Bunuel wrote:
Last year the average (arithmetic mean) cost of 5 computer models was $2,000. What is the average cost of the same 5 computer models this year?
(1) For 3 of the 5 models, the cost this year is 12 percent lower than the cost last year.
(2) For 2 of the 5 models, the cost this year is 10 percent higher than the cost last year.
MANHATTAN GMAT OFFICIAL SOLUTION:Last year, the 5 computer models cost a total of (5)($2,000) = $10,000. We cannot assume that each computer model cost exactly $2,000, as some might be more expensive than others. To determine the average cost of the 5 models this year, we would need the total cost of the 5 models this year.
(1) INSUFFICIENT: Since we do not know the actual costs of any of the computer models, there is no way for us to determine the effect of reducing 3 of them by 12 percent. Further, we do not know how the price of the other 2 models might have changed.
(2) INSUFFICIENT: Since we do not know the actual costs of any of the computers, there is no way to determine the effect of increasing 2 of them. Further, we do not know how the price of the other 3 models might have changed.
(1) AND (2) INSUFFICIENT: Now that we know 3 models decreased by 12% and the other 2 models increased by 10%, it might be tempting to assume that each cost $2,000 last year simply so that we can compute the new total cost:
Total cost this year = (3)(0.88)($2,000) + (2)(1.1)($2,000) = $9,680
However, it is very dangerous to make assumptions on Data Sufficiency questions. Given that the total cost last year was $10,000, it is possible, for example, that the 3 models that decreased in price were $2,500 last year, and the 2 models that increased in price were $1,250. In that case:
Total cost this year = (3)(0.88)($2,500) + (2)(1.1)($1,250) = $9,350
The correct answer is E. _________________