PS11454- In the xy-plane, the points (c,d), (c,-d), and (-c,-d) are
three vertices of a certain square. If c < 0 and d > 0,
which of the following points is in the same quadrant
as the fourth vertex of the square?
(Al (-5,-3)
(Bl (-5,3)
(Cl (5,-3)
(D) (3,-5)
(El (3,5)Geometry
Because the points (c,d) and (c, 动 lie on the same
vertical line (the line with equation x = c), one
side of the square has length 2d and is vertical.
Therefore, the side of the square opposite this side
has length 2d, is vertical, and contains the vertex
(-c, 动. From this it follows that the remaining
vertex is (-c, 心，because (-c, 心lies on the same
vertical line as (-c, 动 (the line with equation
x = -c) and these two vertices are a distance 2d
apart. Because c < 0 and d > 0, the point (-c,d) has
positive x-coordinate and positive y-coordinate.
Thus, the point (-c,d) is in如adrant I. Of the
answer choices, only (3,5) is in如adrant I.Th e correct answer 1s E.
PS05470
123.If the amount of federal estate tax due on an estate
valued at $1.35 million is $437,000 plus 43 percent
of the value of the estate in excess of $1.25 million,
then the federal tax due is approximately what percent
of the value of the estate?A. 30%- 35%
C. 40%
D. 45%
E. 5 0%
＝＝4.5 Answer ExplanationsArithmetic
The amount of tax divided by the value of the
estate is[0.437 + (0.43)(1.35 -1.25)]贮曲而valueas
1.35贮芦 fraction0.437 + (0.43)(0.1)
1.35arithmetic0.48 ＝ 48
1.35 135arithmeticBy long division, 坐isapproximately 35.6, so
135
the closest answer choice is 35%.Al ternat1vel y, —^48 can be estimated b
135y—^48 =—=^6 - = - =^6 1 33%, so the closest answer
136 17 18 3
choice is 35%. Note that—^48. 1s greater than—^48
135 136
and—^6 1s greater. than一^6 ，sothe correct value is
17 18
greater than 33%, which rules out 30% being the
closest.1h e correct answeris B.
PS05924，- If 3 = x%, then X=
104
(Al 0.3
(B) 0.03
(Cl 0.003
(D) 0.0003
(El 0.00003
Arithmetic
3 X
Given that—-=炒Yo,and writing xo/o as—, it
104 100
follows that^3 = x. Multiplying both sides by
104 100(^100) gives x =—^300 =^300 =—^3 =0.03.
104 10, 000 100
Th e correct answer 1s B.