OG - DS - #91

[GMAT 2007]

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.

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (2) alone is not sufficient.
(C) BOTH statements together are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

The correct answer is (E)

The explanation says, there is no explicit information about the household income of Country X or Country Y. And I agree. But my question is - if we add the information (the household income in Country X was same in 1970 and in 1980).

Then can the answer be (C)?

Please help!!

GMAT 2007

[angiekara]

Why is it that the percent change is not enough information to solve this? If you use 100% for the whole and compare the difference, isn't that enough?
Thank you!

[Greg]

angiekara - I believe your statement implicitly assumes that the value of X (or the "100%" you reference in your message) is the same in 1970 & 1980. If this were true, then and only then could we use the information contained in the two statements to arrive at the percent change requested in the problem:
(((1/2)*X) - ((2/3)*X)) / ((2/3)*X) = Requested Percentage Change (you see, the Xs all cancel, leaving us with a straight numerical calculation giving us the actual percentage change, which is what is requestred in the problem).
However, the question stem doesn't state as such (nor do statements 1 and 2), so we're left wondering whether if X changed in 1970 & 1980 - hence, both statements together remain insufficient.

[StaceyKoprince]

Try it with real numbers to see this more concretely.

Statement 1 (1970): X = $15 median household income. That would make the median income of Y = $10

Statement 2 (1980):
a) X = $15 med. HH income. That would make the med. income of Y = $7.5.
b) X = $10 med HH income. That would make the med. income of Y = $5.

Did Y go from 10 to 7.5 or from 10 to 5? Those will give different percentage decreases and both are valid possibilities. Insufficient.