Arithmetic Computation Test
(ACT)
Preparation Guide
CONFIDENTIAL
A.C.T.
PREPARATION
GUIDE
It is important that employees demonstrate that they have basic problem solving skills. The
purpose of the Arithmetic Computation Test is to provide the company with objective
information about future apprentices to ensure they will be successful on the job and in
apprentice training.
This Study Guide for the ACT is provided to you so that you may have an opportunity to
review the types of problems you will be facing in the formal test. The problems in this Study
Guide correspond to the problems in the ACT, but are more lengthy and difficult. When you
are proficient in working the problems in this Study Guide, the formal ACT should not be
difficult for you.
Do not use a calculator to help you solve these problems as none will be provided to you on
the real exam. It is important that you be able to demonstrate your problem-solving ability
without the use of a calculator.
The answers to the questions in this study guide are provided. Try to answer each questions
first before looking at the answer. Be sure to show your work as you will be asked to do this
on the formal exam.
A list of books and references to help you prepare for the ACT is attached. These reference
supplements should help you in completing the problems ahead. Good luck!
PACIFIC GAS AND ELECTRIC COMPANY
Revised 03/23/99
CONFIDENTIAL
ARITHMETIC COMPUTATION TEST (ACT)
REFERENCES TO SUPPLEMENT TEST PREPARATION
The original textbook, Refresher Arithmetic by Edwin I. Stein and published by Allyn &
Bacon had been recommended for test preparation in the ACT Study Form for several years.
In the event this book cannot be located, the following is a list of more recent text books which
are generally available at any local bookstore (e.g. Barnes & Nobles, Borders, Stacey's Books,
etc.) that may help employees prepare for the ACT:
1. Arithmetic: The Easy Way, 3rd Edition by Edward Williams & Katie Prindle. Published by
Barron's Educational Series, 1996
2. The Princeton Review MATH SMART: Essential Math for these Numeric Times by
Marci Lerner. Published by Random House, 1997.
3. Arithmetic Made Simple by A.P. Sperling & Samuel D. Levinson. Published by Doubleday,
revised edition 1988.
4. Mathematics Made Simple by Abraham Sperling & Monroe Stuart. Published by
Doubleday, 1991.
5. Kaplan Math Power by Robert Stanton. Published by Simon & Schuster, 1997.
When used in conjunction with the company provided ACT Study Form, these self-paced books
can act as an excellent refresher to supplement an employee's existing mathematical skills.
PACIFIC GAS AND ELECTRIC COMPANY
Revised 03/23/99
ARITHMETIC COMPUTATION TEST
PREPARATION GUIDE
1) Subtract 269,418 from 350,000. Then subtract 813 from 700,000. Then
subtract 1,759,268 from 2,326,431. Then add all the remainders
together.
ANSWER: 1,346,932
350,000 - 269,418 = 80,582
700,000 - 813 = 699,187
2,326,431 - 1,759,268 = 567,163
80,582 + 699,187 + 567,163 = 1,346,932
S-1
ARITHMETIC COMPUTATION TEST
2)
PREPARATION GUIDE
Round off each number to the nearest hundred thousand and then
add the rounded numbers:
3,269,486
10,491,063
14,346,413
6,050,983
2,467,852
891,432
651,026
26,053
ANSWER: 38,300,000
3,300,000
10,500,000
2,500,000
900,000
700,000
14,300,000
6,100,000
0
38,300,000
S-2
ARITHMETIC COMPUTATION TEST
3)
PREPARATION GUIDE
Round off each number to the nearest tenth and then add the rounded
numbers:
.27
3.6153
.16
4
14
.0027
1.6531
ANSWER: 29.2
.3 + 3.6 + 14.0 + 0 + 1.7 + 5.4 + .2 + 4.0 = 29.2
S-3
5.423
ARITHMETIC COMPUTATION TEST
4)
PREPARATION GUIDE
Add the following decimal numbers (change the words to
numbers and then add the numbers.):
a) Three hundred twenty-seven thousand, one hundred three and six
tenths.
b) Four thousand six and seven thousandths.
c)
Twenty-six.
d) Six hundred and seven hundredths.
e)
Twenty-six thousand, four hundred ninety-one and one tenth.
f)
Fifty-seven and eighty-four thousandths.
ANSWER: 358,283.861
327,103.6 + 4,006.007 + 26. + 600.07 + 26,491.1 + 57.084 =
358,283.861
S-4
ARITHMETIC COMPUTATION TEST
5)
PREPARATION GUIDE
Multiply 3,040 by 904. Then multiply 687 by 394. Then add the
products together.
ANSWER: 3,018,838
3,040 x 904 = 2,748,160
687 x 394 = 270,678
2,748,160 + 270,678 = 3,018,838
S-5
ARITHMETIC COMPUTATION TEST
6)
PREPARATION GUIDE
Divide 14,178 by 286. Then divide 69,418 by 286. Write each
answer showing the remainder as a fraction of the divisor and then
add the answers together. Reduce the results to the lowest terms.
ANSWER: 292
164
286
286 14178
49
206
286
286 69418
242
164
286
206
+ 242
286
−−−−−−
370
84
42
291
= 292
= 292
286
286
143
49
S-6
42
143
ARITHMETIC COMPUTATION TEST
7)
Add:
24,987
6.81
9
4
PREPARATION GUIDE
17.38
206
41,008
3
4
1
2
ANSWER: 66,239.44
24,987 + 9 + 17.38 + 206 + 41,008.75 + 6.81 + 4.5 = 66,239.44
S-7
ARITHMETIC COMPUTATION TEST
8)
Subtract 12
PREPARATION GUIDE
3
1
2
from 26 . Then subtract 2
from the result.
4
3
3
Reduce the answer to the lowest terms.
ANSWER: 10
26
1
4
16
= 26
= 25
3
12
12
12
3
9
= 12
4
12
25
16
9
7
19
- 12
= 13
= 12
12
12
12
12
2
2
8
=2
3
12
12
19
8
11
-2
= 10
12
12
12
S-8
11
12
ARITHMETIC COMPUTATION TEST
9)
Add:
81
62
25
PREPARATION GUIDE
82
32
49 .
Use positive roots only.
ANSWER: 130
9 + 36 + 5 + 64 + 9 + 7 = 130
S-9
ARITHMETIC COMPUTATION TEST
10)
PREPARATION GUIDE
In the following pairs of fractions, decide which of the two fractions is
the larger number. Select the larger number from each pair and add
these three numbers. Reduce the answer to the lowest terms.
a)
5
9
or
6
11
11
2
or
16
3
b)
c)
ANSWER: 2
7
5
or
12
8
7
48
a)
5
55
=
6
66
9
54
=
11
66
11
33
=
16
48
2
32
=
3
48
7
14
=
12
24
5
15
=
8
24
b)
c)
5
11
5
40
33
30
103
+
+ =
+
+
=
6
16
8
48
48
48
48
S - 10
lowest terms = 2
7
48
ARITHMETIC COMPUTATION TEST
11)
Find the product of:
9
3
5
PREPARATION GUIDE
8
1
3
2
5
.
8
ANSWER: 210
9
3
1
5
x 8 x 2 =
5
3
8
48
25
21
x
x
= 2 x 5 x 21 = 210
5
3
8
S - 11
ARITHMETIC COMPUTATION TEST
12)
Add:
2
3
10
16
5
6
7
PREPARATION GUIDE
1
.
2
Reduce to the lowest terms.
ANSWER: 26
2
3
9
=2
10
30
16
5
25
= 16
6
30
7
1
15
=7
2
30
2
9
25
15
19
+ 16
+7
= 26
30
30
30
30
S - 12
19
30
ARITHMETIC COMPUTATION TEST
13)
Add:
4
5
8
26
2
3
13
PREPARATION GUIDE
7
.
12
Reduce to the lowest terms.
ANSWER: 44
4
5
15
=4
8
24
26
2
16
= 26
3
24
13
7
14
= 13
12
24
4
7
8
15
16
14
45
21
7
+ 26
+ 13
= 43
= 44
= 44
24
24
24
24
24
8
S - 13
ARITHMETIC COMPUTATION TEST
14)
Divide 4
PREPARATION GUIDE
3
1
1
by 11 . Then divide 16
by 42. Then add the two
8
4
3
results together and reduce to the lowest terms. Perform all
operations with fractions.
ANSWER :
4
7
9
3
1
35
45
35
4
7
÷ 11
=
÷
=
x
=
8
4
8
4
8
45
18
16
1
49
49
1
7
÷ 42 =
÷ 42 =
x
=
3
3
3
42
18
7
7
14
7
+
=
=
18
18
18
9
S - 14
ARITHMETIC COMPUTATION TEST
15)
PREPARATION GUIDE
Find each of the following numbers and then add the resulting
numbers together:
11 is
3
of what number?
8
8 is
3
of what number?
5
7 is
3
of what number?
4
ANSWER: 52
11 ÷
3
11
8
88
1
=
x =
= 29
8
1
3
3
3
8 ÷
3
8
5
40
1
= x =
= 13
5
1
3
3
3
7 ÷
3
7
4
28
1
= x =
=9
4
1
3
3
3
29
1
1
1
+ 13 + 9 = 52
3
3
3
S - 15
ARITHMETIC COMPUTATION TEST
16)
PREPARATION GUIDE
Subtract .087 from 14; then subtract .863 from .9; then subtract 4.32
from 8.6596; then add the results together.
ANSWER: 18.2896
14.0 - .087 = 13.913
.900 - .863 = .037
8.6596 - 4.3200 = 4.3396
13.913 + .037 + 4.3396 = 18.2896
S - 16
ARITHMETIC COMPUTATION TEST
PREPARATION GUIDE
17) Arrange the following numbers in order of size (from the smallest to
the largest):
.465
.4053
.0059
5.
.47
.046
4.5
.51
.583
.60
ANSWERS:
(Smallest)
(Largest)
S - 17
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
.0059
.046
.4053
.465
.47
.51
.5126
.583
.60
4.5
5.
.5126
ARITHMETIC COMPUTATION TEST
18)
PREPARATION GUIDE
Multiply 462 by .801; then multiply .03 by .009; and then multiply
4.61 by 3.15; and then add all the products together.
ANSWER: 384.58377
462 x .801 = 370.062
.03 x .009 = .00027
4.61 x 3.15 = 14.5215
370.062 + .00027 + 14.5215 = 384.58377
S - 18
ARITHMETIC COMPUTATION TEST
19)
PREPARATION GUIDE
Divide 972 by .0079; then divide 79.86 by 9.61. Find the answers
correct to the nearest thousandths, and add them together.
ANSWER: 123,046.285
123037.975
.0079 9720000.0000
8.310
961 7986.000
S - 19
ARITHMETIC COMPUTATION TEST
20)
PREPARATION GUIDE
Change the following fractions to decimals, correct to the nearest
thousandth, and add them together:
4
16
37
9
13
14
12
1
11
4
7
31
6
1
2
ANSWER: 37.178
.4324
37 16
.9285
14 13
.2258
31 17.0000
.0909
111
1
.5
21
4.432
9.929
12.091
4.226
6.500
37.178
S - 20
ARITHMETIC COMPUTATION TEST
21)
PREPARATION GUIDE
Change the following decimals to fractions and then add the resulting
fractions:
.1875
.5625
.8125
ANSWER: 1
.1875 =
1875
75
3
=
=
10000
400
16
.5625 =
5625
225
9
=
=
10000
400
16
.8125 =
8125
325
13
=
=
10000
400
16
3
9
13
25
9
+
+
= =1
16
16
16
16
16
S - 21
9
16
ARITHMETIC COMPUTATION TEST
22)
Subtract
13.1 by
PREPARATION GUIDE
3
2
from 1.861 ; then subtract
from 1.217 ; then multiply
8
5
1
1
; then divide .5 by ; then add all the results together.
4
4
ANSWER: 7.578
2
= .4
5
1.861 - .4 = 1.461
3
= .375
8
1.217 - .375 = .842
1
= .25
4
13.1 x .25 = 3.275
1
= .25
4
2
.25 .50 = 2.0
1.461 + .842 + 3.275 + 2.0 = 7.578
S - 22
ARITHMETIC COMPUTATION TEST
23)
PREPARATION GUIDE
Change the following percentages into decimals and add the
decimals:
2.03%
16%
94
1
%
2
112
3
%
4
.8%
700%
ANSWER: 9.2658
16 %
.16
2.03 %
.0203
94
1
%
2
112
3
%
4
.945
1.1275
.8 %
.008
700%
7.00
1
%
2
.005
9.2658
S - 23
1
%
2
ARITHMETIC COMPUTATION TEST
24)
PREPARATION GUIDE
Express each of the following percentages as a common fraction or
mixed number (all must be correct for credit):
a)
8%
b) 37
1
%
2
ANSWER :
2
25
ANSWER:
3
8
325%
ANSWER: 3
1
4
d) 18 %
ANSWER :
9
50
c)
e) 33
1
%
3
8%=
8
2
=
25
100
37
ANSWER:
37.5
15
3
1
%=
= =
2
100
40
8
325 % =
18% =
13
1
325
=3
=
4
4
100
18
9
=
100 50
1
33
100 1
1
=
33 % = 3 =
3
300 3
100
S - 24
1
3
ARITHMETIC COMPUTATION TEST
25)
PREPARATION GUIDE
Express each of the following fractions and mixed numbers as
percentages (all must be correct for credit):
a)
7
10
ANSWER: 70 %
b)
14
5
ANSWER: 280 %
c)
1
d)
13
13
e)
17
400
23
50
ANSWER: 146 %
ANSWER: 100 %
ANSWER: 4.25 %
7
=.7 = 70%
10
14
4
= 2 = 2.8 = 280%
5
5
1
23
= 1.46 = 146%
50
13
= 1 = 100%
13
17
.0425 = 4.25%
400
S - 25
ARITHMETIC COMPUTATION TEST
26)
PREPARATION GUIDE
Find 37% of 91; then find 3% of 820; then find
1
% of 11; and then
4
add all these numbers together.
ANSWER: 58.2975
91 x .37 = 33.67
820 x .03 = 24.60
11 x .0025 = .0275
33.67 + 24.60 + .0275 = 58.2975
S - 26
ARITHMETIC COMPUTATION TEST
27)
PREPARATION GUIDE
Find the following percentages (all must be correct for credit):
a)
234 is what percent of 585?
ANSWER: 40 %
b) 37 is what percent of 25?
ANSWER: 148 %
c) 3 is what percent of 100?
ANSWER: 3%
.4
a) 585 234.00 = 40%
1.48
b) 25 37.00 = 148%
.03
c) 100 3.00 = 3%
S - 27
ARITHMETIC COMPUTATION TEST
28)
PREPARATION GUIDE
Find the following numbers and add them together:
128 is 32% of what number? 17 is 4% of what number? 4 is .8% of
what number?
ANSWER: 1325
400
400.
.32 128.00
425
500
1325
425.
.04 17.00
500.
.008 4.000
S - 28
ARITHMETIC COMPUTATION TEST
PREPARATION GUIDE
29) If given the formula: a=bc, (Both must be correct for credit).
a)
What would be the formula for finding b?
ANSWER: b =
a
c
b) What would be the formula for finding c?
ANSWER: c =
a)
a = bc
a
bc
=
c c
a
b=
c
a = bc
b)
a bc
=
b
b
c=
S - 29
a
b
a
b
ARITHMETIC COMPUTATION TEST
30)
PREPARATION GUIDE
Add the following lengths. Give the answer in feet and inches in its
simplest form.
6 ft. 7 in.
47 in.
9 ft 11 in.
13
3
ft.
4
18 ft.
17 in.
ANSWER: 63 ft. 3 in.
6’ 7”
0’ 47”
9’ 11”
13’ 9”
18’ 0”
9’ 8”
0’ 17”
55’ 99”
99”= 8’ 3”
55’
+ 8’ 3”
63’ 3”
S - 30
9
2
ft.
3
ARITHMETIC COMPUTATION TEST
31)
PREPARATION GUIDE
Change the following lengths to feet and inches and add:
14.6 ft.
12.3 ft.
21.7 ft.
9.4 ft.
11.9 ft.
You may use either fractions or decimals in expressing parts of
inches.
ANSWER: 69 ft 10.8 in.
12 x .6 = 7.2 in.
14’
7.2”
12 x .3 = 3.6 in.
12’
3.6”
12 x .7 = 8.4 in.
21’
8.4”
12 x .4 = 4.8 in.
9’
4.8”
12 x .9 = 10.8 in.
+ 11’ 10.8”
67’ 34.8”
67’
+ 2’ 10.8”
69’ 10.8”
S - 31
34.8”= 2’ 10.8”
ARITHMETIC COMPUTATION TEST
32)
PREPARATION GUIDE
Change the following lengths to feet (and tenths of a foot) and then
add:
17 ft. 9 in.
8 ft. 5 in.
19 ft. 11 in.
12 ft. 6 in.
Be sure to round all decimals to tenths before adding.
ANSWER: 64.8 ft
9
=.75
12
5
=.4167
12
11
=.9167
12
6
=.5
12
2
=.166
12
17.8’ + 8.4’ + 19.9’ + 12.5’ + 6.2’ = 64.8’
S - 32
6 ft. 2 in.
ARITHMETIC COMPUTATION TEST
33)
PREPARATION GUIDE
Find the length of time for each of the four periods and then add them
for the total time: The first period is from 8:14 a.m. to 1:56 p.m.;
the second period is from 10:24 a.m. to 4:36 p.m.; the third is from
11:06 a.m. to 5:18 p.m.; and the fourth is from 8:42 a.m. to 3:18 p.m.
ANSWER: 24 hrs. 42 min.
11hrs60 min
11hrs60 min
8hrs14 min
− 10hrs 24 min − 11hrs6 min
−−−−−−−
−−−−−−−− −−−−−−−−
= 3hrs 46 min = 1hr 36 min
+ 1hrs56 min
11hrs60 min
= 0hrs54 min 11hrs60 min
+ 4hrs36 min + 5hrs18 min
−−−−−−−− −−−−−−−− −−−−−−−−
= 4hrs102 min = 5hrs72 min = 5hrs72 min
+ 1hr 42 min + 1hr12 min
+ 1hr12 min
−−−−−−−− −−−−−−−− −−−−−−−−
= 5hrs 42 min = 6hrs12 min
= 6hrs12 min
− 8hrs42 min
−−−−−−−−
= 3hrs18 min
+ 3hrs18 min
−−−−−−−−
= 6hrs36 min
5hrs42min + 6hrs12min + 6hrs12min + 6hrs36min = 24hrs42min
S - 33
ARITHMETIC COMPUTATION TEST
34)
PREPARATION GUIDE
All the following must be correct for credit.
a)
In the formula w =
xy
, what happens to the value of “w” when
z
“y” is tripled?
ANSWER: W is tripled
b) What happens to the value of “w” when “z” is doubled?
ANSWER: W is cut in half
c)
In the formula w =
3xz
, what happens to the value of “w” when
2y
“x” is doubled?
ANSWER: W is doubled.
d) Given the formula in c), what happens to the value of “w” when
“y” is multiplied by 4?
ANSWER: w is cut to ¼ of original value
S - 34
ARITHMETIC COMPUTATION TEST
35)
PREPARATION GUIDE
Add the following numbers:
3.4 x 10 4
1.78 x 1,000
6.006 x 10 5
8.631 x 10 4
.008 x 1,000
5.48761 x 10 3
863 x 100
.0683 x 100,000.
ANSWER: 821,315.61
3.4 x 104 =
34,000.
1.78 x 1000 =
1,780.
8.631 x 104 =
86,310.
.008 x 1000 =
8.
6.006 x 105 =
600,600.
863 x 100 =
86,300.
5.48761 x 103 =
5,487.61
.0683 x 100,000 =
6,830.
821,315.61
S - 35
ARITHMETIC COMPUTATION TEST
36)
PREPARATION GUIDE
Find the following:
a)
12 compared to 60 is the same as 22 compared to what
number?
ANSWER: 110
b) The unknown number in (a) compared to 55 is the same as 13
compared to what number?
ANSWER : 6
c)
1
2
The unknown number in (b) compared to 39 is the same as what
number compared to 54?
ANSWER: 9
simplify :
110 13
=
55
b
12 22
=
60 a
b)
a)
12a = 1,320
a = 110
110b = 715
1
b=6
2
1
2 = c
39 54
6
c)
351 = 39c
c=9
S - 36
ARITHMETIC COMPUTATION TEST
37)
PREPARATION GUIDE
What is the total volume of all three of the following rectangular
spaces? The first is 6 ft. 3 in. long, 4 ft. 6 in. wide, and 8 ft. 8 in.
high. The second is 7 ft. long, 2 ft. 6 in. wide, and 9 ft. 3 in. high.
The third is 5 ft. 2 in. long, 12 ft. wide, and 4 ft. 9 in. high.
ANSWER: 700
3
6
8
1 1 2
x 4 x8 = 6 x 4 x8 =
12 12 12
4 2 3
25 9 26 975
3
x x
=
= 243
4 2 3
4
4
6
3
6
243 = 243
4
8
7
7
161 = 161
8
8
1
4
294 = 294
2
8
−−−−−−−−−
↓
6
3
1 1
x9 = 7 x 2 x9 =
12 12
2 4
7 5 37 1295
7
x x
=
= 161
1 2 4
8
8
7x2
698
3
1
9
2
x12x 4 = 5 x12 x 4 =
4
6
12
12
31 12 19 589
1
x x =
= 294
6 1 4
2
2
5
S - 37
17
1
= 700
8
8
1
Cu. Ft.
8
ARITHMETIC COMPUTATION TEST
38)
PREPARATION GUIDE
Find “a” in the following formulas, when b = 4, c = 2, and d = 3.
Then add the four “a” numbers together.
a = 2b + 4c + d
a=
6bc
d
⎛ 2d ⎞
⎟
c⎠
a=b ⎜
⎝
a = 10bcd
ANSWER: 287
a = 2( 4) + 4( 2) + 3
=8+8+ 3
a=
= 19
⎛ 2( 3) ⎞
⎛ 6⎞
a = 4⎜
⎟ = 4⎜ ⎟ = 4( 3) = 12
⎝ 2⎠
⎝ 2 ⎠
6( 4)( 2) 6( 8) 48
=
=
= 16
3
3
3
a = 10( 4)( 2)( 3) = 10( 24) = 240
19 + 16 + 12 + 240 = 287
S - 38
ARITHMETIC COMPUTATION TEST
39)
PREPARATION GUIDE
Write the following formulas (all must be correct for credit):
a)
The circumference of a circle is equal to twice pi ( π ) times the
radius.
ANSWER: C = 2 πr
b) The area of a circle is equal to pi (π) times the square of the
radius (r).
ANSWER: A = πr 2
c) The area of a triangle is equal to one half the product of the altitude
and base.
ANSWER
A=
1
ab
2
d) The area of a rectangle is equal to the product of the altitude and
the base.
ANSWER A = ab
S - 39
ARITHMETIC COMPUTATION TEST
40)
PREPARATION GUIDE
Simplify the following expressions and add them together:
18x12 x 24
144
25 + 500
25
504 x10
360
33x 9 x14
231
30 + 6
6+ 3
ANSWER: 93
18x12 x 24
= 36
144
25 + 500 525
=
= 21
25
25
33x 9 x14
= 18
231
504x10
= 14
360
36 + 21 + 18 + 14 + 4 = 93
END OF TEST
S - 40
30 + 6 36
=
=4
6+ 3
9