The graph indicates the total amount of residential electricity used

Official Explanation

Analyze the information

This is a Graphics Interpretation question. All answers will be based on information from the graph provided. The graph is a line chart with a separate line for each of four countries. From left to right, each line represents the total amount of residential electricity used for the given country, in billions of kilowatt-hours, from 1971 to 2000.

The country listed with smallest standard deviation in residential energy used between 1971 and 2000 is___________.

Approach strategically

The question asks for the country with the smallest standard deviation from 1971 to 2000. Calculating the value for any one of the countries, let alone all four, would require far too much intensive calculation. Some visual analysis of the lines should be enough to judge the correct answer. Standard deviation is a measure of how spread out values in a set of data are, and it increases as there are more values further away from the average. For Austria, Spain, and Thailand, the values increase steadily over the 30-year period, with a rather broad range of values at either end. Peru, on the other hand, was relatively constant (a fairly flat line), with very little variation from year to year. That constant rate, in comparison to the strong upward trend lines for the other countries, means that Peru has the least deviation of the group.

TAKEAWAY: It's unlikely that the GMAT will ask you to calculate standard deviation. Instead, be able to apply the concept to analyze a data set.

The country with the largest percent increase in total kilowatt-hours used from 1985 to 1990 is___________.

The question asks for the country with the greatest percent increase in residential electricity usage from 1985 to 1990. Peru stayed relatively constant, with almost no increase, so there’s no reason to calculate that value. Thailand went from about 5 billion kilowatt-hours to 8 billion. Spain went from about 23 billion to 30 billion. Australia went from about 32 billion to 39 billion. In terms of actual increase, Spain and Australia are too close to call. However, the question is about percent increase, not actual increase. Because Spain increased the same amount from a lower starting value, its percent increase will be greater, so eliminate Australia. Spain increased 7 billion kilowatt-hours from a starting value of about 23 billion. Because 7 is less than half of 23, the percent increase was less than 50%. Before calculating an actual value, compare that to the remaining country, Thailand. Its usage only increased 3 billion. However, its starting value was only about 5 billion. Because 3 is more than half of 5, the percent increase is over 50% and thus larger than Spain’s. Thus, Thailand is the correct answer. For the record, the percent increase for Spain would be approximately \(\frac{7}{23}\)×100%≈30% while Thailand’s would be considerably larger at approximately \(\frac{3}{5}\)×100%=60%.

TAKEAWAY: Percent change is amount of change divided by starting value. Thus, a large amount of change can be a small percentage change, if the starting value is also relatively large.