The following line graph shows the ratio of wheat production to rice production of a state in India over 7 years, from 1999 to 2006. Answer the question based on this data.
In how many years was wheat production more than the rice production?
Show Hint
Count only the years where the plotted ratio is strictly greater than 1, not equal to 1.
A quick way to answer this without checking each year one by one is to first list all seven ratio values from the graph, then split them into three simple groups.
The seven ratios (1999-2000 to 2005-2006) are: 0.7, 0.4, 1.0, 1.2, 1.5, 1.0, 1.4.
Ratios below 1 (rice more than wheat): 0.7 and 0.4, that is 2 years.
Ratios equal to 1 (wheat equal to rice, not "more"): 1.0 and 1.0, that is 2 years.
Ratios above 1 (wheat more than rice): 1.2, 1.5 and 1.4, that is 3 years.
Since $2+2+3=7$, all seven years are accounted for, confirming no value was missed or double counted.
Let's summarize:
Wheat exceeds rice only when the plotted ratio is strictly greater than 1.
Exactly 3 of the 7 years satisfy this: 2002-2003, 2003-2004 and 2005-2006.
