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题库 / GMATAdvanced-DS-53
When opened and lying flat, a birthday card is in the shape of a regular hexagon. The card must be folded in half along 1 of its diagonals before being placed in an envelope for mailing.Assuming that the thickness of the folded card will not be an issue, will the birthday card fit inside a rectangular envelope that is 4 inches by 9 inches?
(1)Each side of the regular hexagons 4 inches long.
(2)The area of the top surface(which is the same as the area of the bottom surface)of the folded birthday cardis less than 36 square inches.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
原来条件2说的是摺叠后的面积（因为提到了top和bottom surface）
条件2说的是折叠后的梯形面积，我是设的边长为2a，这样好算一点
折叠后的梯形面积就是(3√3·a^2)，让这个数小于36，算得a^2小于4√3，可以粗略算出a小于2.6或大于-2.6，因为是边长所以取区间（0，2.6）
如果a=2.6，折叠后梯形下底边长是4a，所以4*2.6=11.4，大于9，不行；如果a=2，4*2=8，小于9，行。
所以条件2不充分
2）设边长为x ， 面积等于 3根号3*X^ 2小于36*4，主要在于X有两个解
2)卡片折完面積小於36 需確認是否能放進信封 求卡片折後的長寬
設邊長為x,面積36(無限接近) 可求得長寬
(2)设边长为x，则六边形面积=3根号3/4*x^2
请问条件2为什么错呢？
X
设边长为x，要能放进去，则根据对角线9高8能算出来边长要小于等于4.5，边长平方小于等于20.25
(2)六边形面积=3根号3/2*x^2
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