Yesterday, Manhattan GMAT posted a GMAT question on our blog. Today, they have followed up with the answer:
The consumer price index gives us a ratio between prices in 2000 and prices in 2009. We are told that “for every Zeropian dollar spent on consumer goods in 2000, $1.75 on average had to be spent in 2009.” In other words, if something cost X dollars in 2000, it cost 1.75×X dollars in 2009 (as long as the price increased exactly according to the index, which is just an average). In dollar terms, the increase in price would then be 1.75×X – X = 0.75×X dollars.
We are asked for this dollar price increase for Brand Z running shoes. Representing the price of these shoes in 2000 as X, as we already have, we can rephrase the question as “What is 0.75×X?” We can further rephrase this question to “What is X?”
(1) SUFFICIENT. We are told that the price of the shoes in 2009 is $91. We have represented the 2009 price as 1.75×X dollars, staying consistent with our variable naming throughout the problem (never change variable designations midstream unless you’re starting over completely). So we can write an equation:
1.75×X = 91
We know we can solve for X, so we can answer the question. (Incidentally, if we had to solve for this X on a Problem-Solving problem, one fast way would be to convert 1.75 to a fraction. 1.75 = 7/4, so we can quickly write that X = 91×4/7. Since 91/7 = 13, we get X = 13×4 = 52.)
(2) INSUFFICIENT. We are told that the price increase in dollar terms, divided by the price of the shoes in 2009, is 3/7. However, this information is already completely implied by the stem. If the index is 1.75, then any good’s price increase was 75%, or 75 cents for every 2000 dollar. Since the 2009 price is $1.75 for every 2000 dollar, the ratio of the price increase ($0.75) to the 2009 price ($1.75) will always be 0.75/1.75, or 3/7. This holds true no matter what the original 2000 price is, so we cannot determine X through this bit of redundant information.
The correct answer is (A): Statement 1 by itself is sufficient to answer the question, but Statement 2 is not sufficient.