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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Solution to Q1
2842
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
2842
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
Link to reviewNext Question
Solution to Q2
56
14
=Convert into fractions
with LCD = 1212(5 x 2 – 1 x 3)
=
712
The correct answer is .
712
Link to reviewNext Question
Solution to Q3
2714
187
=
÷
2714 18
7x
3
22
= 34
The answer is . 34
reciprocate and multiply
1
Next Question
Solution to Q4
3 143
= 3 – 1 43
= 243
141=
The answer is .141
Link to review
A
B
C
D
Answer for Question 5:
,43
,98
32
43
98
43
98
32
98
98
43
<
<
<
< 32
43
32
32
<
<
<
<
Question 5. Arrange
from the smallest to the largest.
Solution to Q5
, 43
32
We cross multiply to compare the fractions.
The answer is B:
So
98
32
, similarly we have that
43
98
<32
<
43
<43
98
< .
← larger
Solution to Q5
, 43
32
We cross multiply to compare the fractions.
The answer is B:
So
98
32
, similarly we have that
43
98
<32
<
43
<43
98
< .
← larger
43
=
Or multiply by the LCD = 36
36 x98
=32
=36 x 36 x
Link to reviewNext Question
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
,43
,98
32
43
98
43
98
32
98
98
43
32
43
32
32
<
<
<
<
<
<
<
<
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
Answer for Question 6:
Link to reviewNext Question
Solution to Q6
48 x = 4287
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
Link to reviewNext Question
Solution to Q7
The answer is 4.
–3 – (–5) – (–2)
= –3 + 5 + 2
= 4
Link to reviewNext Question
Solution to Q8.
33 =32 x 36
3338
= 35
2+6=8 8–3=5
The answer is 35.
Link to reviewNext Question
Solution to Q9
The answer is 8.
24 ÷ 6 X 2
= 4 x 2
= 8
Link to reviewNext Question
Solution to Q10
The answer is 8.
6 – 3(–3)
= 6 + 9
= 15
Link to reviewNext Question
Solution to Q11
The answer is 1.93.
2.3 – 0.45 + 0.08
= 1.85 + 0.08
= 1.93
Link to reviewNext Question
Solution to Q12
The answer is 0.72.
1.22 x 0.5
= 1.44 x 0.5
= 0.72
Link to reviewNext Question
Solution to Q13
The answer is 0.6.
0.108 ÷ 1.8
= 1.08 ÷ 18
= 0.6
Link to reviewNext Question
Solution to Q14
The answer is –0.6.
43
– 1.35
= 0.75 – 1.35
= –0.6
Link to reviewNext Question
Solution to Q15
The answer is 230.
2.3 X 103
= 2.3 x 1,000
= 2300
C
B
D
Question 16. How many grams of pure alcohol
are there in 300 grams of cough syrup that is
5% alcohol?
Answer for Question 16:
A
1.5 g
150 g
15 g
0.15 g
Link to reviewNext Question
Solution to Q16
The answer is 15 grams.
5% of 300 is
1005
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.
Answer for Question 17:
C 30%
20%
10%
40%
Solution to Q17
The answer is C: 30%
72
= 0.28…
Link to reviewNext Question
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 .
Answer for Question 18:
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:
Link to reviewNext Question
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?
Answer for Question 19:
A
3%,
18%,
15%,
20%,
Solution to Q19
The answer is A:
Link to reviewNext Question
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%,
Solution to Q20
The answer is A:
Link to reviewNext Question
–14
Set x = 4 in 6 – 5x, we get
6 – 5(4)
= 6 – 20
= –14
Solution to Q21
The answer is 9.
Link to reviewNext Question
Set x = 3, y = 6 in xy – x – y
we have 3(6) – 3 – 6 = 9
Solution to Q22
The answer is x = 6.
Link to reviewNext Question
3x – 2 = 16
add 2 to both sides 3x = 18
divide both sides by 3 x = 6
Solution to Q23
The answer is a = 14.
Link to reviewNext Question
If b = 2, the a – 2(2) = 10 so a = 14.
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?
Answer for Question 24:
B
80
72
96
60
Solution to Q24
The answer is 72.
Link to reviewNext Question
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?
Answer for Question 25:
C
60
80
100
120
Solution to Q25
The answer is 100.
Link to reviewNext Question
We have that 75
140x
=
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?
Answer for Question 26:
A $12
$10
$8
$6
Solution to Q26
The answer is $12.
Link to reviewNext Question
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
Answer for Question 27:
D
ft, 1½ ft and 2 ft, what’s its perimeter? 1 23
ft4 56
ft5 16
ft5 56
ft4 16
Solution to Q27
The answer is 5 1/6 ft.
Link to reviewNext Question
The perimeter is
+1 23
1 12
+ 2
= 1 + 1 + 2 + 2/3 + 1/2
= 4 + 1 16
= 5 16
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 23
ft4 56
ft5 16
ft5 56
ft4 16C
D
A
D
B
Question 28.
The perimeter of a square is 16 ft,
what is the area?
Answer for Question 28:
C
256 ft2
144 ft2
16 ft2
12 ft2
Solution to Q28
The answer 16 ft2.
Link to reviewNext Question
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?
Answer for Question 29:
20 ft
30 ft
40 ft
50 ft
C
D
Solution to Q29
The answer D: 50 ft.
Link to reviewNext Question
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?
Answer for Question 30:
C
B0
0
0
0
Solution to Q30
The answer is B.
Link to reviewNext Question
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
B0
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?
Answer for Question 31:
C
B
20
24
30
36
Solution to Q31
The answer is 24.
Link to reviewNext Question
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?
Answer for Question 32:
B
C
36
24
20
10
Solution to Q32
The answer is 20.
Link to reviewNext Question
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?
Answer for Question 33:
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.
Link to reviewNext Question
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?
Answer for Question 34:
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.
Link to reviewNext Question
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?
Answer for Question 35:
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