.

Hence for each of the seven countries, there are only two possible values for the total number of medals. These values are tabulated below:

Table below can be scrolled horizontally

Country Minimum Medals Maximum Medals

China

105N/200

151N/200

Japan

56N/200

102N/200

Kazakhstan

41N/200

103N/200

India

94N/200

94N/200

Singapore

54N/200

116N/200

Malaysia

71N/200

92N/200

Jordon

51N/200

72N/200

All the options except option (D) show a valid arrangement. In option (D) the total number of medals with Singapore must be $\dfrac{116N}{200}$, Japan Could have had either $\dfrac{56N}{200}$ or $\dfrac{102N}{200}$ medals in all.

As Jordon can have a maximum of $\dfrac{72N}{200}$ medals only, this option is not valid.

Note: No intermediate values are possible between the respective maximum & the minimum values for any of the seven countries.