# Difficult Bar Charts Solved QuestionData Interpretation Discussion

Common Information

The residents of a city ‘$X$’ consume only two varieties of rice viz. ‘High Quality’ and ‘Low Quality’.

The following bar - graph provides information about the percentage change in the consumption of the two varieties of rice by the residents of the city ‘$X$’ compared to the previous year for the years $2003$ to $2008$.

The consumption of ‘High Quality’ rice by the residents of the city ‘$X$’ in the year $2002$ was more than that of ‘Low Quality’ rice.

 Q. Common Information Question: 3/3 The total consumption of rice by the residents of city ‘$X$’ in $2006$ was not less than $50%$ of that in the year $2004$. In which of the following years, the consumption of ‘High Quality’ rice was not necessarily more than that of ‘Low Quality’ rice?
 ✖ A. 2008 ✖ B. 2006 ✖ C. 2004 ✖ D. 2007 ✔ E. 2005

Solution:
Option(E) is correct

Let the consumption of ‘High Quality’ and ‘Low Quality’ rice by the residents of the city $X$ in the year $2002$ be ‘$A$’ and ‘$B$’ respectively. It is given that $A > B$

Table below can be scrolled horizontally

2002 2003 2004 2005 2006 2007 2008

A

1.2A

0.3A

0.15A

0.18A

0.225A

0.09A

B

0.8B

0.6B

0.84B

0.21B

0.126B

0.189B

Total consumption of rice by the residents of city $X$ in $2004$:

$= 0.3A + 0.6B$

Total consumption of rice by the residents of city $X$ in $2006$:

$= 0.18A + 0.21B$

$⇒ 18A + 21B ≥ \dfrac{1}{2} (30A + 60B)$

$⇒ 6A ≥ 18B$

$⇒ A ≥ 3B$

Except for the year $2005$, in each of the years in the period $2003 - 2008$, the consumption ‘High Quality’ rice is definitely more than that of ‘Low Quality’ rice.