60 and 120 only
. The two values given are the area of the park and three
out of the four sides of the perimeter of the park. If the side without fencing is
a length, the equation for the overall length of the existing fence is 180 = 2
W
+
L
, so
L
= 180 – 2
W.
The equation for the area of the park is
LW
= 3,600.
With two variables and two equations, it is now possible to solve for the
possible values of
L
:
L
×
W
= 3,600
L
= 180 – 2
W
(180 – 2
W
)
W
= 3,600
180
W
– 2
W
2
= 3,600
90
W
–
W
2
= 1,800
0 =
W
2
– 90
W
+ 1,800
0 = (
W
– 60)(
W
– 30)
So
W
= 30 or 60. Plug each value back into either of the original two
equations to solve for the corresponding length, which is 120 or 60,
respectively.
23.
(B)
. This rectangle problem requires applying the perimeter and area
formulas. The area of a rectangle is equal to length times width (
A
=
LW
) and
the perimeter is 2
L
+ 2
W
= 268. The question states that the length equals
168% of the width,
L
= 1.68
W
.
2
L
+ 2
W
= 268
L
+
W
= 134
1.68
W
+
W
= 134
2.68
W
= 134
W
= 50
Solve for
L
by plugging 50 in for
W
in either equation:
L
+ 50 = 134
L
= 84
A
= 84(50) = 4,200
24.
(C)
. From the first sentence, calculate Randall’s change (20.00 – 19.44 =
0.56). Then it’s a matter of systematic tests to determine the various
combinations of dimes and pennies that Randall could have received,
stopping when one matches an answer choice listed:
5 dimes (0.50) + 6 pennies (0.06) = 11
coins
Not an option in the
choices
4 dimes (0.40) + 16 pennies (0.16) = 20
coins
Not an option in the
choices
3 dimes (0.30) + 26 pennies (0.26) = 29
coins
Correct answer
25.
(C)
. To double from the current population of 7 billion people, the
population would need to increase by 7 billion. If the population increases by
1 billion every 13 years, an increase of 7 billion would take 7 × 13 = 91 years.
26.
(A)
. Gerald spent $1,200 + $305 = $1,505 total on purchase and repairs.
The selling price was 20% more, or 1.2 times this amount. Either plug 1.2 ×
1,505 into the calculator to get $1,806, or recognize that 1.2 of $1,500 is
exactly $1,800, so Quantity A is a little more than that.
27.
(A)
. There are a few options for solving the given problem. First, you
could find out exactly what
x
equals by setting up an equation: “1,500 is
x
percent of 300,000” translates algebraically to 1,500 =
(300,000).
Solving the equation will reveal that
x
= 0.5, so the commission is 0.5%.
Taking 0.5% of $180,000 gives $900 for Quantity A, which is greater than
Quantity B.
Alternatively, you could reason by proportion:
=
.
This works because the commission the salesman earns represents the same
proportion of the total in all cases, so any changes to the total will be reflected
in changes to the commission. This gives the same value for Quantity A,
$900, and is still greater than Quantity B.
|