Given an area of 12,000 square feet, the shortest possible rectangular perimeter is achieved with a square, in which all sides are the same length.. This corral would require more fence
Trang 1segments remain ahead Since the
boat’s average speed is the same
before and after buoy 10, it takes the
boat 5 3 5 = 25 minutes to travel
from buoy 10 to buoy 15
10 The correct answer is (A) Given n
= 2, the 25th term of Set R = 25n +
25 = 25(2) + 25 = 75 Given n = 2, the
24th term of Set S = n + 23 = 2 + 23
= 25, and two times that 24th term is
50
11 The correct answer is (C) There’s
no need to calculate either quantity,
and you can cancel the product st
from both columns To make the
comparison, observe the place-value
shifts from the decimal number 9.3
In Column A, the decimal point
shifts 3 places left (9,300) and 3
places right (.0093), so the quantity
is equivalent to (9.3)(9.3) You can
now see that Quantity B, which is
(9.3)(9.3), is the same as Quantity A
12 The correct answer is (B) There’s
no need to calculate either quantity
Given an area of 12,000 square feet,
the shortest possible rectangular
perimeter is achieved with a square,
in which all sides are the same
length Column B describes a corral
with a width of 300 feet and a length
of 400 feet This corral would require
more fence posts than a square
corral
Think of Cynthia’s average rate as
the average of eight equally
weighted one-hour trips Seven of
those trips receive a weight of 50,
and one of the trips receives a weight
of 60 You can express this
algebra-ically as follows:
8
8
410
Cynthia’s average rate during the entire trip was 51.25 mph (There’s
no need to round either up or down
to the nearest hundredth.)
14 The correct answer is (D)
Sep-tember and October each saw pre-cipitous declines in the price of BioFirm stock and CompuWin stock, but only a modest increase in the price of Ardent stock During each of these two months, the aggregate change was clearly negative In July, however, a substantial price increase
in CompuWin stock more than offset the combined decrease in the price of the other two stocks
15 The correct answer is (E) The
investor paid about $800 for 40 shares of Ardent stock (priced at about $20 per share), and then sold those 40 shares for about $2,200 (priced at about $55 per share)
Accordingly, the investor’s profit amounted to approximately $1,400
16 The correct answer is (B) The
area of any triangle = 1
2 3 base 3 height Using 7 kilometers as the base of the triangle in this problem, the triangle’s height is the north-south (vertical) distance from A to an imaginary line extending west from
B Given that farmhouse A is located
a total of 10 kilometers farther west than farmhouse C, the extension is 3 kilometers long The triangle’s height is 4 kilometers (32 + 42 = 52,
by the Pythagorean theorem)
Accordingly, the area of triangle ABC
= 1
2 3 7 3 4 = 14 km2
Practice Test 2 433
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Trang 217 The correct answer is (B) You can
make the comparison quickly by rec-ognizing that Quantity A is the
“dif-ference of two squares” (x2 2 y2) in
the factored form (x + y)(x 2 y), where y = 2 Or, you can multiply the
two binomials in Column A, and then
simplify: (x + 2)(x 2 2) = x2+ 2x 2 2x
2 4 = x22 4 Since x22 4 , x22 2, Quantity A , Quantity B
18 The correct answer is (A) K
percent is based on $100 Therefore,
K percent = K dollars, and Quantity
B will always be $1 less than Quantity A
19 The correct answer is (A) Apply
the formula for determining arith-metic mean (called AM below), or
simple average Letting x equal the other number, solve for x:
= +
− =
x x x x
2
2 2
2
20 The correct answer is (D) Letting
x equal the number of ounces of soy sauce added to the mixture, 18 + x
equals the total amount of the mixture after the soy sauce is added
The amount of peanut sauce (5.76 ounces) must equal 12% of the new total amount of the mixture, which is
18 + x You can express this as an algebraic equation and solve for x: 5.76 5 0.12~x + 18!
576 5 12~x + 18!
576 5 12x + 216
360 5 12x
30 5 x
30 ounces of soy sauce must be added
to achieve a mixture that includes 12% peanut sauce
21 The correct answer is (C) x + y +
the measure of the third interior
angle (let’s call it w) = 180 Also, w +
z = 180 (because their angles combine to form a straight line) So, you have two equations:
x + y + w = 180 or x + y = 180 2 w
w + z = 180 or z = 180 2 w Therefore, x + y = z (Quantity A =
Quantity B)
22 The correct answer is (D) The
centered information establishes that Quantity B, pq, must be negative, because the product of a positive number and a negative number is always negative As for Quantity A, try substituting some
simple numbers for p and q If p = 1 and q = 21, then p + q = 0 while pq =
21, and therefore p + q pq But if p
=1
4and q = 2
1
2, p + q = 2
1
4while pq
=1
8, and therefore p + q , pq Thus, which quantity is greater depends on
the values of p and q.
23 The correct answer is (B) The
range of D = 10 2 3 = 7 The median
of D = the arithmetic mean of 6 and 9 (the two middle terms) = 7.5
PART VI: Five Practice Tests 434
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Trang 324 The correct answer is (B) Let {A,
B, C, D, E} represent the set of ice
cream flavors 10 triple-scoop
combi-nations are available:
{ABC}{ABD}{ABE}{ACD}{ACE}{ADE}
{BCD}{BCE}{BDE}{CDE}
Each of these combinations is
available on either of the two cone
types Thus, the total number of
dis-tinct triple-scoop cones having three
different ice cream flavors is 20
25 The correct answer is (C) The
question asks you to select the choice
that does NOT describe sales
totaling at least 10,000 Choice (C)
describes 1.7K + 4.9K + 2.2K = 8.8K
sales, which is less than $10,000
Choice (A) describes 8.5K + 1.9K =
10.4K sales Choice (B) describes
7.5K + 1.0K + 2.0 + 0.8 = 11.3K sales
Choice (D) describes 4.9K + 5.1K =
10.0K sales Choice (E) describes
8.5K + 4.9K = 13.4K sales
26 The correct answer is (A) The
number of basic models was 13,800
(the sum of all numbers in the
“Basic” column) The number of
standard models sold was 29,900
(the sum of all numbers in the
“Standard” column) The difference
is 16,100 To find the average premium paid for a standard model, divide $41,000,000 by $16,100
Rounding these figures to $40 million and $16,000, the quotient is
$2,500
Without the square hole, each of the cube’s six outer surfaces contains 9 square inches, for a total of 54 square inches of outer surface area
The square hole reduces that total outer surface area by 2 square inches, to 52 Each of the four inner surfaces (inside the hole) accounts for an additional 3 square inches, for
a total of 12 square inches of inner surface areas The solid’s total surface area is 52 + 12 = 64 square inches
28 The correct answer is (B) Since x
is a negative number (less than 21),
x3 is negative and x2 is positive
Hence, Quantity A is a negative
number less than x3 Quantity B, on the other hand, is a positive number
greater than x2
Practice Test 2 435
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Verbal Reasoning
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28. j A j B j C j D j E
(ii)
(iii)
30. j A j B j C j D j E
Practice Test 3
441
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