题目信息
If cubical blocks in a display are stacked one on top of the other on a flat surface, what is the volume of the stack of blocks in cubic centimeters?
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.
参考答案及共享解析
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已选答案：
正确答案：
E:Statements (1) and (2) TOGETHER are NOT sufficient.
Geometry Volume
It is given that the volume of the top cube in the stack is 8 cubic centimeters, from which it follows that the top block has edges of length 2 cm, but no information is given about the size of the other blocks in the stack or how many blocks the stack contains; NOT sufficient. It is given that the height of the stack of blocks is 10 cm, but no information is given about the size of any of the blocks in the stack or how many blocks are in the stack.
Taking (1) and (2) together gives no information about the size of the blocks below the top block or how many blocks are in the stack. For example, there could be two blocks with edges of lengths 2 cm and 8 cm. The volume of the top block would be 8 cubic centimeters, the height of the stack would be 10 cm, and the volume of the stack of blocks would be 520 cubic centimeters. But there could also be three blocks with edges of lengths 2 cm, 3 cm, and 5 cm. The volume of the top block would be 8 cubic centimeters, the height of the stack would be 10 cm, and the volume of the stack of blocks would be 160 cubic centimeters.
The correct answer is E;both statements together are still not sufficient.
Tip Do not assume anything that is not explicitly stated in the problem. In this problem, it is tempting to assume that all of the blocks are identical, in which case there would be five blocks, each with height 2 cm to give the whole stack a height of 10 cm and a volume of 40 cubic centimeters. Under the assumption that all of the blocks are identical, the correct answer would be C.
It is given that the volume of the top cube in the stack is 8 cubic centimeters, from which it follows that the top block has edges of length 2 cm, but no information is given about the size of the other blocks in the stack or how many blocks the stack contains; NOT sufficient. It is given that the height of the stack of blocks is 10 cm, but no information is given about the size of any of the blocks in the stack or how many blocks are in the stack.
Taking (1) and (2) together gives no information about the size of the blocks below the top block or how many blocks are in the stack. For example, there could be two blocks with edges of lengths 2 cm and 8 cm. The volume of the top block would be 8 cubic centimeters, the height of the stack would be 10 cm, and the volume of the stack of blocks would be 520 cubic centimeters. But there could also be three blocks with edges of lengths 2 cm, 3 cm, and 5 cm. The volume of the top block would be 8 cubic centimeters, the height of the stack would be 10 cm, and the volume of the stack of blocks would be 160 cubic centimeters.
The correct answer is E;both statements together are still not sufficient.
Tip Do not assume anything that is not explicitly stated in the problem. In this problem, it is tempting to assume that all of the blocks are identical, in which case there would be five blocks, each with height 2 cm to give the whole stack a height of 10 cm and a volume of 40 cubic centimeters. Under the assumption that all of the blocks are identical, the correct answer would be C.
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