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  3. 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

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

admin2022-10-18  45
问题 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?
(1) The volume of the top block is 8 cubic centimeters.
(2) The height of the stack of blocks is 10 centimeters.
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E
解析 (1)     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.
(2)     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 length; 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.
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