题目信息
Bowls X and Y each contained exactly 2 jelly beans, each of which was either red or black. One of the jelly beans in bowl X was exchanged with one of the jelly beans in bowl Y. After the exchange, were both of the jelly beans in bowl X black?
A:Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B:Statement (2) ALONE is sufficient, but statement (1) 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.
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正确答案：
E:Statements (1) and (2) TOGETHER are NOT sufficient.
Arithmetic Sets
Determine after an exchange of one jelly bean if both jelly beans in bowl X are black.
Bowl X has two black jelly beans, but bowl Y could have two red or two black or one of each color. If bowl Y has two red jelly beans, then bowl X will have one red and one black jelly bean after the exchange, not two black. However, if bowl Y has two black jelly beans, then bowl X will have two black after the exchange; NOT sufficient. After the exchange, bowl Y has one red and one black. If, before the exchange, bowl X had two black and bowl Y had two red, then after the exchange, each of bowl Y and bowl X will have one of each color. However, if bowl Y had two black jelly beans, bowl X had one of each color, and bowl X obtained a black in exchange for the red, then bowl Y will have one of each color and bowl X will have two black; NOT sufficient.
Taking (1) and (2) together, bowl X had two black jelly beans to start with and bowl Y ended up with one of each color after the exchange. bowl Y had to have had at least one red because bowl X had no red jelly beans to give to bowl Y. If bowl Y has two red and exchanges a red for one of bowl X's blacks, then, after the exchange, bowl Y will have one of each color, but bowl X will not have two black. On the other hand, if bowl Y has one of each color and exchanges its black for one of bowl X's blacks, then after the exchange, bowl Y will have one of each color and bowl X will have two blacks.
The correct answer is E;both statements together are still not sufficient.
Determine after an exchange of one jelly bean if both jelly beans in bowl X are black.
Bowl X has two black jelly beans, but bowl Y could have two red or two black or one of each color. If bowl Y has two red jelly beans, then bowl X will have one red and one black jelly bean after the exchange, not two black. However, if bowl Y has two black jelly beans, then bowl X will have two black after the exchange; NOT sufficient. After the exchange, bowl Y has one red and one black. If, before the exchange, bowl X had two black and bowl Y had two red, then after the exchange, each of bowl Y and bowl X will have one of each color. However, if bowl Y had two black jelly beans, bowl X had one of each color, and bowl X obtained a black in exchange for the red, then bowl Y will have one of each color and bowl X will have two black; NOT sufficient.
Taking (1) and (2) together, bowl X had two black jelly beans to start with and bowl Y ended up with one of each color after the exchange. bowl Y had to have had at least one red because bowl X had no red jelly beans to give to bowl Y. If bowl Y has two red and exchanges a red for one of bowl X's blacks, then, after the exchange, bowl Y will have one of each color, but bowl X will not have two black. On the other hand, if bowl Y has one of each color and exchanges its black for one of bowl X's blacks, then after the exchange, bowl Y will have one of each color and bowl X will have two blacks.
The correct answer is E;both statements together are still not sufficient.
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