Prep t2 ps 95,127,170

[a-jan]

The total of Company C's assets in 1994 was 300 percent greater than the total in 1993, which in turn was 400 percent greater than the total in 1992. If the total of Company C's assets in 1992 was N dollars, which of the following represents the total of Company C's assets, in dollars, in 1994 ?

(A) 7N
(B) 8N
(C) 9N
(D) 12N
(E) 20N

ANS: E ( 選不到 >< ，不知是腦袋又在那邊卡住了)

In May, Xiang sold 15 used cars. For these 15 cars, the range of the selling prices was $15,000 and the lowest selling price was $4,500. In June, Xiang sold 10 used cars. For these 10 cars, the range of the selling prices was $16,500 and the lowest selling price was $6,100. What was the range of the selling prices of the 25 used cars sold by Xiang in May and June?

(A) $15,600
(B) $15,750
(C) $16,820
(D) $18,100
(E) $19,200

ANS: D

For any triangle T in the xy-coordinate plane, the center of T is defined to be the point whose x-coordinate is the average (arithmetic mean) of the x-coordinates of the vertices of T and whose y-coordinate is the average of the y-coordinates of the vertices of T. If a certain triangle has vertices at the points (0,0) and (6,0) and center at the point (3,2), what are the coordinates of the remaining vertex?

(A) (3,4)
(B) (3,6)
(C) (4,9)
(D) (6,4)
(E) (9,6)

ANS: B ( 為什麼是B, 也可能我對題目有誤解 )

好心人解說一下，感恩

[oneseven]

1.
1994=(1+300%)1993
1993=(1+400%)1992
把1992用N帶入就得到1994=20N

2.
In May
lowest price=4500
因為range是15000
可以得highest price=19500

In June
lowest price=6100
因為range是16500
可以得highest price=22600

用最大-最小得到May and June的range =18100

3.
題目是說三角形的中心點是T
如果三角形的三頂點與一個圓相切(也就是外接一個圓)
此圓的圓心就是三角形的中心點(T)
此中心點是原直徑的 1/3

所以(3,2) 就是在那1/3的位置
這樣就可以推出三角形另一頂點是(3,6)

[oneseven]

第三題好像說的很複雜
希望這樣對你理解有幫助

[a-jan]

呵~ 看來第一題我腦袋真的是卡到了... ( 下次偶自己要注意嚕 )

謝謝你的解題，很清楚 ( 還有很用心的附上圖 )

[pimi]

第三題我的理解是這樣
題目中定義三角形的中心點是由三頂點的x軸的平均值以及三頂點y軸的平均值可得知
之後題目告知三頂點中的兩點(0,0) and (6,0)
又告之中心點是(3,2) 問剩餘的那一頂點的座標為何?

直接用題目給予的公式來做套用 : 三角形的中心點是由三頂點的x軸的平均值以及三頂點y軸的平均值可得知

設剩餘頂點為(a, b)
a+6+0/3=3
b+0+0/3=2
得出(a,b)=(3,6)