The graph above shows the cost of manufacturing of two products, A and B, per year. According to the graph, during which year was the cost of manufacturing both products the same?
(A) \(\ \ 2000\)
(B) \(\ \ 2001\)
(C) \(\ \ 2002\)
(D) \(\ \ 2003\)
(E) \(\ \ 2004\)
Correct Answer: C
Tip: If two functions, \(f\) and \(g\), intersect at point \((x,y),\) then \(f(x) = y = g(x)\).
The two lines intersect at (2002, 40). So, in the year 2002, the two products had the same manufacturing cost, $40,000.
(A), (B), (D), and (E)
The two lines do not intersect in any of these years. Therefore, the manufacturing costs for the two products were different in these choices.
The bar graph above shows the distribution of recipes in a certain cookbook. Which of the following pie charts most accurately displays the same data?
Correct Answer: A
In the bar graph, each cookbook item is represented by a rectangle with a certain area, a percentage, and a different pattern. In the pie chart, the areas of the sectors should correspond to the percentages in the bar graph. In other words, desserts should take up 13% of the area of the circle, main entrees should take up 64% of the area of the circle, and so on. Also, that corresponding shapes should have matching patterns. We analyze each of the answer choices.
(A) This seems to be the correct answer. According to the bar graph, the desserts (dots) and the salads (solid black) have the same percentage. The dotted and the solid black sectors in the pie chart indeed have about the same area. There are about half as many snacks as salads, and the area taken up by the snacks (little squares) in the pie chart is about half the area taken up by the salads (solid black). Only 3% of the cookbook is devoted to soups, and the sector with the slanted stripes in the pie chart is the smallest, as expected. 64% of the cookbook is devoted to main entrees, and they seem to take up about two thirds of the circle, as is expected.
(B) Here, the dessert section is hardly discernible, but it is supposed to take up 13% of the area of the circle. And the main section takes up about 80%, instead of 64%. We eliminate this choice.
(C) This pie chart only has 4 categories, but we are given five. We eliminate this choice.
(D) Here, the desserts, snacks, salads, and soups sections seem to have equal areas. But we're given that only the desserts and the salads have the same percentage. This choice is wrong.
(E) Here, the soups and the salads sections have the same area. But we're told that the desserts and the salads have the same percentage, not the soups and the salads. This choice is wrong.
Only the pie chart in choice (A) corresponds to the given bar graph. Therefore, it is the correct answer.
(B), (C), (D), and (E)
The Solution explains why these choices are wrong.