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Uploaded by ChefAtomEchidna44
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|
The
Official
Guide
for
GMAT®
Review
2017
5.3
Practice
Questions
@
the
problem
and
indicate
the
best
of
the
answer
choices
given.
s:
All
numbers
used
are
real
numbers.
A
figure
accompanying
a
problem
solving
question
is
intended
to
provide
information
useff
in
solving
the
problem.
Figures
are
drawn
as
accurately
as
possible.
Exceptions
will
be
clearl
noted.
Lines
shown
as
straight
are
straight,
and
lines
that
appear
jagged
are
also
straight.|§
positions
of
points,
angles,
regions,
etc.,
exist
in
the
order
shown,
and
angle
measures
arg
greater
than
zero.
All
figures
lie
in
a
plane
unless
otherwise
indicated.
|
(
1.
The
price
of
a
coat
in
a
certain
store
is
$500.
If
the
4.
Today
Rebecca,
who
is
34
years
old,
and
her
daughts
price
of
the
coat
is
to
be
reduced
by
$150,
by
what
who
is
8
years
old,
celebrate
their
birthdays.
How
percent
is
the
price
to
be
reduced?
many
years
will
pass
before
Rebecca’s
age
is
twice
hg
daughter's
age?
'
(A
10%
(B)
15%
(A)
10
(C)
20%
B)
14
(D)
25%
(C)
18
E)
30%
0y
22
’
(E)
26
/
D
On
a
vacation,
Rose
exchanged
$500.00
for
euros
e
,
.
"
at
an
exchange
rate
of
0.80
euro
per
dollar
and
@
When
traveling
at
a
constant
speed
of
32
miles
per
hou;
a
certain
motorboat
consumes
24
gallons
of
fuel
3
.
spent
-
of
the
euros
she
received.
If
she
exchanged
per
hour.
What
is
the
fuel
consumption
of
this
boat
at
the
remaining
euros
for
dollars
at
an
exchange
rate
this
speed
measured
in
miles
traveled
per
gallon
of
fuel
of
$1.20
per
euro,
what
was
the
dollar
amount
she
received?
(A)
%
‘
()
$60.00
m
B
‘:
(B)
$80.00
4
(C)
$100.00
.
(C)
%
‘
(D)
$120.00
4
)
$140.00
B3
3
1,1
5
1.1
9_
(€
g
6
20
6.
A
case
contains
¢
cartons.
Each
carton
contains
A
g
b
boxes,
and
each
box
contains
100
paper
clips.
(B)
5
How
many
paper
clips
are
contained
in
2
cases?
2
(A)
100bc
©
5
100b
B
—=
9
c
)
(€
200bc
5
200b
o
By
=
€
Z
O
=
200
(E)
b
150
N
usefyl
P
‘»”V,’-‘:f».’f‘i\‘/
ight.
The
S
are
‘
7‘)
Atechnician
makes
a
round-trip
to
and
from
a
certain
I
senice
center
by
the
same
route.
If
the
technician
completes
the
drive
to
the
center
and
then
completes
10
percent
of
the
drive
from
the
center,
what
percent
of
the
round-trip
has
the
technician
completed?
A
5%
B
10%
(€
25%
(D)
40%
{E)
55%
On
the
graph
above,
when
x
=
%
y=2;
and
when
X=1,y=1.
The
graph
is
symmetric
with
respect
to
the
vertical
line
at
x
=
2.
According
to
the
graph,
when
5,000,
the
difference
is
X=3,y=
A
-1
1
B
-
3
g
0
1
(D)
3
(E)
1
1
When
0
(A)
0
B
50
(C)
450
(D)
495
(E)
500
percent
of
5,000
is
subtracted
from
-
of
Which
of
the
following
is
the
value
of
4/3/0.000064
?
(A)
0.004
(B)
0.008
(C)
0.02
(D)
0.04
(E)
0.2
Raffle
tickets
numbered
consecutively
from
101
through
350
are
placed
in
a
box.
What
is
the
probability
that
a
ticket
selected
at
random
will
have
a
number
with
a
hundreds
digit
of
2
?
(A)
%
@
2
o
3
(D)
%
(E)
%g—g
When
Leo
imported
a
certain
item,
he
paid
a
7
percent
import
tax
on
the
portion
of
the
total
value
of
the
item
in
excess
of
$1,000.
If
the
amount
of
the
import
tax
that
Leo
paid
was
$87.50,
what
was
the
total
value
of
the
item?
(A)
$1,600
(B)
$1,850
(C)
$2,250
(D)
$2,400
(E)
$2,750
A
collection
of
16
coins,
each
with
a
face
value
of
either
10
cents
or
25
cents,
has
a
total
face
value
of
$2.35.
How
many
of
the
coins
have
a
face
value
of
25
cents?
(A)
3
(B)
5
(C)
7
(D)
9
()
11
5.3
Problem
Solving
Practice
Questions
The
Official
Guide
for
GMAT®
Review
2017
14.
The
number
of
cars
sold
at
a
certain
dealership
on
15.
16.
152
six
of
the
last
seven
business
days
were
4,
7,
2,
8,
3,
and
6,
respectively.
If
the
number
of
cars
sold
on
the
seventh
business
day
was
either
2,
4,
or
5,
for
which
of
the
three
values
does
the
average
(arithmetic
mean)
number
of
cars
sold
per
business
day
for
the
seven
business
days
equal
the
median
number
of
cars
sold
per
day
for
the
seven
days?
.
2
I
4
.5
(A)
[l
only
(B)
lilonly
(C)
landll
only
(D)
Il'and
Il
only
(E)
1,
I,
and
lll
If
it
is
assumed
that
60
percent
of
those
who
receive
a
questionnaire
by
mail
will
respond
and
300
responses
are
needed,
what
is
the
minimum
number
of
questionnaires
that
should
be
mailed?
(A)
400
(B)
420
(C)
480
(D)
500
(E)
600
A
rectangular
garden
is
to
be
twice
as
long
as
it
is
wide.
If
360
yards
of
fencing,
including
the
gate,
will
completely
enclose
the
garden,
what
will
be
the
length
of
the
garden,
in
yards?
(A)
120
(B)
140
(C)
160
(D)
180
(E)
200
|
|
17.
Arectangular
floor
that
measures
8
meters
by
10
meters
is
to
be
covered
with
carpet
squares
that
each
measure
2
meters
by
2
meters.
If
the
carpet
squares
cost
S12
apiece,
what
is
the
total
cost
for
f!
number
of
carpet
squares
needed
to
cover
the
floor!
(A)
$200
(B)
$240
(C)
$480
(D)
$960
(E)
$1,920
18.
1f
893
x
78
=
p,
which
of
the
following
is
equal
to
893
x
797
A
p+1
B)
p+78
(C)
p+79
(D)
p+893
(E)
p+894
e
@
Thabo
owns
exactly
140
books,
and
each
book
is
either
paperback
fiction,
paperback
nonfiction,
or
hardcover
nonfiction.
If
he
owns
20
more
paperback
nonfiction
books
than
hardcover
nonfiction
books,
and
“
twice
as
many
paperback
fiction
books
as
paperback
1
nonfiction
books,
how
many
hardcover
nonfiction
books
does
Thabo
own?
(A)
10
B)
20
(€)
30
(D)
40
(E)
50
20.
If
the
average
(arithmetic
mean)
of
the
four
numbers
3,15,32,and
(N+1)is
18,
then
N=
(A
19
B)
20
€
21
D)
22
(E)
29
i
22
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2,
If
ry—%
<
121,
which
of
the
following could
be
a
value
ofy?
A
-1
11
(B)
@1
11
(C)
>
e
11
i
22
90
[f
k%=
m2,
which
of
the
following
must
be
true?
A
k=m
B
k=-m
€
k=|m
D)
k=-m|
€
|K=m|
148
Wakoto,
Nishi,
and
Ozuro
were
paid
a
total
of
$780
\/
for
waxing
the
floors
at
their
school.
Each
was
paid
in
proportion
to
the
number
of
hours
he
or
she
worked.
If
Makoto
worked
15
hours,
Nishi
worked
20
hours,
and
QOzuro
worked
30
hours,
how
much
was
Makoto
paid?
()
$52
B
S117
(€)
$130
(D)
$180
[
5234
24.
25.
26.
5.3
Problem
Solving
Practice
Questions
R
The
figure
above
shows
a
path
around
a
triangular
piece
of
land.
Mary
walked
the
distance
of
8
miles
from
P
to
Q
and
then
walked
the
distance
of
6
miles
from
Q
to
R.
If
Ted
walked
directly
from
P
to
R,
by
what
percent
did
the
distance
that
Mary
walked
exceed
the
distance
that
Ted
walked?
(A)
30%
(B)
40%
(C)
50%
(D)
60%
(E)
80%
At
a
supermarket,
John spent
%
of
his
money
on
fresh
fruits
and
vegetables,
%
on
meat
products,
and
%
on
bakery
products.
If
he
spent
the
remaining
$6
on
candy,
how
much
did
John
spend
at
the
supermarket?
(A
$60
B)
$80
€
$90
D)
$120
(E)
$180
On
Monday,
a
person
mailed
8
packages
weighing
an
average
(arithmetic
mean)
of
12%
pounds,
and
on
Tuesday,
4
packages
weighing
an
average
of
15211—
pounds.
What
was
the
average
weight,
in
pounds,
of
all
the
packages
the
person
mailed
on
both
days?
(A
13%
®)
13%_2.
©)
15%
D)
15%
(E)
16%
153
The
Official
Guide
for
GMAT®
Review
2017
27.
f(1-1.25N=1,then
N=
(A)
-400
(B)
-140
(C)
-4
(D)
4
(E)
400
28.
0.1+(0.12+(0.13=
(A)
0.1
(B)
0.111
(C)
0.1211
(D)
0.2341
B¢
Q.3
29.
A
carpenter
constructed
a
rectangular
sandbox
with
a
capacity
of
10
cubic
feet.
If
the
carpenter
were
to
make
a
similar
sandbox
twice
as
long,
twice
as
wide,
and
twice
as
high
as
the
first
sandbox,
what
would
be
the
capacity,
in
cubic
feet,
of
the
second
sandbox?
(A)
20
(B)
40
(C)
60
(D)
80
(E)
100
30.
A
bakery
opened
yesterday
with
its
daily
supply
of
40
dozen
rolls.
Half
of
the
rolls
were
sold
by
noon,
and
80
percent
of
the
remaining
rolls
were
sold
between
noon
and
closing
time.
How
many
dozen
rolls
had
not
been
sold
when
the
bakery
closed
yesterday?
(A)
OB
W
N
=
154
a1,
|
f;3/2>
[
\\,,,
33.
If2x+y=7andx+2y=5,then%_y=
34,
150
(A)
1
(A)
|
B)
|
®
&
|
3
(C)
|
L
(D)
(C)
5
;
18
(D)
5
(E)
4
City
X
has
a
population
4
times
as
great
as
the
population
of
City
Y,
which
has
a
popuiation
twice
as
great
as
the
population
of
City
Z.
What
is
the
ratio
of
the
population
of
City
X
to
the
population
of
City
Z?
(A)
1:8
B
14
)
2
D)
41
)
81
Tides
at
Bay
Cove
on
July
13
11:30
a.m
2214t
3
kS
'%0
t
/
time
=
_1
6am.
noon
midnight
6
p.m.
-0.5
ft
The
graph
above
shows
the
height
of
the
tide,
in
feet,
above
or
below
a
baseline.
Which
of
the
following
is
closest
to
the
difference,
in
feet,
between
the
heights
of
the
highest
and
lowest
tides
on
July
13
at
Bay
Cove’
A
1.7
37,
(B
LS
(C)
2.2
D)
25
(B
247
The
Official
Guide
for
GMAT®
Review
2017
42.
43.
e
45.
(a4,
The
positive
two-digit
integers
x
and
y
have
the
same
digits,
but
in
reverse
order.
Which
of
the
following
must
be
a
factor
of
x
+y?
(A6
B
9
(€
10
)
11
(E)
14
In
a
certain
sequence
of
8
numbers,
each
number
after
the
first
is
1
more
than
the
previous
number.
If
the
first
number
is
=5,
how
many
of
the
numbers
in
the
sequence
are
positive?
(A)
None
(B)
One
(C)
Two
(D)
Three
(E)
Four
A
total
of
s
oranges
are
to
be
packaged
in
boxes
that
will
hold
r
oranges
each,
with
no
oranges
left
over.
When
n
of
these
boxes
have
been
completely
filled,
what
is
the
number
of
boxes
that
remain
to
be
filled?
(A)
s-nr
(B)
s
r
(C)
rs=n
(D)
S_or
n
E)
2-n
If
0
<
a<
b
<
c,
which
of
the
following
statements
must
be
true?
|
2a>b+¢
Il
c-a>b-a
.
Zgl
a
a
(A)
lonly
(B)
Il
only
(C)
lonly
(D)
landll
(E)
landlll
46.
Which
of
the
following
equations
is
NOT
equivalent
to
102
=(x+2)x-2)?
(A)
30y2=3x2-12
(B)
20y°=(2x-4)x+
2)
(C)
10y2+4=x2
(D)
5y2=x2-2
49.
2=x—4
(E)
vy
o
(
Monday
|
Tuesday
|
Wednesday
Thursdafl
Company
A
|
45
55
50
50
|
Company
B
10
30
30
10
Company
C
34
28
28
30
o
Company
D
|
39
42
41
38
EO>
\Company
E
|
50
60
60
70
)
A~
[
47.
48.
The
table
shows
the
numbers
of
packages
shipped
daily by
each
of
five
companies
during
a
4-day
period.
The
standard
deviation
of
the
numbers
of
packages
shipped
daily
during
the
period
was
greatest
for
which
of
the
five
companies?
(A
A
(B)
B
€
c
O
D
()
E
S
E
A
D
B
C
The
dial
shown
above
is
divided
into
equal-sized
intervals.
At
which
of
the
following
letters
will
the
pointer
stop
if
it
is
rotated
clockwise
from
S
through
1,174
intervals?
(A
A
B)
B
€
C
O)
D
‘
()
E
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1,
The
graph
of
the
equation
xy
=
k,
where
k
<
0,
lies
in
which
two
of
the
quadrants
shown
above?
(A)
landll
(B)
landlll
(C)
Iland
I
(D)
IlandIV
(E)
Illand
IV
9
When
n
liters
of
fuel
were
added
to
a
tank
that
was
already
é—
full,
the
tank
was
filled
to
i
of
its
capacity.
In
9
terms
of
n,
what
is
the
capacity
of
the
tank,
in
liters?
—
o
(A)
3
n
(B)
%”
©
5
(D)
%n
©)
%n
51
52.
5.3
Problem
Solving
Practice
Questions
w
ft
100
ft
150
ft
w
ft
Note:
Not
drawn
to
scale.
The
smaller
rectangle
in
the
figure
above
represents
the
original
size
of
a
parking
lot
before
its
length
and
width
were
each
extended
by
w
feet
to
make
the
larger
rectangular
lot
shown.
If
the
area
of
the
enlarged
lot
is
twice
the
area
of
the
original
lot,
what
is
the
value
of
w?
(A
25
(B)
50
(€
75
(D)
100
(E)
200
1
-,
0.75-1
(A
-4
(B)
-0.25
(€
0.25
(0
0.75
(E)
4
The
harvest
yield
from
a
certain
apple
orchard
was
350
bushels
of
apples.
If
x
of
the
trees
in
the
orchard
each
yielded
10
bushels
of
apples,
what
fraction
of
the
harvest
yield
was
from
these
x
trees?
X
(A)
35
X
B
1-
£
(C)
10x
(D)
35-x
The
Official
Guide
for
GMAT®
Review
2017
54.
55,
56.
57,
58.
158
If
nis
an
integer,
which
of
the
following
must
be
even?
A)
n+1
B
n+?2
(C)
2n
D)
2n+1
E)
n?
The
sum
Z+
1
is
between
879
(A)
%
and
%
(B)
%
and
1
(C)
1land
1%
0)
1%
and
1%
(E)
1%
and
2
Car
X
averages
25.0
miles
per
gallon
of
gasoline
and
Car
Y
averages
11.9
miles
per
gallon.
If
each
car
is
driven
12,000
miles,
approximately
how
many
more
gallons
of
gasoline
will
Car
Y
use
than
Car
X
?
(A)
320
(B)
480
(C)
520
(D)
730
(E)
920
If
yis
an
integer,
then
the
least
possible
value
of
|23
-5y
is
A
1
B)
2
)
3
D)
4
E)
5
J80
++/125
=
A
956
B)
205
(C)
415
(D)
205
(E)
100
Fwh
T
et
S
S
T
e
T
59.
60.
61.
~_
y=kx+3
In
the
equation
above,
k
is
a
constant.
If
y
=
17
when
X
=
2,
what
is
the
value
of y
when
x=47
(A)
34
B)
31
(C)
14
0)
11
()
7
Of
the
land
owned
by
a
farmer,
90
percent
was
cleared
for
planting.
Of
the
cleared
land,
40
percent
was
planted
with
soybeans
and
50
percent
of
the
cleared
land
was
planted
with
wheat,
If
the
remaining
720
acres
of
cleared
land
was
planted
with
corn,
how
many
acres
did
the
farmer
own?
(A)
5,832
(B)
6,480
(C)
7,200
(D)
8,000
(E)
8,889
At
the
start
of
an
experiment,
a
certain
population
consisted
of
3
animals.
At
the
end
of
each
month
after
the start
of
the
experiment,
the
population
size
was
double
its
size
at
the
beginning
of
that
month.
Which
of
the
following
represents
the
population
size
at
the
end
of
10
months?
A
23
B)
3?
(C)
2(319)
(D)
3(219)
(E)
3(109
"62.)
If
x
and
y
are
positive
integers
such
that
y
is
a
multiple
of
5
and
3x
+
4y
=
200,
then
x
must
be
a
multiple
of
which
of
the
following?
(A3
B)
6
€
7
0
8
(E)
10
63.
W
o~
=
64.
63.
Which
of
the
following
expressions
can
be
written
as
an
integer?
L
[(ve2+vB2f
Il
(82)(v82)
V)
'
82
(A
None
(B)
lonly
(€
lronly
D)
landll
(E)
landll
b4,
Four
staff
members
at
a
certain
company
worked
on
a
project.
The
amounts
of
time
that
the
four
staff
members
worked
on
the
project
were
in
the
ratio
2
to
3to
5
to
6.
If
one
of
the
four
staff
members
worked
on
the
project
for
30
hours,
which
of
the
following
CANNOT
be
the
total
number
of
hours
that
the
four
staff
members
worked
on
the
project?
A
80
B
96
(C)
160
D
192
(E)
240
65.
Pumping
alone
at
their
respective
constant
rates,
one
inlet
pipe
fills
an
empty
tank
to
%
of
capacity
in
3
hours
and
a
second
inlet
pipe
fills
the
same
empty
tank
to
%of
capacity
in
6
hours.
How
many
hours
will
it
take
both
pipes,
pumping
simultaneously
at
their
respective
constant
rates,
to
fill
the
empty
tank
to
capacity?
A}
3.25
B)
3.6
€
4.2
D)
4.4
Bl
55
o
Which
of
the
following
fractions
is
closest
to
1
?
5.3
Problem
Solving
Practice
Questions
In
the
xy-coordinate
plane,
which
of
the
following
points
must
lie
on
the
line
kx
+
3y
=
6
for
every
possible
value
of
k?
A
(1,1
B)
(0,2
‘
|
€
(2,0
|
D
(3,6)
|
E)
(6,3
If
x>
-
2
<
0,
which
of
the
following
specifies
all
the
possible
values
of
x
?
(A)
O0<x<2
B)
O<x<+2
€
—2<x<2
D)
-2<x<0
(E)
-2<x<2
In
Western
Europe,
x
bicycles
were
sold
in
each
of
the
years
1990
and
1993.
The
bicycle
producers
of
Western
Europe
had
a
42
percent
share
of
this
market
in
1990
and
a
33
percent
share
in
1993.
Which
of
the
following
represents
the
decrease
in
the
annual
number
of
bicycles
produced
and
sold
in
Western
Europe
from
1990
to
19937
X
0,
(A)
9%
of
—100
X
0,
(B)
14%
of
100
X
0,
(C)
75601‘——100
(D)
9%
of
x
(E)
14%
of
x
>
(A)
%
(®)
g
(c)
%
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The
Official
Guide
for
GMAT®
Review
2017
\71)
73.
160
72.)
;
/
N\
i
g
.
p
70;
If
p=0andp-
o
&
E,
then
r
=
(A
p+1
B
2p-1
€
p?+1
D)
2p?-1
E)
pP+p-1
If
the
range
of
the
six
numbers
4,
3,
14,
7,
10,
and
xis
12,
what
is
the
difference
between
the
greatest
possible
value
of
x
and
the
least
possible
value
of
x
?
A
0
B
2
cy
12
(D)
13
(E)
15
A
doctor
prescribed
18
cubic
centimeters
of
a
certain
drug
to
a
patient
whose
body
weight
was
120
pounds.
If
the
typical
dosage
is
2
cubic
centimeters
per
15
pounds
of
body
weight,
by
what
percent
was
the
prescribed
dosage
greater
than
the
typical
dosage?
(A
8%
B)
9%
C)
11%
(D)
12.5%
(E)
14.8%
Company
P
had
15
percent
more
employees
in
December
than
it
had
in
January.
If
Company
P
had
460
employees
in
December,
how
many
employees
did
it
have
in
January?
(A
391
(B)
400
(C)
410
(D)
423
(E)
445
74.
The
function
fis
defined
by
f(x)
=
vx
-
10
for
all
positive
numbers
x.
if
u
=
f(t)
for
some
positive
numbers
t
and
u,
what
is
t
in
terms
of
u?
76.
17.
(A)
(B)
(C)
(D)
(E)
Ju?
+10
(u+100
(?
+10)
A
glass
was
filled
with
10
ounces
of
water,
and
0.01
ounce
of
the
water
evaporated
each
day
during
a
20-day
period.
What
percent
of
the
original
amount
of
water
evaporated
during
this
period?
(A)
(B)
(C)
(D)
(E)
g
o<
o|x
x|<
alo
ke
0.002%
0.02%
0.2%
2%
20%
ola
o
=3
=4
o
|
T
olx
Tl<
oo
I
|
and
Il
only
I
and
Il
only
I,
11,
and
Il
,
which
of
the
following
must
be
true!
If
k
is
an
integer
and
(0.0025)(0.025)(0.00025)
x
10*
is
an
integer,
what
is
the
least
possible
value
of
k
?
(A)
(B)
(C)
(D)
(E)
-12
-6
0
6
12
78.
79.
80.
The
Official
Guide
for
GMAT®
Review
2017
84.
85.
86.
In
the
xy-plane,
what
is
the
slope
of
the
line
with
equation
3x+
7y
=97
7
(A)
-3
3
(B
-
7
3
(C)
7
b
3
(E)
7
Working
simultaneously
and
independently
at
an
identical
constant
rate,
four
machines
of
a
certain
type
can
produce
a
total
of
x
units
of
product
P
in
6
days.
How
many
of
these
machines,
working
simultaneously
and
independently
at
this
constant
rate,
can
produce
a
total
of
3x
units
of
product
P
in
4
days?
(A)
24
(B)
18
(C)
16
D)
12
()
8
At
a
certain
school,
the
ratio
of
the
number
of
second
graders
to
the
number
of
fourth
graders
is
8
to
5,
and
the
ratio
of
the
number
of
first
graders
to
the
number
of
second
graders
is
3
to
4.
If
the
ratio
of
the
number
of
third
graders
to
the
number
of
fourth
graders
is
3
to
2,
what
is
the
ratio
of
the
number
of
first
graders
to
the
number
of
third
graders?
(A)
16to1b
(B
9tob
(C)
5Htole
(D)
bHto4d
(E)
4tob
87.
90.
The
average
distance
between
the
Sun
and
a
certain
planet
is
approximately
2.3
x
104
inches.
Which
of
the
following
is
closest
to
the
average
distance
between
the
Sun
and
the
planet,
in
kilometers?
(1
kilometer
is
approximately
3.9
x
104
inches.)
(A)
7.1x108
(B)
5.9x10°
(C)
1.6x101°
(D)
1.6x10!
(E)
5.9x101
The
average
(arithmetic
mean)
score
on
a
test
taken
by
10
students
was
x.
If
the
average
score
for
5
of
the
students
was
8,
what
was
the
average
score,
in
terms
of
x,
for
the
remaining
5
students
who
took
the
test?
(A)
2x-8
B)
x-4
(C)
8-2x
D)
16-x
X
(E)
8-
2
If
mn
=
0
and
25
percent
of
n
equals
37%
percent
of
m,
what
is
the
value
of
%
?
(A)
18
32
(B)
3
C)
8
D)
3
9
(E)
s
In
the
coordinate
plane,
a
circle
has
center
(2,-3)
and
passes
through
the
point
(5,0).
What
is
the
area
of
the
circle?
(A)
3z
B)
3V2r
(C)
3V3r
D)
9z
(E)
18z
93.11
ken
of
the
terms
est?
[
/\
\91)‘
Last
year
Joe
grew
1
inch
and
Sally
grew 200
percent
more
than
Joe
grew.
How
many
inches
did
Sally
grow
last
year?
9%2.
83,
A
0
B)
1
€
2
b
3
(E)
4
The
cost
C,
in
dollars,
to
remove
p
percent
of
a
certain
pollutant
from
a
pond
is
estimated
by
using
the
formula
0o
100,000P
100-P
much
more
would
it
cost
to
remove
90
percent
of
the
pollutant
from
the
pond
than
it
would
cost
to
remove
80
percent
of
the
pollutant?
.
According
to
this
estimate,
how
(A
$500,000
(B)
$100,000
(€)
$50,000
(D)
$10,000
(E)
$5,000
If
xy
#
0
and
x2y
—
xy
=
6,
which
of
the
following
could
be
yin
terms
of
x
?
fhocci
L
B
1
c2X
Il
—g
X
Il
§
X
(A)
lonly
(B)
Ilonly
(C)
landll
(D)
landli
(E)
llandlll
5.3
Problem
Solving
Practice
Questions
94.
At
a
certain
instant
in
time,
the
number
of
cars,
N,
traveling
on
a
portion
of
a
certain
highway
can
be
estimated
by
the
formula
_
20Ld
600
+
52
where
L
is
the
number
of
lanes
in
the
same
direction,
dis
the
length
of
the
portion
of
the
highway,
in
feet,
and
s
is
the
average
speed
of
the
cars,
in
miles
per
hour.
Based
on
the
formula,
what
is
the
estimated
number
of
cars
traveling
on
a
%-mile
portion
of
the
highway
if
the
highway
has
2
lanes
in
the
same
direction
and
the
average
speed
of
the
cars
is
40
miles
per
hour?
(5,280
feet
=
1
mile)
(A)
155
(B)
96
(C)
80
(D)
48
(E)
24
95.
J4.8x10?
is
closest
in
value
to
(A)
2,200
(B)
70,000
(C)
220,000
(D)
7,000,000
(E)
22,000,000
(
95)
Three
printing
presses,
R,
S,
and
T,
working
together
at
their
respective
constant
rates,
can
do
a
certain
printing
job
in
4
hours.
S
and
T,
working
together
at
their
respective
constant
rates,
can
do
the
same
job
in
5
hours.
How
many
hours
would
it
take
R,
working
alone
at
its
constant
rate,
to
do
the
same
job?
A
8
(B)
10
(€
12
(D)
15
()
20
163
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The
Official
Guide
for
GMAT®
Review
2017
97.
98.
99.
For
a
party,
three
solid
cheese
balls
with
diameters
of
2
inches,
4
inches,
and
6
inches,
respectively,
were
combined
to
form
a
single
cheese
ball.
What
was
the
approximate
diameter,
in
inches,
of
the
new
cheese
ball?
(The
volume
of
a
sphere
is
%nr3,
where
ris
the
radius.)
(A
12
(B)
16
€
316
D)
3%8
(E)
2336
The
sum
of
all
the
integers
k
such
that
—-26
<
k
<
24
is
(A)
0
B
-2
(C)
-25
(D)
-49
(E)
-51
R
S
T
P
L
T
et
6
J
e
The
number
line
shown
contains
three
points
R,
S,
and
T,
whose
coordinates
have
absolute
values
r,
s,
and
t,
respectively.
Which
of
the
following
equals
the
average
(arithmetic
mean)
of
the
coordinates
of
the
points
R,
S,
and
T?
(A)
s
B)
s+t-r
r-s-—t
(C)
3
r+s+t
(D)
3
(E)
S+t-r
lb@
Mark
and
Ann
together
were
allocated
n
boxes
of
cookies
101.
102.
103.
to
sell
for
a
club
project.
Mark
sold
10
boxes
less
thani
and
Ann
sold
2
boxes
less
than
n.
If
Mark
and
Ann
have
each
sold
at
least
one
box
of
cookies,
but
together
they
have
sold
less
than
n
boxes,
what
is
the
value
of
n?
Ay
11
B)
12
(C)
13
(D)
14
(E)
15
A
certain
high
school
has
5,000
students.
Of
these
students,
x
are
taking
music,
y
are
taking
art,
and
Z
are
taking
both
music
and
art.
How
many
students
are
taking
neither
music
nor
art?
(A)
5,000
-z
(B)
5,000-x-y
(C)
5,000-x+2z
(D)
5,000-x-y-z
(E)
5,000-x-y+2z
Yesterday’s
closing
prices
of
2,420
different
stocks
listed
on
a
certain
stock
exchange
were
all
different
from
today's
closing
prices.
The
number
of
stocks
that
closed
at
a
higher
price
today
than
yesterday
was
20
percent
greater
than
the
number
that
closed
at
a
lower
price.
How
many
of
the
stocks
closed
at
a
higher
price
today
than
yesterday?
(A)
484
(B)
726
(C)
1,100
(D)
1,320
(E)
1,694
Each
person
who
attended
a
company
meeting
was
either
a
stockholder
in
the
company,
an
employee
of
the
company,
or
both.
If
62
percent
of
those
who
attended
the
meeting
were
stockhqlders
and
47
percent
were
employees,
what
percent
were
stockholders
who
were
not
employees?
(A)
34%
(B)
38%
(C)
45%
(D)
53%
(E)
62%
\‘
104.
If
105.
S
Yy
t
106.
104,
If
y[—3—xz‘—5]
—yandy
=
0,then
x
=
2
(A
3
5
(B)
3
7
B
(C)
3
0
1
E)
4
.
Agym
class
can
be
divided
into
8
teams
with
an
equal
number
of
players
on
each
team
or
into
12
teams
with
an
equal
number
of
players
on
each
team.
What
is
the
lowest
possible
number
of
students
in
the
class?
(A
20
B)
24
€
36
(D)
48
(E)
96
B
P
A
C
In
the
figure
above,
triangle
ABC
is
equilateral,
and
point
P
is
equidistant
from
vertices
A,
B,
and
C.
If
triangle
ABC
is
rotated
clockwise
about
point
P,
what
is
the
minimum
number
of
degrees
the
triangle
must
be
rotated
so
that
point
B
will
be
in
the
position
where
point
A
is
now?
(A
60
B)
120
(C)
180
(D)
240
£
270
110.
According
to
a
certain
estimate,
the
depth
N(t),
in
5.3
Problem
Solving
Practice
Questions
107.
At
least Z
of
the
40
members
of
a
committee
must
3
vote
in
favor
of
a
resolution
for
it
to
pass.
What
is
the
greatest
number
of
members
who
could
vote
against
the
resolution
and
still
have
it
pass?
(A)
19
B)
17
(C)
16
(D)
14
(E)
13
108.
If
n=20!
+
17,
then
nis
divisible
by
which
of
the
following?
.
15
17
n.
19
(A)
None
(B)
lonly
(C)
Ilonly
(D)
landll
(E)
llandlll
N
109.)
The
product
of
two
negative
numbers
is
160.
If
the
lesser
of
the
two
numbers
is
4
less
than
twice
the
greater,
what
is
the
greater
number?
(A
=20
(B)
-16
(€)
-10
0
-8
()
-4
centimeters,
of
the
water
in
a
certain
tank
at
t
hours
past
2:00
in
the
morning
is
given
by
N(D)
=
-20(t
-
5)2
+
500
for
0
<
t
<
10.
According
to
this
estimate,
at
what
time
in
the
morning
does
the
depth
of
the
water
in
the
tank
reach
its
maximum?
(A)
5:30
(B)
7:00
(C)
7:30
(D)
8:00
(E)
9:00
165
tant
hours.
oduces
any
ts
é
Number
of
Percent
of
Marbles
)
Marbles
in
in
Each
Bag
That
Are
Each
of
Three
Blue
(to
the
nearest
Bags
tenth)
Bag
P
37
10.8%
Bag
Q
X
66.7%
@ag
R
32
50.0%
)
16.
If%
of
the
total
number
of
marbles
in
the
three
bags
listed
in
the
table
above
are blue,
how
many
marbles
are
there
in
bag
Q
?
(A)
(B)
€
12
b
23
(E)
46
117,
Leona
bought
a
1-year,
$10,000
certificate
of
deposit
that
paid
interest
at
an
annual
rate
of
8
percent
compounded
semiannually.
What
was
the
total
amount
of
interest
paid
on
this
certificate
at
maturity?
W
$10,464
B
3864
©
3816
D
$800
B
$480
g
0003628)
_
(0.04)0.1/0.003)
M
840.0
B
84.0
©
84
D
084
B
0084
119.
f
nis
an
integer
greater
than
6,
which
of
the
following
must
be
divisible
by
3
?
(A)
nln+1)n-4)
B
nn+2)n-1)
(C)
n(n+
3)n-5)
D)
nin+4)n-2)
(E}
n(n+5)n-6)
|
5.3
Problem
Solving
Practice
Questions
Age
Category
Number
of
A
(in
years)
Employees
Less
than
20
29
20-29
58
30-39
36
40-49
21
50-59
-
10
60-69
5
QO
and
over
2
W,
PN
t1120.1>The
table
above
gives
the
age
categories
of
the
~—
161
employees
at
Company
X
and
the
number
of
121.
employees
in
each
category.
According
to
the
table,
if
m
is
the
median
age,
in
years,
of
the
employees
at
Company
X,
then
m
must
satisfy
which
of
the
following?
A
20<m<29
B)
25<m<34
C)
30<m<39
D)
35<m<44
(E)
40<m<49
(
(
(
(
If
x
and
y
are
positive
numbers
such
that
x
+
y=1,
which
of
the
following
could
be
the
value
of
100x
+
200y
?
l.
80
I
140
.
199
(A)
Il
only
(B)
il
only
(C)
landll
(D)
landlil
(E)
Ilandlll
167
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The
Official
Guide
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GMAT®
Review
2017
122.
If
nis
a
positive
integer
and
the
product
of
all
the
integers
from
1
to
n,
inclusive,
is
divisible
by
990,
what
is
the
least
possible
value
of
n?
124.
(A)
(B)
(C)
(D)
(E)
The
probability
that
event
M
will
not
occur
is
0.8
and
the
probability
that
event
R
will
not
occur
is
0.6.
If
events
M and
R
cannot
both
occur,
which
of
the
following
is
the
probability
that
either
event
M
or
event
R
will
occur?
W
®)
-25-
©
3
0)
%
(E)
%
The
total
cost
for
Company
X
to
produce
a
batch
of
tools
is
$10,000
plus
$3
per
tool.
Each
tool
sells
for
S8.
The
gross
profit
earned
from
producing
and
selling
these
tools
is
the
total
income
from
sales
minus
the
total
production
cost.
If
a
batch
of
20,000
tools
is
produced
and
sold,
then
Company
X's
gross
profit
per
tool
is
(A
$3.00
(B)
$3.75
(C)
$4.50
(D)
$5.00
(E)
$5.50
125.
If
Qis
an
odd
number
and
the
median
of
Q
consecutie
integers
is
120,
what
is
the
largest
of
these
integers?
w
Lz
(®)
%+119
©)
%+120
o
L8
o
2
126.
A
ladder
of
a
fire
truck
is
elevated
to
an
angle
of
60°
and
extended
to
a
length
of
70
feet.
If
the
base
of
the
ladder
is
7
feet
above
the
ground,
how
many
feet
above
the
ground
does
the
ladder
reach?
(A)
35
B)
42
C)
353
D)
7+35V3
E)
7+42V3
qr
<«
4
ft
>
10
ft
¥
@
The
window
in
the
figure
above
consists
of
a
rectangle
and
a
semicircle
with
dimensions
as
shown.
What
is
the
area,
in
square
feet,
of
the
window?
(A)
40+
8m
(B)
40+2m
(C)
32+8m
(D)
32+4n
(E)
32+2nm
\1@
lf
there
are
fewer
than
8
zeros
between
the
decimal
point
and
the
first
nonzero
digit
in
the
decimal
t
gxpansion
of
[mj
.
which
of
the
following
numbers
could
be
the
value
of
t?
(A)
None
(B)
lonly
(C)
Ilonly
(D)
Il
only
(E)
Iland
Il
129,
A
three-digit
code
for
certain
locks
uses
the
digits
0,1,2
3,4,5,6,7,
8,9
according
to
the
following
constraints.
The
first
digit
cannot
be
O
or
1,
the
second
digit
must
be
0
or
1,
and
the
second
and
third
digits
cannot
both
be
0
in
the
same
code.
How
many
different
codes
are
possible?
(A)
144
(B)
152
(C)
160
(D)
168
)
176
130
Jackie
has
two
solutions
that
are
2
percent
sulfuric
acid
and
12
percent
sulfuric
acid
by
volume,
tespectively.
If
these
solutions
are
mixed
in
appropriate
quantities
to
produce
60
liters
of
a
solution
that
is
§
percent
sulfuric
acid,
approximately
how
many
liters
of
the
2
percent
solution
will
be
required?
(A
18
B
20
(C)
24
D)
36
)
42
5.3
Problem
Solving
Practice
Questions
131.
If
Jake
loses
8
pounds,
he
will
weigh
twice
as
much
as
his
sister.
Together
they
now
weigh
278
pounds.
What
is
Jake's
present
weight,
in
pounds?
(A
131
(B)
135
(C)
139
(D)
147
(E)
188
@
Last
year
26
members
of
a
certain
club
traveled
to
England,
26
members
traveled
to
France,
and
32
members
traveled
to
Italy.
Last
year
no
members
of
the
club
traveled
to
both
England
and
France,
6
members
traveled
to
both
England
and
Italy,
and
11
members
traveled
to
both
France
and
Italy.
How
many
members
of
the
club
traveled
to
at
least
one
of
these
three
countries
last
year?
(A)
52
(B)
67
)
71
D)
73
(E)
79
133.
A
store
reported
total
sales
of
$385
million
for
February
of
this
year.
If
the
total
sales
for
the
same
month
last
year
was
$320
million,
approximately
what
was
the
percent
increase
in
sales?
(A
2%
(B)
17%
(C)
20%
(D)
65%
(E)
83%
134.
When
positive
integer
x
is
divided
by
positive
integer
y,
the
remainder
is
9.
If
§=
96.12,
what
is
the
value
of
y?
(A)
96
(B
75
(C)
48
(D)
25
(B)
12
The
Official
Guide
for
GMAT®
Review
2017
136.
137.
170
"
%
®
1
©)
%
D)
%
®
o
Water
consists
of
hydrogen
and
oxygen,
and
the
approximate
ratio,
by
mass,
of
hydrogen
to
oxygen
is
2:16.
Approximately
how
many
grams
of
oxygen
are
there
in
144
grams
of
water?
A
16
®
72
©
112
D)
128
€
142
If
x(2x
+
1)
=
0
and
[x
.
%)(2x
%
=0,
Hign
%=
A)
-3
1
B
-
©
0
1
o
3
3
®
14]
X
Y
138.
Figures
X
and
Y
above
show
how
eight
identical
triangular
pieces
of
cardboard
were
used
to
form
a
square
and
a
rectangle,
respectively.
What
is
the
ratio
&
14
of
the
perimeter
of
X
to
the
perimeter
of
Y?
A)
2:3
B)
2:2
()
242:3
o)
11
€
V2:1
139.
On
a
scale
that
measures
the
intensity
of
a
certain
phenomenon,
a
reading
of
n+
1
corresponds
to
an
intensity
that
is
10
times
the
intensity
corresponding
to
a
reading
of
n.
On
that
scale,
the
intensity
corresponding
to
a
reading
of
8
is
how
many
times
as
great
as
the
intensity
corresponding
to
a
reading
of
3?
Ab
5
(B)
50
(C)
10°
D)
5
(F)
8l0_3l0
140>A
certain
experimental
mathematics
program
was
tried
“~—"out
in
2
classes
in
each
of
32
elementary
schools
and
involved
37
teachers.
Each
of
the
classes
had
1
teacher
and
each
of
the
teachers
taught
at
least
1,
but not
more
than
3,
of
the
classes.
If
the
number
of
teachers
who
taught
3
classes
is
n,
then
the
least
and
greatest
possible
values
of
n,
respectively,
are
(A)
Oand13
(B)
0Oand14
(C)
landl10
(D)
1land9
(E)
2and8
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The
Official
Guide
for
GMAT®
Review
2017
NUMBER
OF
SHIPMENTS
OF
MANUFACTURED
HOMES
IN
THE
UNITED
STATES,
1990-2000
400,000
5
§
300,000
=
5
200,000
g
E
100,000~
1990
1992
1994
1996
1998
2000
year
148.
According
to
the
chart
shown,
which
of
the
following
is
closest
to
the
median
annual
number
of
shipments
of
manufactured
homes
in
the
United
States
for
the
years
from
1990
to
2000,
inclusive?
(A)
250,000
(B)
280,000
(C)
310,000
(D)
325,000
(E)
340,000
149.
For
the
positive
integers
a,
b,
and
k,
ak||b
means
that
a“
is
a
divisor
of
b,
but
a**!
is
not
a
divisor
of
b.
If
k
is
a
positive
integer
and
2kH72,
then
k
is
equal
to
A
2
B
3
€
4
b))
8
(E)
18
150.
A
certain
characteristic
in
a
large
population
has
a
distribution
that
is
symmetric
about
the
mean
m.
If
68
percent
of
the
distribution
lies
within
one
standard
deviation
d of
the
mean,
what
percent
of
the
distribution
is
less
than
m
+
d
?
(A
16%
(B)
32%
(C)
48%
(D)
84%
(E)
92%
172
15].
/f\
@
d
153,
Four
extra-large
sandwiches
of
exactly
the
same
siz
154.
were
ordered
for
m
students,
where
m
>
4.
Three
of
the
sandwiches
were
evenly
divided
among
the
students.
Since
4
students
did
not
want
any
of
the
fourth
sandwich,
it
was
evenly
divided
among
the
remaining
students.
If
Carol
ate
one
piece
from
each
of
the
four
sandwiches,
the
amount
of
sandwich
that
she
ate
would
be
what
fraction
of
a
whole
extraarge
sandwich?
m+4
(A)
mm=4)
2m-4
B
m=a
dm-4
O
m=a
4m-8
(D)
-
155
dm-12
©
m(m—4)
Which
of
the
following
equations
has
1
+
/2
as
one
of
its
roots?
(A)
x2+2x-1=0
B
x2-2x+1=0
(C)
x2+2x+1=0
D)
x2-2x-1=0
(E)
x2-x-1=0
In
Country
C,
the
unemployment
rate
among
15
construction
workers
dropped
from
16
percent
on
September
1,
1992,
to
9
percent
on
September
1,
1996.
If
the
number
of
construction
workers
was
20
percent
greater
on
September
1,
1996,
than
on
September
1,
1992,
what
was
the
approximate
percent
change
in
the
number
of
unemployed
construction
workers
over
this
period?
(A)
50%
decrease
(B)
30%
decrease
(C)
15%
decrease
(D)
30%
increase
(E)
55%
increase
193
|n
a
certain
sequence,
the
term
x,
is
given
by
the
formula
xn=2xn,1—%(xn,2)
foralln>2n.If
xg=3
and
x,
=
2,
what
is
the
value
of
x5
?
A
2.5
B
3.125
€
4
D)
5
)
6.75
(194)
On
Saturday
morning,
Malachi
will
begin
a
camping
N7
yacation
and
he
will
return
home
at
the
end
of
the
first
day
on
which
it
rains.
If
on
the
first
three
days
of
the
vacation
the
probability
of
rain
on
each
day
is
0.2,
what
is
the
probability
that
Malachi
will
return
home
at
the
end
of
the
day
on
the
following
Monday?
(A)
0.008
B)
0.128
(C)
0.488
b))
0.512
(E)
0.640
195,
During
a
trip,
Francine
traveled
x
percent
of
the
total
distance
at
an
average
speed
of
40
miles
per
hour
and
the
rest
of
the
distance
at
an
average
speed
of
60
miles
per hour.
In
terms
of
x,
what
was
Francine’s
average
speed
for
the
entire
trip?
"
1802"‘
B
x+460
o
B
o
p
2
196.
If
n=
(33)*3
+
(43)33,
what
is
the
units
digit
of
n?
A
0
B
2
C
4
D)
6
E)
8
5.3
Problem
Solving
Practice
Questions
197.
A
border
of
uniform
width
is
placed
around
a
rectangular
photograph
that
measures
8
inches
by
10
inches.
If
the
area
of
the
border
is
144
square
inches,
what
is
the
width
of
the
border,
in
inches?
(A
3
(B
4
€
o
(D)
8
(E}y
9
198.
Ifd=
;7
is
e);pressed
as
a
terminating
decimal,
23x5
how
many
nonzero
digits
will
d
have?
(A)
One
(B)
Two
(C)
Three
(D)
Seven
(E)
Ten
199.
For
any
positive
integer
n,
the
sum
of
the
first
n(n+1)
n
positive
integers
equals
all
the
even
integers
between
99
and
301
?
(A)
10,100
(B)
20,200
(C)
22,650
(D)
40,200
(E)
45,150
200.
How
many
prime
numbers
between
1
and
100
are
factors
of
7,150
?
(A)
One
(B)
Two
(C)
Three
(D)
Four
(E)
Five
.
What
is
the
sum
of
179
S
The
Official
Guide
for
GMAT®
Review
2017
202.
203.
180
ZEfl
A
sequence
of
numbers
aj,
ap,
as,
.
.
.
is
defined
as
~—"
follows:
a;
=
3,
a,
=5,
and
every
term
in
the
sequence
after
a,
is
the
product
of
all
terms
in
the
sequence
preceding
it,
e.g.,
az
=
(a;)(@,)
and
a4
=
(a;)(a5)(a3).
If
a,=tand
n
>
2,
what
is
the
value
of
a,
,
,
in
terms
of
t?
(A)
4t
B)
C
£
D)
t
E)
Last
year
the
price
per
share
of
Stock
X
increased
by
k
percent
and
the
earnings
per
share
of
Stock
X
increased
by
m
percent,
where
k
is
greater
than
m.
By
what
percent
did
the
ratio
of
price
per
share
to
earnings
per
share
increase,
in
terms
of
k
and
m?
n
Ky
m
B)
(k—m%
100(k
—m),
€
100
+k
b
100(k
—m),
D)
100+
m
b
100k
—m)
,
(€)
1OO+k+m/0
Of
the
300
subjects
who
participated
in
an
experiment
using
virtual-realhity
therapy
to
reduce
their
fear
of
heights,
40
percent
experienced
sweaty
palms,
30
percent
experienced
vomiting,
and
75
percent
experienced
dizziness.
If
all
of
the
subjects
experienced
at
least
one
of
these
effects
and
35
percent
of
the
subjects
experienced
exactly
two
of
these
effects,
how
many
of
the
subjects
experienced
only
one
of
these
effects?
(A)
105
(B)
125
(C)
130
(D)
180
(E)
195
204,
fm™
=
—%,
then
m~2
is
equal
to
A
-9
B)
-3
1
(€)
-5
1
(D)
3
|
(E)
9
205.
A
photography
dealer
ordered
60
Model
X
cameras
fo
be
sold
for
$250
each,
which
represents
a
20
percert
markup
over
the
'dealer’s
initial
cost
for
each
camera.
Of
the
cameras
ordered,
6
were
never
sold and
were
returned
to
the
manufacturer
for
a
refund
of
50
percent
of
the
dealer’s
initial
cost.
What
was
the
dealer's
approximate
profit
or
loss
as
a
percent
of
the
dealer’s
initial
cost
for
the
60
cameras?
(A)
7%
loss
(B)
13%loss
(C)
7%
profit
(D)
13%
profit
(E)
15%
profit
206.
Seven
pieces
of
rope
have
an
average
(arithmetic
mean)
length
of
68
centimeters
and
a
median
length
of
84
centimeters.
If
the
length
of
the
longest
piece
of
rope
is
14
centimeters
more
than
4
times
the
length
of
the
shortest
piece
of
rope,
what
is
the
maximum
possible
length,
in
centimeters,
of
the
longest
piece
of
rope?
(A)
82
(B)
118
(C)
120
(D)
134
(E)
152
207.
What
is
the
difference
between
the
sixth
and
the
fifth
terms
of
the
sequence
2,
4,
7,
...
whose
nth
term
is
p+2-12
(A)
2
(B)
€
6
(D)
16
(E)
17
208.
209
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208.
From
the
consecutive
integers
=10
to
10,
inclusive,
20
integers
are
randomly
chosen
with
repetitions
allowed.
What
is
the
least
possible
value
of
the
product
of
the
20
integers?
A
(-10%
B
(-10)°
©
0
D)
-(10)*
€
-10%
2C09)
The
letters
D,
G,
|,
|,
and
T
can
be
used
to
form
5-letter
strings
such
as
DIGIT
or
DGIIT.
Using these
letters,
how
many
5-letter
strings
can
be
formed
in
which
the
two
occurrences
of
the
letter
|
are
separated
by
at
least
one
other
letter?
A
12
B)
18
(C)
24
D)
36
(E)
48
210,
Last
Sunday
a
certain
store
sold
copies
of
Newspaper
A
for
$1.00
each
and
copies
of
Newspaper
B
for
$1.25
gach,
and
the
store
sold
no
other
newspapers
that
day.
If
r
percent
of
the
store’s
revenue
from
newspaper
sales
was
from
Newspaper
A
and
if
p
percent
of
the
newspapers
that.the
store
sold
were
copies
of
Newspaper
A,
which
of
the
following
expresses
rin
terms
of
p
?
(A)
1%050—_%
(B)
Z—IE%O_D—p
0
w2
(D)
%O_Lp
(E)
g
625-p
211,
212.
213.
5.3
Problem
Solving
Practice
Questions
0.99999999
0.99999991
_
1.0001
1.0003
A)
1078
B)
3(107%)
(C)
3(107)
D)
2(107%)
E)
107
y
0
P
(4,0)
In
the
rectangular
coordinate
system
above,
if
point
R
(not
shown)
lies
on
the
positive
y-axis
and
the
area
of
triangle
ORPis
12,
what
is
the
y-coordinate
of
point
R
?
(A3
B)
6
€
9
D)
12
(E)
24
Car
A
is
20
miles
behind
Car
B,
which
is
traveling
in
the
same
direction
along
the
same
route
as
Car
A.
Car
A
is
traveling
at
a
constant
speed
of
58
miles
per
hour
and Car
B
is
traveling
at
a
constant
speed
of
50
miles
per
hour.
How
many
hours
will
it
take
for
Car
A
to
overtake
and
drive
8
miles
ahead
of
Car
B
?
(A)
1.5
(B)
2.0
(C)
25
(D)
3.0
[E}
&9
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