Data Sufficiency

LulaBrazilia wrote:By what percent did the median household income in Country Y decrease from 1970 to 1980?

1) In 1970 the median household income in Country Y was 2/3 of the median household income in Country X

2) In 1980 the median household income in Country Y was 1/2 of the median household income in Country X.

Target question: By what percent did the median household income in Country Y decrease from 1970 to 1980?

Statement 1: In 1970 the median household income in Country Y was 2/3 of the median household income in Country X
There's no information about 1980, so there's no way to determine the percent change from 1970 to 1980
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: In 1980 the median household income in Country Y was 1/2 of the median household income in Country X.
There's no information about 1970, so there's no way to determine the percent change from 1970 to 1980
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
If we're not sure where to go from here, we can always TEST some cases. If we keep getting the same results, we can be reasonably confident that the combined statements are sufficient. Conversely, if we get conflicting results, we can be certain that the combined statements are not sufficient.

case a:
1970: Country X = $6 and Country Y = $4
1980: Country X = $6 and Country Y = $3
In this case, the change from $4 to $3 represents a 25% decrease in country Y

case b:
1970: Country X = $6 and Country Y = $4
1980: Country X = $12 and Country Y = $6
In this case, the change from $4 to $6 represents a 50% INCREASE in country Y
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent