Maths Practice Difficult
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School
Carnegie Mellon University *
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Course
607
Subject
Mathematics
Date
Jan 9, 2024
Type
Pages
10
Uploaded by MateOstrich3958
Math
Practice
Section:
Hard
20
Questions
35
Minutes
For
questions
in
the
Quantitative
Comparison
format
(“Quantity
A”
and
“Quantity
B”
given),
the
answer
choices
are
always
as
follows:
(A)
Quantity
A
is
greater.
(B)
Quantity
B
is
greater.
(C)
The
two
quantities
are
equal.
(D)
The
relationship
cannot
be
determined
from
the
information
given.
Where
answer
choices
do
not
appear
on
Quantitative
Comparison
questions
in
this
book,
you
should
choose
A,
B,
C
or
D
based
on
the
above.
For
questions
followed
by
a
numeric
entry
box
|
I,
you
are
to
enter
your
own
answer
in
the
box.
For
questions
followed
by
a
fraction-style
numeric
entry
box
,
you
are
to
enter
your
answer
in
the
form
of
a
fraction.
You
are
not
required
to
reduce
fractions.
For
example,
if
the
answer
is
—,
you
may
enter
or
any
equivalent
fraction.
100
All
numbers
used
are
real
numbers.
All
figures
are
assumed
to
lie
in
a
plane
unless
otherwise
indicated.
Geometric
figures
are
not
necessarily
drawn
to
scale.
You
should
assume,
however,
that
lines that
appear
to
be
straight
are
actually
straight,
points
on
a
line
are
in
the
order
shown,
and
all
geometric
objects
are
in
the
relative
positions
shown.
Coordinate
systems,
such
as
xy-planes
and
number
lines,
as
well
as
graphical
data
presentations
such
as
bar
charts,
circle
graphs,
and
line
graphs,
are
drawn
to
scale.
A
symbol
that
appears
more
than
once
in
a
question
has
the
same
meaning
throughout
the
question.
70°
Quantity
A
Quantity
B
X
6
Quantity
A
Quantity
B
(Zé)x
X
7%
7%
For
a
group
of
test-takers,
the
scores
on
an
aptitude
test
were
normally
distributed,
had
a
mean
of
154,
and
a
standard
deviation
of
3.
Quantity
A
Quantity
B
The
fraction
of
test-takers
in
the
l
group
who
scored
greater
than
158
3
3x+5y+2z=20
6x
+4z=10
Quantity
A
Quantity
B
y
by
itself
2
Romero
Automobiles
sells
cars
only
from
manufacturer
X
and
manufacturer
Y.
The
range
of
the
list
prices
of
the
cars
from
manufacturer
X
is
$22,000.
The
range
of
the
list
prices
of
the
cars
from
manufacturer
Y
is
$15,000.
Quantity
A
5
The
range
of
the
list
prices
of
all
Quantity
B
.
automobiles
sold
by
Romero
$22,000
Automobiles
The
operation
#
is
defined
by
x#
=
—
+
x.
X
Quantity
A
Quantity
B
6.
(4#)#
4.5
The
cube
above
has
side
length
of
4.
Quantity
A
Quantity
B
7.
After
selecting
one
vertex
of
the
=~
When
the
cube
is
placed
on
a
flat
cube,
the
number
of
straight
line
surface,
the
maximum
number
of
segments
longer
than
4
that
can
be
edges
of
the
cube
that
can
be
touching
the
flat
surface
at
once.
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drawn
from
that
vertex
of
the
cube
to
another
vertex
of
the
cube.
8.
If
160%
=
16x,
then
x
is
equivalent
to
which
of
the
following?
(A)
10
B)
235
(C)
2%5?
(D)
2652
(E)
2053
B
40
C
yo
X
p
A
E
9.
In
the
triangle
shown
above,
BA
is
parallel
to
CE.
What
is
the
value
of
x
+y?
10.
If
the
tick
marks
on
the
number
line
below
are
evenly
spaced,
what
value
is
represented
by
x?
v
A)
2°
(B)
2
©)
22°
D)
(3)2°
B
42
11.
If
the
volume
of
a
cube
is
v,
what
is
the
surface
area
of
the
cube
in
terms
of
v?
A
6y
®
()
©
6(%)
(D)
(3/7)2
®
63
12.
What
is
the
area
of
an
equilateral
triangle
with
vertices
at
(-1,
—3),
(9,
—
3),
and
(m,
n)
where
m
and
»n
are
both
positive
numbers?
A)
25/
B)
50./2
(©)
10/3
D)
253
(B)
50,/3
Questions
13—15
are
based
on
the
following
charts.
Marital
Status
of
Military
Personnel
by
Gender
and
Branch
Marital
Status
Army
Navy
Air
Force
Marines
Skl
ol
s
Men
164,513
107,349
94,800
90,949
than
18
years
old
Women
27,492
24,757
25,247
6,338
Single,
with
children
less
Men
26,571
10,506
2,544
4,807
than
18
years
old
Women
11,037
5,859
6,313
1,263
Married,
spouse
is
also
Men
15,058
8,638
20,760
4,719
military
personnel
or
retired
military
Women
14,633
8,832
18,574
3,676
Married
spouseisa
Men
275,953
147,255
142,573
88,233
civilian
Women
21,687
11,175
13,982
1,858
Number
of
Military
Personnel
by
Gender
and
Branch
550,000
500,000
450,000
-
400,000
350,000
-
300,000
M
Men
250,000
-
0,000
B
Women
200,000
1
50,000
C
EE
o
o
—_—
.
100,000
50,000
—
—
.
—
0
.
Army
Navy
Air
Force
Marines
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13.
Women
who
are
single
with
children
less
than
18
years
old
are
the
greatest
percent
of
all
women
within
which
military
branch?
(A)
Army
(B)
Navy
(C)
AirForce
(D)
Marines
(E)
It
cannot
be
determined
from
the
information
given.
14.
If
a
man
whose
spouse
is
also
military
personnel
or
retired
military
were
to
be
selected
at
random,
what
would
the
probability
be
that
he
was
not
in
the
Air
Force?
(A)
72%
(B)
58%
(C)
42%
(D)
24%
E)
13%
15.
Which
of
the
following expressions
approximates
the
number
of
women
who
would
have
to
enlist
in
the
Army
to
make
the
fraction
of
Army
personnel
who
are
women
equal
the
fraction
of
Air
Force
personnel
who
are
women?
(Assume
that
the
number
of
men
in
the
Army
and
the
number
of
men
and
women
in
the
Air
Force
remain
unchanged
from
what
is
shown
in
the
tables.)
482,000
-268,000
75,000
—
64,000
(482,000)(64,000)—(75,000)(268,000)
482,000
(482,000)(75,000)
—(64,000)(268,000)
482,000
(B)
(©)
(482,000)(75,000)
(D)
—64,000
268,000
482,000)(64,000
(E)
(
)(
)
—75,000
268,000
16.
A
cable
car
travels
from
Seabreeze
to
Resortville,
making
two
stops
in
between.
Between
Seabreeze
and
the
first
stop,
the
cable
car
travels
E
of
the
total
distance
between
Seabreeze
and
Resortville.
Between
the
first
stop
and
the
second
stop,
the
cable
car
travels
—
of
the
remaining
5
distance
between
the
first
stop
and
Resortville.
What
fraction
of
the
entire
distance
from
Seabreeze
to
Resortville
remains
between
the
second
stop
and
Resortville?
A
1-+-3
3
5
®)
1_1_3(1]
3
5(3
1
3(.
1)
©)
Tl
T=—
3
5\
3
[
2)
©
1-1-1[1-3
3
3\
DJ
(
®
1-+
-1
1_1_1]
3
5{
3
5
17.
If
p
and
g
are
integers
and
20p
+
3¢
is
odd,
which
of
the
following
must
be
odd?
(A)
p—q
B)
pt+t2q
€)
3p+gq
D)
2p+q’
(E)
3p+3q
18.
In
a
study,
4,400
participants
were
surveyed
regarding
side
effects
of
a
new
medication,
and
x
percent
reported
experiencing
drowsiness.
If
x
1s
rounded
to
the
nearest
integer,
the
result
is
8.
Which
of
the
following
could
be
the
number
of
survey
participants
who
reported
experiencing
drowsiness?
Indicate
all
such
values.
[
325
1
330
352
1375
53
(445
_
443
)27
2252
(A)
443
(B)
445
(C)
495
(D)
4865333
(E)
4°95%33
19.
is
equivalent
to
which
of
the
following?
20.
The
following
table
shows
the
price
of
a
plane
ticket
for
an
April
1st
flight,
based
on
the
date
of
purchase.
Price
|
When
Purchased
On
$210
March
16
$168
March
2
$140
March
1
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Harpreet
purchased
a
ticket
on
March
1st.
If
he
had
purchased
the
ticket
on
March
2nd,
he
would
have
paid
x
percent
more.
If
he
had
purchased
the
ticket
on
March
16th,
he
would
have
paid
y
percent
more
than
he
would
have
paid
on
March
2nd.
What
is
the
positive
difference
between
x
and
y?
(A)
5
B)
14
(C)
20
(D)
25
(E)
28
Answers
to
Math
Practice
Section
3
1.
(C).
The
leftmost
triangle
has
two
angles
labeled
40°
and
70°.
Subtract
these
from
180°
(the
sum
of
the
angles
in
any
triangle)
to
determine
that
the
third
angle
is
70°.
Subtract
130
—
70
=
60°
to
get the
measure
of
the
adjoining
angle
in
the
rightmost
triangle.
Since
the
leftmost
triangle
is
isosceles,
the
two
long
sides
are
each
equal
to
10.
Since
the
rightmost
triangle
is
a
30—60—90
triangle,
the
sides
are
in
the
proportion
x
:
\/gx
:
2x.
Because
the
hypotenuse
is
8
and
also
the
2x
in
the
ratio,
the
shortest
leg
of
this
triangle
is
x
=
4.