Algebra ready-sample-test

This is a sample test for the
algebra–ready placement test
at the Harbor College
The solution and a link to a review
are given for each problem. The review–links
of all the topics may be accessed here.
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A
B
C
D
Question 1.
Answer for Question 1:
28
42
The reduced form of is
6
7
3
4
4
7
2
3

Solution to Q1
28
42
The correct answer is 2/3.
To reduce a fraction, we divide the numerator
and the denominator by their greatest common
factor (i.e. the largest number that can go into
both numbers) which is 14.
=

Link to reviewNext Question
Solution to Q1
28
42
The correct answer is 2/3.
To reduce a fraction, we divide the numerator
and the denominator by their greatest common
factor (i.e. the largest number that can go into
both numbers) which is 14.
=
÷1428
42 ÷14
= 2
3

Correct!
Next Question
A
B
C
D
Question 1. 28
42
The reduced form of
6
7
3
4
4
7
2
3
is

A
B
C
D
Question 2.
5
6
1
4
=
4
2
5
12
7
12
13
24

Solution to Q2
5
6
1
4
=
Convert into fractions
with LCD = 1212
(5 x 2 – 1 x 3)
=
7
12
The correct answer is .
7
12

Correct!
Next Question
A
B
C
D
Question 2. 5
6
1
4
=
4
2
5
12
7
12
13
24

A
B
C
D
Question 3.
27
14
18
7
=÷
3
4
9
4
9
8
3
8

Solution to Q3
27
14
18
7
=
÷
27
14 18
7
x
The answer is .3
4
reciprocate and multiply

Solution to Q3
27
14
18
7
=
÷
27
14 18
7
x
3
22
= 3
4
The answer is .3
4
reciprocate and multiply
1

Correct!
Question 3. 27
14
18
7
=÷
Next Question
A
B
C
D
3
4
9
4
9
8
3
8

A
B
C
D
Question 4.
4
2
3 1
4
3
=
3
4
2
1
4
1
1
4
1
3

Next Question
Solution to Q4
3 1
4
3
= 3 – 1 4
3
= 2
4
3
1
4
1=
The answer is .1
4
1
Link to review

Correct!
Next Question
A
B
C
D
Question 4.
4
2
3 1
4
3
=
3
4
2
1
4
1
1
4
1
3

A
B
C
D
,4
3
,9
8
3
2
4
3
9
8
4
3
9
8
3
2
9
8
9
8
4
3<
<
<
< 3
2
4
3
3
2
3
2
<
<
<
<
Question 5. Arrange
from the smallest to the largest.

Solution to Q5
, 4
3
3
2
We cross multiply to compare the fractions.
The answer is B:
So
98
3
2
, similarly we have that
4
3
9
8<3
2
<
4
3
<
4
3
9
8< .
← larger

Solution to Q5
, 4
3
3
2
We cross multiply to compare the fractions.
The answer is B:
So
98
3
2
, similarly we have that
4
3
9
8<3
2
<
4
3
<
4
3
9
8< .
← larger
4
3
=
Or multiply by the LCD = 36
36 x 9
8
=3
2
=36 x 36 x
9 4 12
27 32 24
the largestthe middle the smallest

Question 5. Arrange
from the smallest to the largest.
Correct!
Next Question
A
B
C
D
,4
3
,9
8
3
2
4
3
9
8
4
3
9
8
3
2
9
8
9
8
4
3
3
2
4
3
3
2
3
2
<
<
<
<
<
<
<
<

Question 6. A bag has 48 pieces of candies.
Joe ate 7/8 of the whole bag. How many
pieces of candies did Joe eat?
D
B
C
A 42
36
40
30

Solution to Q6
48 x = 42
8
7
6
The answer is 42.

Question 6. A bag has 48 pieces of candies.
Joe ate 7/8 of the whole bag. How many
pieces of candies did Joe eat?
Correct!
Next Question
42
36
40
30D
B
C
A

6
4
0
–4
A
D
C
B
Question 7. –3 – (–5) – (–2) =

Solution to Q7
The answer is 4.
–3 – (–5) – (–2)
= –3 + 5 + 2
= 4

6
4
0
–4
Correct!
Next Question
Question 7. –3 – (–5) – (–2) =
A
D
C
B

39
37
35
34
A
B
D
C
Question 8.
33 =
32 x 36

Solution to Q8
33 =32 x 36
33
38
2+6=8
The answer is 35.

Solution to Q8.
33 =32 x 36
33
38
= 35
2+6=8 8–3=5
The answer is 35.

39
37
35
34
Correct!
Next Question
Question 8.
33 =
32 x 36
A
B
D
C

2
4
6
8
A
B
C
D
Question 9. 24 ÷ 6 x 2

Solution to Q9
The answer is 8.
24 ÷ 6 X 2
= 4 x 2
= 8

Correct!
Next Question
2
4
6
8
A
B
C
D
Question 9. 24 ÷ 6 x 2

15
–9
6
0D
B
C
A
Question 10. 6 – 3(–3) =

Solution to Q10
The answer is 8.
6 – 3(–3)
= 6 + 9
= 15

Correct!
Next Question
Question 10. 6 – 3(–3) =
15
–9
6
0D
B
C
A

A
D
C
B
Question 11. 2.3 – 0.45 + 0.08 =
1.93
1.83
1.73
2.03

Solution to Q11
The answer is 1.93.
2.3 – 0.45 + 0.08
= 1.85 + 0.08
= 1.93

Correct!
Next Question
Question 11. 2.3 – 0.45 + 0.08 =
1.93
1.83
1.73
2.03A
D
C
B

A
B
C
D
Question 12. 1.22 x 0.5 =
0.36
0.6
0.24
0.72

Solution to Q12
The answer is 0.72.
1.22 x 0.5
= 1.44 x 0.5
= 0.72

Correct!
Next Question
Question 12. 1.22 x 0.25 =
A
B
C
D
0.36
0.6
0.24
0.72

D
B
C
A
Question 13. 0.108 ÷ 1.8 =
0.6
0.06
0.006
0.0006

Solution to Q13
The answer is 0.6.
0.108 ÷ 1.8
= 1.08 ÷ 18
= 0.6

Correct!
Next Question
A
B
C
D
Question 13. 0.108 ÷ 1.8 =
0.6
0.06
0.006
0.0006

A
B
D
Question 14.
–0.5
–0.8
–0.7
4
3
– 1.35 =
C –0.6

Solution to Q14
The answer is –0.6.
4
3
– 1.35
= 0.75 – 1.35
= –0.6

Correct!
Next Question
A
B
D
Question 14.
–0.5
–0.8
–0.7
4
3
– 1.35 =
C –0.6

A
B
D
Question 15. 2.3 X 103 =
C
0.00023
0.023
230
2300

Solution to Q15
The answer is 230.
2.3 X 103
= 2.3 x 1,000
= 2300

Correct!
Next Question
A
B
D
Question 15. 2.3 X 103 =
C
0.00023
0.023
230
2300

C
B
D
Question 16. How many grams of pure alcohol
are there in 300 grams of cough syrup that is
5% alcohol?
A
1.5 g
150 g
15 g
0.15 g

Solution to Q16
The answer is 15 grams.
5% of 300 is
100
5
x 300

Solution to Q16
The answer is 15 grams.
5% of 300 is
100
5
x 300
= 15
3

Correct!
Next Question
Question 16. How many grams of pure alcohol
are there in 300 grams of cough syrup that is
5% alcohol?
C
B
D
A
1.5 g
150 g
15 g
0.15 g

A
B
D
Question 17. Which of the following
percentages is the closest to 2/7.
C 30%
20%
10%
40%

Solution to Q17
The answer is C: 30%
7
2
= 0.28…

Correct!
Next Question
A
B
D
Question 17. Which of the following
percentages is the closest to 2/7.
C 30%
20%
10%
40%

A
C
D
Question 18. Arrange the numbers 60%, 2/3,
0.61 from the smallest to the largest .
B
60%, 2/3, 0.61
60%, 0.61, 2/3,
2/3, 0.61, 60%,
0.61, 60%, 2/3,

Solution to Q18
The answer is B:
60%, 0.61, 2/3,
60% = 0.60
2/3 ≈ 0.66

Correct!
Next Question
A
C
D
Question 18. Arrange the numbers 60%, 2/3,
0.61 from the smallest to the largest .
B
60%, 2/3, 0.61
60%, 0.61, 2/3,
2/3, 0.61, 60%,
0.61, 60%, 2/3,

B
C
D
Question 19. Joe got a raise from $15/hr to
$18/hr. What is the % increase in Joe’s hourly
wages?
A
3%,
18%,
15%,
20%,

Solution to Q19
The answer is A:
20%
From $15 Joe got a of raise of 3$.
so the % increase is 3/15 = 20% .

Correct!
Next Question
B
C
D
Question 19. Joe got a raise from $15/hr to
$18/hr. What is the % increase in Joe’s hourly
wages?
A
3%,
18%,
15%,
20%,

B
C
A
Question 20. Let x = 4, then 6 – 5x is
D –14
–4
14
4

Solution to Q20
The answer is A:
–14
Set x = 4 in 6 – 5x, we get
6 – 5(4)
= 6 – 20
= –14

Correct!
Next Question
B
C
A
Question 20. Let x = 4, then 6 – 5x is
D –14
–4
14
4

B
C
A
Question 21. If x = 3, y = 6, then xy – x – y is
D 9
0
6
–3

Solution to Q21
The answer is 9.
Set x = 3, y = 6 in xy – x – y
we have 3(6) – 3 – 6 = 9

Correct!
Next Question
B
C
A
Question 21. If x = 3, y = 6, then xy – x – y is
D 9
0
6
–3

B
D
A
Question 22. If 3x – 2 = 16, then x is
C
12
8
6
4

Solution to Q22
The answer is x = 6.
3x – 2 = 16
add 2 to both sides 3x = 18
divide both sides by 3 x = 6

Correct!
Next Question
B
D
A
Question 22. If 3x – 2 = 16, then x is
C
12
8
6
4

B
D
C
Question 23.
If b = 2, and a – 2b = 10 then a =
A 14
8
–12
6

Solution to Q23
The answer is a = 14.
If b = 2, the a – 2(2) = 10 so a = 14.

Correct!
Next Question
B
D
C
Question 23.
If b = 2, and a – 2b = 10 then a =
A 14
8
–12
6

A
D
C
Question 24. A medium bag of chocolates has
24 pieces and a small bag has 6 pieces.
We bought 2 medium bags and 4 small bags.
How many pieces of chocolates we have in
total?
B
80
72
96
60

Solution to Q24
The answer is 72.
We have 2 x 24 + 4 x 6 = 72.

Correct!
Next Question
A
D
C
Question 24. A medium bag of chocolates has
24 pieces and a small bag has 6 pieces.
We bought 2 medium bags and 4 small bags.
How many pieces of chocolates we have in
total?
B
80
72
96
60

A
D
B
Question 25. From experience, it’s sunny every
5 out of 7 days at Sunny Hills. In a period of
140 days, how many sunny days are expected?
C
60
80
100
120

Solution to Q25
The answer is 100.
We have that
7
5
140
x=
700 = 7x or
100 = x

Correct!
Next Question
A
D
B
Question 25. From experience, it’s sunny every
5 out of 7 days at Sunny Hills. In a period of
140 days, how many sunny days are expected?
C
60
80
100
120

D
C
B
Question 26. A bag of chocolates cost $24 and
a bag of peanuts cost $6. We bought 2 bags of
chocolates and 6 bags of peanuts. What is the
difference between the cost for chocolates and
the cost for the peanuts?
A $12
$10
$8
$6

Solution to Q26
The answer is $12.
The chocolates cost 2 x 24 = $48,
the peanuts cost 6 x 6 = $36,
so the difference is 48 – 36 = $12.

Correct!
D
C
B
Question 26. A bag of chocolates cost $24 and
a bag of peanuts cost $6. We bought 2 bags of
chocolates and 6 bags of peanuts. What is the
difference between the cost for chocolates and
the cost for the peanuts?
A $12
$10
$8
$6 Next Question

A
C
B
Question 27.
A triangle has sides with lengths of
D
ft, 1½ ft and 2 ft, what’s its perimeter?1 2
3
ft4 5
6
ft5 1
6
ft5 5
6
ft4 1
6

Solution to Q27
The answer is 5 1/6 ft.
The perimeter is
+1 2
3
1 1
2 + 2
= 1 + 1 + 2 + 2/3 + 1/2
= 4 + 1 1
6
= 5 1
6

Correct!
Next Question
A
B
Question 27.
A triangle has sides with lengths of
ft, 1½ ft and 2 ft, what’s its perimeter?1 2
3
ft4 5
6
ft5 1
6
ft5 5
6
ft4 1
6C
D

A
D
B
Question 28.
The perimeter of a square is 16 ft,
what is the area?
C
256 ft2
144 ft2
16 ft2
12 ft2

Solution to Q28
The answer 16 ft2.
The perimeter is 16 ft so the square is
4 ft x 4 ft with area 4 x 4 = 16 ft2

Correct!
Next Question
A
D
B
Question 28.
The perimeter of a square is 16 ft,
what is the area?
C
256 ft2
144 ft2
16 ft2
12 ft2

A
B
Question 29.
Which of the following is the closest to the
circumference of a circle with a 8–ft radius?
20 ft
30 ft
40 ft
50 ft
C
D

Solution to Q29
The answer D: 50 ft.
The circumference of circle is 2πr
where π ≈ 3.14,
if r = 8 then the circumference is
16 π ≈ 16 x 3.1 ≈ 50.

Correct!
Next Question
A
B
20 ft
30 ft
40 ft
50 ft
C
D
Question 29.
Which of the following is the closest to the
circumference of a circle with a 8–ft radius?

A
D
Question 30.
Which of the following pictures represents
A, B and C on the real line most accurately
if A = 3, B = 9 and C = 12?
C
B
0
0
0
0

Solution to Q30
The answer is B.
0 6 1293

Correct!
Next Question
A
D
Question 30.
Which of the following pictures represents
A, B and C on the real line most accurately
if A = 3, B = 9 and C = 12?
C
B
0
0
0
0

A
D
Question 31.
The vertices of a rectangle are (1, 1), (6, 1),
(1, 8), and (6, 8). What is the perimeter of
this rectangle?
C
B
20
24
30
36

Solution to Q31
The answer is 24.
We have the following 5 x 7 rectangle:
(1, 1) (6, 1)
(6, 8)(1, 8)
So the perimeter is
5 + 5 + 7 + 7
= 245
7

Correct!
Next Question
0
A
D
Question 31.
The vertices of a rectangle are (1, 1), (6, 1),
(1, 8), and (6, 8). What is the perimeter of
this rectangle?
C
B
20
24
30
36

A
D
Question 32.
The vertices of a rectangle are (–1, 1), (4, 1),
(–1, 3), and (4, 3). What is the area of this
rectangle?
B
C
36
24
20
10

Solution to Q32
The answer is 20.
We have the following 5 x 4 rectangle:
(–1, 1) (4, 1)
(4, 3)(–1, 3)
So the area is
5 x 4
= 205
4

Correct!
Next Question
A
D
Question 32.
The vertices of a rectangle are (–1, 1), (4, 1),
(–1, 3), and (4, 3). What is the area of this
rectangle?
B
C
36
34
20
10

A
D
Question 33.
The following are the temperatures recorded
from 1 pm to 5 pm, what is the largest
difference in the temperature during this time
period given this data?
B
C
20o
15o
10o
5o
1 pm 2 pm 3 pm
(1, 16o)
(2, 10o)
(4, 20o)
(3, 17o)
(5, 11o)
4 pm 5 pm

Solution to Q33
The answer is 100.
The highest temperature is 20o and the
lowest is 10o so the largest difference is
20 – 10 = 10o

Correct!
A
D
Question 33.
The following are the temperatures recorded
from 1 pm to 5 pm, what is the largest
difference in the temperature during this time
period given this data?
B
C
20o
15o
10o
5o
1 pm 2 pm 3 pm
(1, 16o)
(2, 10o)
(4, 20o)
(3, 17o)
(5, 11o)
4 pm 5 pm
Next Question

C
D
Question 34. Given the following right triangle,
what is the length of A?
B
A 8 ft
8 ½ ft
9 ft
9 ½ ft
10 ft
6 ft
A

Solution to Q34
The answer is 8 ft.
By Pythagorean Theorem that
A2 + 62 = 102
A2 + 36 = 100
A2 = 64
A = 8

Next Question
C
D
Question 34. Given the following right triangle,
what is the length of A?
B
A 8 ft
8 ½ ft
9 ft
9 ½ ft
10 ft
6 ft
A
Correct!

A
D
Question 35. Which of the following value is
closest to √20?
B
C
7.5
6.5
4.5
3.5

Solution to Q35
The answer is 4.5 ft.
Link to review
√16 < √20 < √25
4 < √20 < 5
So √20 ≈ 4.5

Correct!
A
D
Question 35. Which of the following value is
closest to √20?
B
C
7.5
6.5
4.5
3.5

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