ASTB Math Skills Test MST

188 cards

IE or Firefox are the preferred browsers.  For each question, select the option that is most nearly correct. If you answer the questions in order: the ASTB Marine Gouge Math Test questions were the first questions to be added to this set, from #3-52. the Peterson's Master the Officer Candidate Tests Math Skills ebook questions start from #53-82. the Barron's Official Candidate School Tests Book practice...


 
  
Created Apr 13, 2010
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  Side A   Side B
1
Which is the following fractions is the largest?
1/2 3/4 5/8 11/16 23/32
 
3/4
2
Arrange these fractions in order of size from largest to smallest: 1/3, 2/5, 4/15
4/15,...
 
2/5, 1/3, 4/15
3
What is the total nbr of degress in 3 angles of a triangle?
90
100 120 180
 
180
4
(0.2)²
0.02
0.04 0.2
0.4
 
0.04
5
300% is the same as
.03 .3 3
300
 
3
6
A marine fired X rounds of ammunition, gave 2X to his buddy, and had 27 remaining in a magazine....
 
31
7
In the figure, if ACD is a straight line and AB = BC, then X =
90
135 145 180
 
135
8
Which is true?
2/25 < 1/10 1/10 >3/30 2/28 < 3/35 5/13 = 4/5
 
2/25 < 1/10
9
X/4 + X =
x/4
2x/4 4x
5x/4
 
5x/4
10
X-X/2
X/2 2x 4x 3x/2
 
X/2
11
Perimeter of a rectange is 180 ft, the width is 1/2 of the length, what is the length?
30 60 90
100
 
60
12
If 3 times X exceeds 1/3 of y by 9, which of the following is the equation that shows the relationship...
 
3x - 1/3y = 9
13
The avg of 1/25 and 1/100 is
1/50 1/40
1/20 5/100
 
1/40
14
The destruction of a particular bridge requires 3 1/2 tons of C4 explosive. How many tons of...
 
1 1/6
15
If (Y*Y*Y)/(Y+Y) = 2, then Y =
0 1 2 4
 
2
16
74 - (12-20)=
42 56 66 82
 
82
17
If 100 times x is between 50 and 100, then x could be .50 .25 .75 1.00
 
.75
18
The avg temperature during a 4 day period was 73°. If the temperature on the first 3 days...
 
73
19
If 20% of a number is 2.5, what is the nbr?
1.25 10
12.5 25
 
12.5
20
What is the area, in square ft, of the figure?
32 54 63 72
 
63
21
The equation x= 1/2 t(y-z) is equivalent to the equation y=
1/2t( y - z ) 1/2x + zt 2x/t...
 
2x/t + z
22
The expeditionary airfields with the same length are 100 ft wide and 200 ft wide, respectively....
 
1200
23
Two amino cans contain various nbrs of live bullets and blank bullets. Ammo can X contains...
 
The one selected from ammo can X
24
In the square WXYZ figure, AX = 1, YZ =2 and XB =BY. What is the perimeter of polygon WABYZ?
10 8...
 
6 + √2
25
While assulting a fortified machine gun bunker, a marine fired 2000 rounds during two engagements....
 
1400
26
A square tarp is x feet on a side. If 4 ft of another tarp is sewn across one end so that the...
 
x² + 4x
27
It will take 4 hrs 32 min 30 sec to dig one part of a mortar pit. If the other part will take...
 
3 hrs 24 min 22.5 sec
28
In the right triangle XYZ, /_Y =
72° 54° 18° 22°
 
72°
29
In the figure, if O is the center of the circle, and all the sides of the polygon are equal,...
 
90°
30
At a mess night, there are only captains, 2nd lieutenants, and 1st lieutenants (sounds like...
 
55
31
What is the closent approximation to (0.0010197)(5001)(42.974)?
1000 28 215 74
 
215
32
There are exactly four times as many V-22s as CH-53Es in a marin expeditionary composite squadron....
 
35
33
6 M16s and 4 pistols cost J dollars. 4 M16s and 6 pistols cost T dollars which of the following...
 
1/10(J + T)
34
At most, less than one third the round in PRivate Banotz's magazines are tracers. If there...
 
< 50
35
Two F-18s are catapulted off an aircraft carrier and fly on courses that diverge at a 60°...
 
2 2/5
36
For all real numbers, x and y, x * y = y(x+1)
If -4 * j = -6, then j =
-6 6 2 4
 
j = 2
37
What is the formula for a cube?
V= Bh V= 1/3bh V= π r² h V=4/3 r³
 
V=Bh or wh
38
What is the formula for the area of a square?
A= (S² √3 ) /4
A = 4S
A =...
 
A = S²
39
What is the area of a triangle?
A = 2(L+W)
A = 4S
A= S² √3 /4
A =...
 
A = 1/2 bh
40
Area of a rectangle?
A = 2(L+W)
A = Lwh
A = LW
A= S² √3 /4
A...
 
A = LW
41
Area of a trapezoid?
A = 4s
A = π d² /4
A = h 1/2(b1 + b2)
A = 4/3 πr³
A=...
 
A = h 1/2(b1 + b2) or
A = hm
42
What is the formula to find the hypotenuse of a triangle?

1/3 Bh
1/2 bh
c²...
 
c² = a² + b²
43
What is the square root of .09?
.3
.03
3
.09
 
.3
44
If a fuel mixtures required 3 1/2 gallons of gasoline, how many gallons would be needed for...
 
7/8
45
If 35% of X is 3.5, what is X?
20 30 10 15
 
10
46
There are 3 times as many red balls as blue balls. How many balls can there be?
13 9 10 16
 
9
47
The coordinates of point X are (1,2), the coordinates of point Y are (4/6). What is the length...
 
5
48
(x² -x-2)/(x+1)
x+1
x-2
x+2
x² 
 
x-2
49
The volume of a cube A to the volume of cube B is 8:1. If an edge of cube C is twice as long...
 
1:64
50
1432.678
In the nbr above, what are the values for the following?
Tens Units Hundreds Thousands Tenths Thousandths Hundredths
 
Tens               3 Units               2 Hundreds        4 Thousands...
51
In the diagram, the area of rectangle ABCD is 10 and the distance from point D to point A is...
 
5
52
What is the area of the triangle shown?
36
6
18√3
9√3
 
9√3
53
A 6 ft tall farmer wants to determine the height of his barn. He notices that his shadow is...
 
45 ft
54
What is the square root of 16 raised to the 4th power?
16
64
128
256

 
256
55
If the sum of the edges of a cube is 48 in, the volume of the cube is
4 cubic inches
8...
 
64 cubic inches
56
If the tax rate is 3 1/2 % and the amount to be raised is 6440, what is the base?
180,000
181,000
182,000
184,000
 
184,000
57
Each corridor contains 8 to 10 classrooms and each classrom contains 20 -24 students. If all...
 
160
58
At 0800, two trains started out from the same station. One travels north at the rate of 60...
 
1300
59
How much pure acid must be added to 12 ounces of a 40% acid solution in order to produce a...
 
6 ounces
60
If x varies directly as y² and if x = 9 when y = 2, what is the value of x when y = 8?
32
130
144
168
 
144
61
The hour hand of a clock is 3 ft long. How many ft does the tip of this hand move between 1300...
 
62
Find the second of 3 consecutive integers if the sum of the first and the third is 26
10
11
12
13
 
13
63
Find the area of a square circumscribed about a circle whose radius is 10
31 3/7
62...
 
400
64
An island is defended by a battery of coastal guns placed at the easternmost point of the island...
 
30 minutes
65
A team won 25 games in a 40-game season. Find the ratio of games won to games lost.
3...
 
5 : 3
66
If the entrance requirement of a certain college is 82, what mark must a student have in geometry...
 
79
67
Two planes started at the same time from the same airport and flow in opposite directions....
 
285 mph
68
One recruit can complete a certain assignment in 40 min; another recruit can complete the same...
 
24 min
69
If (x - y)² = 40 and x² + y² = 60, then xy=
40
20
12
10
 
10
70
If a triangle of base 6 has the same area as a circle of radius 6, what is the altitude of...
 
12π
71
What is next
5 3 9 7 21 19 __
41
45
49
57
 
57
72
In the figure, what is the measure of angle x?
35°
45°
55°
70°
 
55°
73
Two trains running on the same track travel at the rates of 30 and 35 mph, respectively. If...
 
6 hours
74
A naval detachment has enough rations to feed 16 ppl for 10 days. If four more ppl join the...
 
2 days
75
A field can be plowed by 9 machines in 5 hrs. If 3 machines are broken and cannot be used,...
 
7 1/2 hrs
76
What is the square root of 9 raised to the fourth power?
12
27
49
81
 
81
77
If 2˟ˉ² = 32, then x =
5
7
8
12
 
7
78
Jane received grades of 90, 88, and 75 on 3 tests. What grade must she receive on the next...
 
91
79
A family drove from New York to San Francisco, a distance of 3000 miles. They drive 1/10 of...
 
2400 miles
80
In a 3 hr examination of 320 questions, there are 40 mathematics problems. If twice as much...
 
40 minutes
81
100,000 may be represented as 
10^4
10^5
10^6
10^7
 
10^5
82
If a = 3b and 6b =12c, then a =
6c
9c
12c
15c
 
6c
83
The Hair Palace gives a 5 1/2 % discount to senior citizens. If Pam is 67 yrs old, and her...
 
70.88
84
2x (3xy + y) =
6xy + 2xy
6x²y + 2xy
3xy + 2xy
3x²y+ xy
 
6x²y + 2xy
85
What is the area of a circle?
 
A = π r²
86
Find the area of the shaded portion of the figure

10.57 square feet
11.17 square...
 
12.86 square feet
87
You are in charge of purchasing food for the annual Fourth of July picnic. If you purchase...
 
1623.10
88
Yolanda invested $500 in an invest account and received $650 after 3 yrs. How much was her...
 
10%
89
Susan can paint a room in 6 hrs, while Tom can paint the same room in 5 hrs. Working together,...
 
2.73 hrs
90
(5.37 x 10²) x (2.54 x 10^5) =
13.6398 x 10
13.6398 x 10^10
13.6398 x 10^3
13.6398...
 
13.6398 x 10^7
91
This Mathematical Property or technique lets you multiply a sum by multiplying each addend...
 
Distributive Property
92
Apply the Distributive Property and simplify the following: -7(4x+5) -8
-28x + 43
28x...
 
-28x - 43
93
1/2x - 1/10 = 1/5x + 1/2
2
4
6
8
 
2
94
What is the area of a triangle?
 
1/2 bh
95
Given the radius, how do u find the diameter
 
The radius is 1/2 a diameter, so multiply by 2.
96
What is the area of the shape?
4π  + 12 square feet
6(π + 4) square feet
9π/2...
 
9π/2 + 12 square feet
97
How do u find the area of a rectangle?
 
A = L x W
98
How many square inches in a square ft?
 
12 in. x 12 in. = 1 square ft.
144 square in.
99
If each brick is 3 inches wide and 5 inches long, how many bricks would u need to build a wall...
 
1536
100
An imaginary number "i" is defined solely by the property that its square is 
 
i² = -1
In Electrical Engineering, j is used instead of i
101
(9i + 6)(3i - 7) =
27i² - 7i
-45i - 69
18i - 4
18i + 4
 
-45i - 69
102
Gravel is mixed with cement at a ratio of 5 parts of cement to 1 part of gravel. How many pounds...
 
40 lbs
103
How much carpet would be necessary to cover a room which is 8 ft long and 6 ft wide?
14...
 
60 square feet
104
A bakery specializes in peach and apple pies. Out of a batch of 26 pies, four are peach. What...
 
15.4 percent
105
Convert 6.39 x 10^5 to regular notation
(6.39)^5 x 10
639,000
639.10
0.000639
 
639,000
106
A refrigerator costs $400 to purchase outright, so it can be rented for a non-refundable deposit...
 
14 months
107
Courier charges for packages to a certain destination are 65 cents for the first 250 grams...
 
1155
108
If x/y is an integer, which of the following statements must be true?
both x and y are...
 
x = ny where n is an integer
109
This is a list of numbers is the sum of all of the list divided by the number of items in the...
 
Mean
110
The first term in a sequence is 1 and the second term is 5. From the third term on, each term...
 
3
The avg of 1 and 5 = 3
The avg of 1, 5, and 3 = 3
The avg of 1, 5, 3 and...
111
(3x + 2)(2x - 5)=ax² + kx + n.
What is the value of a - n + k?

5
8
9
10
 
5
112
What is the simplified result of ff the steps in order?
(1) add 5y to 2x
(2) multiply...
 
5x + 14y
113
What is the avg of four tenths and five thousandths?
25002
2502
0.225
0.2025
 
0.2025
114
Which of the integers is not a prime number?
3
5
7
9
 
9
115
If 3ª = 9 What is the value of 4^(a+1) ?
25
30
35
64
 
64
116
If the ratio of 3x to 5y is 1:2, what is the ratio of x to y?
1/2
2/3
3/4
5/6
 
5/6
117
1 ton has how many lbs?
 
2000 lbs
118
If the floor area in a Navy warehouse measures 200 ft by 200 ft., what is the maximum safe...
 
200 lbs per square foot
119
Assume that the United States Mint produces one million nickels a month. The total value of...
 
$600000
120
There are 20 cigarettes in one pack and 10 packs of cigarettes in a carton. A certain brand...
 
2.4 grams
121
A certain government agency had a budget last year of $1,100,500. Its budget this year was...
 
1,271,700
122
How many seconds per question does one have to complete all questions in the Math Section of...
 
50
25 min x 60 sec/min =
1500 sec / 30 problem =
50 sec / problem
123
If x = 4z and Y = 6z then Y =
6/4 X
4/6 X
3/2 Y
3/2 X
 
3/2 X
124
Simplify the following: 4x² - 5x + 1
     x-1

4x - 1
4x + 1
4x...
 
4x - 1
125
Simplify
n + 6n²
6n + 1

N + 1
N + 6

N
 
N
126
How many seconds are in one hour?
60
1200
2400
3600
 
3600
127
How many inches are in one mile?

1,760
63,360
72,913
160,934
 
63360

5280 ft x 12 inches
5280 ft = 1 mile
1760 yards = 1 mile
72,913...
128
An aircraft flies 250 mph for 30 mins, then 300 mph for 10 mins, and flies at 240 mph for 40...
 
335 mi
129
Two trains are 100 miles apart traveling towards each other at 40 mph and 30 mph. How far apart...
 
65 mi
130
Formula for distance
 
Rate x Time
131
If a car tavels 42 mph, how far does it travel in 1200 seconds?
14 mi
21 mi
28.57...
 
14 mi
132
When adding bases containing exponents you can add the exponents even if the bases are the...
 
False
133
When multiplying bases containing exponents you can add the exponents even if the bases are...
 
True
134
What are the perfect squares, from 11-15?
 
121, 144, 169, 196, 225
135
What are the first 6 perfect cubes?
 
1, 8, 27, 64, 125, 196
136
5n+1 = 125
n=?

2
3
4
5
 
2
137
4n4=64 ; n = ?
2
3
4
5
 
2
138
½bh solves for the area of a
circle
parallelogram
rectangle
trapezoid
triangle
 
triangle
139
l x w solves for the area of a
circle
parallelogram
rectangle
trapezoid
triangle
 
rectangle
140
½(b1 + b2) h solves for the area of a 

circle
parallelogram
rectangle
trapezoid
triangle
 
trapezoid
½ multiplied by the sum of bases times the height
141
base multiplied by the height (bh) solves for the area of a

circle
parallelogram
rectangle
trapezoid
triangle
 
parallelogram
142
πr2 solves for the area of a 

circle
parallelogram
rectangle
trapezoid
triangle
 
circle
143
2πr solves for the circumference of a

circle
cyclinder
sphere
oval
 
circle
144
a2 + b2 = c2 is also known as
 
Pythagorean Theorem
145
sin A = a / c
opposite/adjacent
adjacent/hypotenuse
opposite/hypotenuse
 
opposite/hypotenuse
146
cos A = b / c
adjacent/hypotenuse
opposite/adjacent
opposite/hypotenuse
 
adjacent/hypotenuse
147
tan A = a / b

adjacent/hypotenuse
opposite/adjacent
opposite/hypotenuse
 
opposite/adjacent
148
An equilateral trangle has a side of 4. What is the length of the blue line?
√12
2√3
√8
2√5
 
2√3
149
The formula for simple interest is the lump sum multiplied by the interest rate. What is compound...
 
all of the above
150
What is the formula for the "future value" or the compounded interest and the principal?
 
FV = PV (1 + i)n
151
How much interest is accrued on $1000 lump sum at 10% compounded over 2 years?
$100
$210
$221
$240
 
$221
according to the book, $221.
152
How do u find the average?
 
Sum of the numbers / number of items
153
John shoots 75, 82, 83 his first 3 rounds of golf. What score must he post on his last round...
 
80
80 x 4 = 320
320 - (75 + 82 + 83) = 80
154
The probability of an event occurring is equal to the number of events that you want to occur...
 
flipping a coin, 50% chance
Kudos to those that can identify the first one.
155
In a 52 card deck, what is the probability of selecting a face card?
1/13
2/13
3/13
4/13
 
12/52 or 3/13
156
If 5x + 3y = 29 and x - y = 1, then x = ?
1
2
3
4
5
 
4
157
Solve for x: 2x / 7 = 2x²

1/7
2/7
2
7
14
 
1/7
158
If x is an odd integer, which one of the following is an even integer?
2x + 1
2x...
 
x² - x
159
10˟ divided by 10ʸ
10x/y
10xy
10x+y
10x-y
none of the above
 
10x-y
160
   x - 2    x² - 6x + 8

The formula can be reduced to

 1...
 
 1  
x-4
161
If 3˟ = 27, what is the value of 4˟+1
24
48
65
108
none of the...
 
65
162
The expression √28 - √7 reduces to

√4
√7
3√7
√21
-√35
 
√7
163
Mr. Norwalk bought 24 gallons of gasoline, which enables him to drive 648 miles. On the average,...
 
27
164
How many blocks 6" x 4" x 4" can fit in a box 8' x 6' x 4'?

2
48
576
3456
 
3456
165
Steve played in 14 basketball games. He scored a total of 53 field goals (2 points each) and...
 
9
166
There are 800 employees at a company. If 60% drive to work and 30% take the train, how many...
 
480
167
Min reads 3 hardcover mysteries and 4 soft cover mysteries. She reads 3 times as many nonfiction...
 
21
168
In the election for Fairfield County Selectman, Mr. Williams got 33,172 votes, and Mr. Stevens...
 
7420
169
What mathematical statement best represents the following?

Six less a number is four?

6...
 
n - 6 = 4 
170
A cylinder whose height is 8 inc has a volume of 128p³. If the radius is doubled and its height...
 
256p cm³ 
171
Fencing costs $4.75 per foot. Posts cost $12.50 each. How much will it cost to fince a garden...
 
$286.50
172
Multiply (2x + 1)(2x - 1)

2x² + 1
4x² + 1
4x² + 2x + 1
4x² + 4x + 1 
 
4x² + 4x + 1 
173
How much change would you get back from a $20 bill if you purchased 8 CD covers costing $1.59...
 
$7.28
174
The sum of 2 feet 2½ inches, 4 feet 3 3/8 inches, and 3 feet 9 ¾ inches is

9 feet...
 
10 feet 3 5/8 inches
175
The scale on a map shows 500 feet for every 1/4 inch. If two cities are 6 inches apart on the...
 
12000 feet
176
What is the probablility of rolling a sume of 9 using two dice?

1/4
1/9
5/12
7/36
 
1/9
177
Three boxes are needed to hold 18 reams of paper. How many boxes are needed for 90 reams?

5
6
9
15
 
15
178
One gallon of paint covers 400 square feet. How many gallons are needed to cover 2225 square...
 
6 gallons
179
The sum of v50 + 3v72 is

4 + v122
4v122
7v2
23v2
 
23v2
180
An appliance originally costing 1000 goes on sale one week for 25% off. The following week,...
 
$675
181
Dennis ran a race is 2.2 minutes. Kayla ran the same race in 124 seconds. What is the difference...
 
8 seconds
182
What is the diameter of a circle whose circumference is equivalent to its area?

2
3
4
6
 
4
183
If 3 cans of soup cost $5.00, how much do 10 cans cost?

$15.00
$16.45
$16.67
$17.33
 
$16.67
184
A savings account earns 2¼ % interest each year. How much interest is earned on a $1000 deposit...
 
112.50
185
The product of 2 numbers is 117. If one of the numbers is , what is the other?

11
13
15
17
 
13
186
Vanda put some water in the freezer. When she removed it, the water's temperature was 0° C....
 
5 hrs 
187
Sandy brought 4½ lbs of apples and 6 kiwi fruits. Brandon bought 3¼ lbs of apples and 9 kiwi...
 
0.24
188
-3(-4-5)-2(-6)=

0
-5
15
39
 
39


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