Directions: For this section, solve each problem and decide which is the best of the choices given.. They are drawn as accurately as possible EXCEPT when it is stated in a spe-cific probl
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3. In the figure above, what is the value of x?
(A) 40 (B) 45 (C) 60 (D) 75 (E) 90
1. If n is 3 times an even number, then which of
the following could be n?
(A) 14
(B) 15
(C) 16
(D) 17
(E) 18
2. A machine can produce 50 computer chips in
2 hours At this rate, how many computer
chips can the machine produce in 7 hours?
(A) 175
(B) 200
(C) 225
(D) 250
(E) 275
2x°
x°
20 questions
Turn to Section 3 of your answer sheet to answer the questions in this section. Directions: For this section, solve each problem and decide which is the best of the choices given Fill in
the corresponding circle on the answer sheet You may use any available space for scratchwork
1 The use of a calculator is permitted
2 All numbers used are real numbers
3 Figures that accompany problems in this test are intended to provide information useful in solv-ing the problems They are drawn as accurately as possible EXCEPT when it is stated in a spe-cific problem that the figure is not drawn to scale All figures lie in a plane unless otherwise indicated
4 Unless otherwise specified, the domain of any function f is assumed to be the set of all real num-bers x for which f(x) is a real number.
The number of degrees of arc in a circle is 360
The sum of the measures in degrees of the angles of a triangle is 180
r
A = πr2
C=2 πr
ᐉ
w
A = ᐉw A = 1 / 2bh V = ᐉwh V = πr2h c2= a2+ b2 Special right triangles
h
w h
r
h b c
a
2x
x
x s s
s
3
2
30 °
60°
45° 45°
Trang 23 3 3 3 3 3
GO ON TO THE NEXT PAGE
4. Any positive integer that is divisible by 6 and
15 must also be divisible by
(A) 12
(B) 21
(C) 30
(D) 72
(E) 90
5. If n percent of 20 is 4, what is n?
(A) 1⁄5
(B) 2
(C) 5
(D) 20
(E) 500
6. If f (x) = 3x + n, where n is a constant, and
f(2) = 0, then f(0) =
(A) −6
(B) −2
(C) 0
(D) 2
(E) 6
7. A square has the same area as a right triangle
with sides of lengths 6, 8, and 10 What is the
length of one side of the square?
(A) 4
(B)
(C)
(D)
(E) 12
8. If 12v = 3w and v ≠ 0, then which of the
fol-lowing is equivalent to 2w − 8v?
(B) 4w
(C) −6w
(D) 2v
(E) −2v
2 6
15
2 3
9. If x is a negative number and 2 x + 1 > 5, then
which of the following must be true?
(A) x < −3 (B) x < −2.5 (C) x < −2 (D) x > −2 (E) x > −5
10. If x = −2, then −x2− 8x − 5 =
(A) 3 (B) 7 (C) 15 (D) 23 (E) 25
11. If , then what is the smallest possible
positive value of m?
(A) 6 (B) 6.5 (C) 7 (D) 7.5 (E) 8
12. Theo wants to buy a sweater that is priced at
$60.00 before tax The store charges a 6% sales tax on all purchases If he gives the cashier
$70.00 for the sweater, how much should he receive in change?
(A) $3.60 (B) $6.40 (C) $7.40 (D) $9.40 (E) $66.40
5 2 3
m≤
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Which of the following expresses the result
when 2m is added to s?
(A) s + 2n − 2r
(B) s + 2n + 2r
(C) 2s + 2n − 2r
(D) 2s + 2n + 2r
(E) s − 2n + 2r
Note: Figure not drawn to scale
14. In the figure above, the slope of line l is
and the area of the triangle is 48 square units
What is the value of x + y?
(A) 13
(B) 14
(C) 19
(D) 22
(E) 96
15. Ellen takes a trip that is y miles long in total,
where y > 20 She travels the first 15 miles at
an average speed of 30 miles per hour and the
rest of the trip at an average speed of 40 miles
per hour Which of the following represents
the total time of the trip, in hours?
(A)
(B)
(C)
(D) 2 + 40(y − 15)
(E) 1
2+40(y−15)
1
2+40y−15
2 15
40 + −y
1
2
15 40 + −y
3 5
O
ᐉ
(10, y)
(x, 0) x y
square of n, and if y = 8 when m = 16 and
n = 1, then what is the value of y when m = 8 and n= 4?
(A) 0.125 (B) 0.25 (C) 0.5 (D) 1 (E) 2
17. If a + b = s and a − b = t, then which of the fol-lowing expresses the value of ab in terms of s and t?
(A) st
(B) (C) (D) (E)
18. If y = m4 = n3 and y is greater than 1, then
mn= (A) y1/12
(B) y1/7
(C) y7/12
(D) y7
(E) y12
(s2 t2) 2
−
(s2 t2) 4
−
(s t+ ) 2 (s t− ) 2
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Note: Figure not drawn to scale.
19. In the figure above, if AB = 6 and BC = 12, what
is the area of the shaded region?
(A) 20
(B) 22
(C) 24
(D) 26
(E) 28
4
A
20. Every car at a certain dealership is either a convertible, a sedan, or both If one-fifth of the convertibles are also sedans and one-third of the sedans are also convertibles, which of the following could be the total number of cars at the dealership?
(A) 28 (B) 29 (C) 30 (D) 31 (E) 32
STOP
If you finish before time is called, you may check your work on this section only Do not turn to any other section of the test.
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1. A square has a perimeter of 36 centimeters
What is its area in square centimeters?
(A) 24
(B) 36
(C) 49
(D) 64
(E) 81
2. If b is a positive integer less than 100, then how many integer pairs (a, b) satisfy the
equation ?
(A) 7 (B) 8 (C) 9 (D) 10 (E) 11
a
b= 1 10
18 questions
Turn to Section 4 of your answer sheet to answer the questions in this section. Directions: This section contains two types of questions You have 25 minutes to complete both types.
For questions 1–8, solve each problem and decide which is the best of the choices given Fill in the cor-responding circle on the answer sheet You may use any available space for scratchwork
1 The use of a calculator is permitted
2 All numbers used are real numbers
3 Figures that accompany problems in this test are intended to provide information useful in solv-ing the problems They are drawn as accurately as possible EXCEPT when it is stated in a spe-cific problem that the figure is not drawn to scale All figures lie in a plane unless otherwise indicated
4 Unless otherwise specified, the domain of any function f is assumed to be the set of all real num-bers x for which f(x) is a real number.
The number of degrees of arc in a circle is 360
The sum of the measures in degrees of the angles of a triangle is 180
r
A = πr2
C=2 πr
ᐉ
w
A = ᐉw A = 1 / 2bh V = ᐉwh V = πr2h c2= a2+ b2 Special right triangles
h
w h
r
h b c
a
2x
x
x s s
s
3
2
30°
60 °
45 ° 45°
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GO ON TO THE NEXT PAGE
3. According to the table above, how much will it
cost, in dollars, to clean each bathroom twice
and each office once in the McKenzie Office
Building?
(A) 200
(B) 400
(C) 450
(D) 600
(E) 850
4. If a2− b2= 10 and a − b = 2, what is the value
of a + b?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
5. For all integers n greater than 1, let f(n) = k,
where k is the sum of all the prime factors of
n What is the value of f(14) − f(6)?
(A) 4
(B) 5
(C) 6
(D) 9
(E) 14
6. The average (arithmetic mean) of four different positive integers is 20 What is the greatest pos-sible value of any of these integers?
(A) 68 (B) 70 (C) 73 (D) 74 (E) 77
7. The radius of circle A is twice the radius of circle B If the sum of their circumferences is
36π, then what is the radius of circle A?
(A) 9 (B) 12 (C) 14 (D) 16 (E) 18
8. The figure above shows a cube How many different planes can be drawn such that each
contains exactly two edges of the cube?
(A) 4 (B) 5 (C) 6 (D) 7 (E) 8
Number of Rooms
in the Building
Cost per Room
to Clean
Room
Type
Bathrooms
Offices
10
30
$20
$15 CLEANING COSTS IN THE McKENZIE OFFICE
BUILDING
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• Mark no more than one circle in any column
• Because the answer sheet will be machine-scored,
you will receive credit only if the circles are filled
in correctly.
• Although not required, it is suggested that you write
your answer in the boxes at the top of the columns to
help you fill in the circles accurately
• Some problems may have more than one correct
answer In such cases, grid only one answer
• No question has a negative answer
3.5 or 7/2 (If is gridded, it will be
interpreted as , not 31 )
2
31 2
1 2
with more digits than the grid can accommodate, it may be either rounded or truncated, but it must fill the entire grid For example, if you obtain an answer such as 0.6666 , you should record your result as
.666 or 667 A less accurate value such as 66 or
.67 will be scored as incorrect.
Acceptable ways to grid 2/3are:
.
0
2 3 4 5
1 0
2 3 4 5
1 0
2 3 4 5
1 2
3 4 5
1
0
2 3 4 5
1 0
2 3 4 5
1 0
2 3 4
1 2
3 4 5 1
Answer: 201 Either position is correct.
Note: You may start your answers
in any column, space permitting.
Columns not needed should be left blank.
.
0
2 3 4 5 6 7 8 9
1 0
2 3 4 5 6 7 8 9
1 0
2 3 4 5 6 7 8 9
1 2
3 4 5 6 7 8 9
1
Grid in
result.
Fraction line
Write answer
in boxes.
Answer: 7 12
.
0
2 3 4 5 6 7 8 9
1 0
2 3 4 5 6 7 8 9
1 0
2 3 4 5 6 7 8 9
1 2
3 4 5 6 7 8 9
1
Decimal point Answer: 2.5
.
0
2 3 4 5 6
1 0
2 3 4 5 6
1 0
2 3 4 5 6
1 2
3 4 5 6
1
.
6 6
0
2 3 4 5 6
1 0
2 3 4 5 6 7
1 0
2 3 4 5 6
1 2
3 4 5 6
1
.
6 6
0
2 3 4 5 6 7
1 0
2 3 4 5 6 7
1 0
2 3 4 5 6 7 8
1 2
3 4 5 6 7 1
Each of the remaining ten questions requires you to solve the problem and enter your answer by mark-ing the circles in the special grid, as shown in the examples below You may use any available space for scratchwork
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9. If 10 less than 2x is 22, then what is the value
of x?
10. In the figure above, if x = 2y, then what is the
value of y?
11. If 8x + 4y = 20, then what is the value of 2x + y =
12. In the xy-plane, the line mx − 3y = 21 passes
through the point (3, 5) What is the value
of m?
13. The ratio of men to women in a room is 4:5
If the room contains three more women than
men, how many women are in the room?
14. If, for some constant value b, the equation
is satisfied by the point (5, 2),
then what is one possible value of b?
y=2x b−
15. A mixture of water and sucrose is 10% su-crose by weight How many grams of pure sucrose must be added to a 200-gram sample
of this mixture to produce a mixture that is 20% sucrose?
16. A runner runs a 16-mile race at an average speed of 8 miles per hour By how many minutes can she improve her time in this race if she trains and increases her average speed by 25%?
Note: Figure not drawn to scale.
17. The area of the figure above is 78 What is its perimeter?
18. Every sophomore at Hillside High School is re-quired to study at least one language among Spanish, French, and Latin, but no one may study more than two If 120 sophomores study Spanish, 80 study French, 75 study Latin, and
50 study two of the three languages, how many sophomores are there at Hillside High School?
4
12 7
x°
y° y°
y°
STOP
If you finish before time is called, you may check your work on this section only Do not turn to any other section of the test.
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1. The - with which the advisor managed the
funds forced his clients to seek more reliable
advice regarding investment
(A) skill
(B) caution
(C) ineptitude
(D) recognition
(E) bitterness
2. As an Armenian born in Iran and educated in Lebanon, Vartan Gregorian brought - fla-vor to the presidency of Brown University that was unprecedented in the Ivy League
(A) a perpetual (B) an authoritative (C) a structured (D) an artificial (E) a cosmopolitan
3. The lawyers did not have time to consider the contract in great detail; rather, they were able
to give it only a - reading before they had
to make their presentation on its merits (A) verbatim
(B) meandering (C) tormented (D) cursory (E) substantial
4. The - in many parts of the city has made the - of infectious diseases more rapid, because pathogens spread quickly in close quarters
(A) overcrowding propagation (B) squalor circulation (C) poverty deterioration (D) congestion elimination (E) proximity resilience
24 questions
Turn to Section 5 of your answer sheet to answer the questions in this section. Directions: For each question in this section, select the best answer from among the choices given and
fill in the corresponding circle on the answer sheet
Each sentence below has one or two blanks,
each blank indicating that something has been
omitted Beneath the sentence are five words
or sets of words labeled A through E Choose
the word or set of words that, when inserted
in the sentence, best fits the meaning of the
sentence as a whole
EXAMPLE:
Rather than accepting the theory
unquestion-ingly, Deborah regarded it with -
(A) mirth
(B) sadness
(C) responsibility
(D) ignorance
(E) skepticism
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Questions 6–7 are based on the following passage.
Towards the middle and the end of the
six-teenth century there were many students and
scholars possessing a great deal of erudition,
but very little means of subsistence Nor were
their prospects very encouraging They first
went through that bitter experience, which,
since then, so many have made after them—
that whoever seeks a home in the realm of
in-tellect runs the risk of losing the solid ground
on which the fruits for maintaining human life
grow The eye directed towards the Parnassus
is not the most apt to spy out the small
tortu-ous paths of daily gain To get quick returns of
interest, even though it be small, from the
capi-tal of knowledge and learning has always been,
and still is, a question of difficult solution
6. The “fruits” mentioned in line 10 represent
(A) spiritual growth
(B) artistic skill
(C) technological progress
(D) the means of acquiring food and shelter
(E) scientific knowledge
GO ON TO THE NEXT PAGE
5. Much research in neuroscience today
endeav-ors to - the mechanisms by which our
brains turn the - data from our sense
organs into coherent and understandable
information
(A) enhance quality of
(B) restore absence of
(C) enlighten source of
(D) attenuate dearth of
(E) elucidate deluge of
7. The “question” in line 16 is whether (A) money can buy happiness (B) intellectuals can earn a good living (C) society can construct effective schools (D) old ideas are relevant to modern society (E) scholars are happier than merchants
Questions 8–9 are based on the following passage.
When there exists an inherited or instinctive tendency to the performance of an action, or
an inherited taste for certain kinds of food, some degree of habit in the individual is often
or generally requisite We find this in the paces of the horse, and to a certain extent in the pointing of dogs; although some young dogs point excellently the first time they are taken out, yet they often associate the proper inherited attitude with a wrong odour, and even with eyesight I have heard it asserted that if a calf be allowed to suck its mother only once, it is much more difficult afterwards
to rear it by hand Caterpillars which have been fed on the leaves of one kind of tree, have been known to perish from hunger rather than to eat the leaves of another tree, although this afforded them their proper food, under a state of nature
8. The “pointing of dogs” (line 7) is mentioned primarily as an example of
(A) an innate habit (B) a behavior that humans find useful (C) a skill that is hard to learn
(D) an ability that many other animals also have
(E) a skill that helps animals to find food
First passage: Jacob Feis Shakespeare and Montaigne, c 1890 Public domain
Second passage: Charles Darwin The Expression of the Emotions in Man and Animals 1872 Public domain
Line 5
10
15 Line
5
10
15
The passages below are followed by questions
based on their content Answer the questions
on the basis of what is stated or implied in the
passage and in any introductory material that
may be provided