4.5 .lu ， I Answer Explanations
PS07058
- David used part of $100,000 to purchase a house. Of
1
the remaining portion, he invested—of it at 4 percent
3
simple annual interest and -of it at 6 percent simple
3
annual interest. If after a year the income from the
two investments totaled $320, what was the purchase
price of the house?
(A)
(B)
(C)
(D)
(E)
$96,000
$94,000
$88,000
$75,000
$40,000
Algebra
Let x be the amount, in dollars, that David used
to purchase the house. Then David invested
1
(100,000 - x) dollars, —at 4% simple annual
2 3
interest and - at 6% simple annual interest. After
3
one year the total interest, in dollars, on this
1
investment was -(100,000 - x)(0.04) +
2 3
—(100,000 - x)(0.06) = 320. Solve this equation
3
to find the value of x.
1
- (100,000 - x)(0.04) +
3
2
3
—(100,000 - x)(0.06) = 320
(100,000 - x)(0.04) +
2(100,000 - x)(0.06) = 960
4,000 - 0.04x +
12,000-0.12x = 960
16,000 - 0.16x = 960
given
multiply both
sides by 3
distributive
property
combine like
terms
16,000 - 960 = 0.16x add
0.16x - 960 to
both sides
PS11537
- In the sequence x。, X 1 , Xz, ..., Xn, each term from x 1 to
xk is 3 greater than the previous term, and each term
from xk + 1 to Xn is 3 less than the previous term, where
n and k are positive integers and k < n. If x0 = Xn = 0
and if xk = 15, what is the value of n?
(A)
(B)
(Cl
(D)
(E)
56905
11
Algebra
Since x。= 0 and each term from x 1 to xk is 3
greater than the previous term, then
xk = 0 + (k)( 3 ). Since xk = 15 , then 15 = 3k and
k = 5. Since each term from xk + 1 to xn is 3 less
than the previous term, then Xn = xk - (n - k)(3).
Substituting the known values for xk, Xm and k
gives O = 15 - (n - 5)(3), from which it follows
that 3n = 30 and n = 10.
The correct answer is D.
p Q R
M T S
Note: Not drawn to scale.
PSJ 1145
- In the figure shown above, line segment QR has length
12, and rectangle MPQT is a square. If the area of
rectangular region MPRS is 540, what is the area of
rectangular region TQRS?
(A)
(8)
(Cl
(D)
(E)
144
216
324
360
396
100,000 - 6,000
94,000
=x divide both
sides by 0.16
=x
Therefore, the purchase price of the house
was $94,000.
The correct answer is B.
