2. 外语
  3. Three dice, each with faces numbered 1 through 6, were tossed onto a game board. If one of the dice turned up 4, what was the su

Three dice, each with faces numbered 1 through 6, were tossed onto a game board. If one of the dice turned up 4, what was the su

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问题 Three dice, each with faces numbered 1 through 6, were tossed onto a game board. If one of the dice turned up 4, what was the sum of the numbers that turned up on all three dice?
(1) The sum of two of the numbers that turned up was 10.
(2) The sum of two of the numbers that turned up was 11.
选项 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.
答案B
解析 Determine the sum of the numbers that turned up when three dice were tossed, given that one of the dice turned up 4.
(1)     Given that the sum of two of the numbers was 10, the numbers that turned up on the three dice could be 5,4, and 5 (5 + 5 = 10) for a total sum of 14. On the other hand, they could be 2,4, and 6 (4 + 6 = 10) for a total sum of 12; NOT sufficient.
(2)     The number 4 could not have been one of the two numbers whose sum was 11 because 11-4 = 7 and 7 is not a number that can turn up on the dice. Therefore, since 11 can be obtained only when the other two numbers are 5 and 6, the numbers that turned up on the three dice must be 4, 5, and 6 for a total sum of 15; SUFFICIENT.
The correct answer is B;
statement 2 alone is sufficient.
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