求教几道机考题 - ChaseDream

1. A rectangular tabletop consists of a piece of laminated wood bordered by a thin metal strip along its four edges. The surface area of the tabletop is x square feet, and the total length of the strip before it was attached was x feet. If the tabletop is 3 feet wide, what is its approximate length, in feet ?
(A) 12 (B) 10 (C) 9 (D) 8 (E) 6
答案是E，
有一个人给我的解释是：“这题就是说这个长方形的边长和面积都是x，所以设lenth为L，
那么2(L+3)=3L，好像x都没用。解方程得到答案。”
可我没弄明白他的解释。

2.A student is asked to pick marbles from a bag that contains 18 marbles. Eight marbles are red, 4 are green, and 6 are black. What is the minimum number of marbles that a blindfolded student would have to draw from the bag to be certain of having at least three marbles of the same color?

答案是7，为什么啊，我觉的是5，三个都是同色的，那8个里面有2*3，4个里面有1*3，6个里面有2*3，不是5吗？

3.A ranch has horses and ponies. Five-sixths of the ponies have horseshoes. Half of the ponies with horseshoes are Icelandic. If there are three more horses than ponies, what is the minimum number of horses and ponies on the ranch?

答案是27，怎么求出来的呢？设，H+P=X， 5/6X=H，P=1/6X， 1/2*5/6X= 5/12X，最小的话不应该是12吗？

4.A rectangular tiled floor consists of 70 square tiles. The rectangular floor is being rearranged so that 2 tiles will be removed from each row of tiles and 4 more rows of tiles will be added. After the change in layout, the floor will still have 70 tiles, and it will still be a rectangle. How many rows were in the tile floor before the change in layout?

答案是10，我设长的row=L ，短的row=W， LW=70，（L-2）（W+4）=70 = LW+4L-2W-8，方程最后多了个4L-2W=8，下面该怎么做啊？

以下是引用yoo_hoo在2004-4-25 15:00:00的发言：

2(L+3)=x周长；3L=x(面积）

答案是7，为什么啊，我觉的是5，三个都是同色的，那8个里面有2*3，4个里面有1*3，6个里面有2*3，不是5吗？

数学上称为“抽屉原则”，很简单：2(每组数）*3(组数)+1=7

答案是27，怎么求出来的呢？设，H+P=X， 5/6X=H，P=1/6X， 1/2*5/6X= 5/12X，最小的话不应该是12吗？

没看懂：horseshoe: HS; Horse: H; Pony: P

H-P=3; 5/6*P有HS; 5/6P*1/2是I ？？？

谁来讲讲

答案是10，我设长的row=L ，短的row=W， LW=70，（L-2）（W+4）=70 = LW+4L-2W-8，方程最后多了个4L-2W=8，下面该怎么做啊？

W=2L-4代入LW=70解一元二次方程。

谢谢先

总数是 1/2*5/6*P+(P+3) = 5/12*P+P+3。为使5/12*P有意义，P最小是12，所以总数最小是27。