Solve and choose the answer to test your knowledge.
Multiple Choice: Select the correct answer on the list.
1. If 10x + 2 = 7, what
is the value of 2x?
o
-0.5
o
0.5
o
1
o
5
o
10
2. A long distance runner does a first lap around
a track in exactly 50 seconds. As she tires, each subsequent lap takes 20%
longer than the previous one. How long does she take to run 3 laps?
o
182
seconds
o
160
seconds
o
180
seconds
o
72
seconds
o
150
seconds
3. A number N is multiplied by 3. The result is
the same as when N is divided by 3. What is the value of N?
o
-1
o
0
o
3
o
1
o
-3
4. Which of the following equations satisfies the
five sets of numbers shown in the above table?
o
y = 2x
o
y = x3 + 4
o
y = 2x2 = 7
o
y = 3x + 1
o
y = 6x
5. John buys 100 shares of stock at $100 per
share. The price goes up by 10% and he sells 50 shares. Then, prices drop by
10% and he sells his remaining 50 shares. How much did he get for the last 50?
o
$5050
o
$4900
o
$5000
o
$5500
o
$4950
6. The sides of a triangle are equal to integral
numbers of units. Two sides are 4 and 6 units long, respectively; what is the
minimum value for the triangle's perimeter?
o
11
units
o
13
units
o
10
units
o
9
units
o
12
units
7.
Herbert plans to use the earnings from his lemonade stand according to the table above, for the first month of operations. If he buys $70 worth of lemons, how much profit does he take home?
o
$15
o
$30
o
$20
o
$35.50
o
$40
8. A teacher has 3 hours to grade all the papers
submitted by the 35 students in her class. She gets through the first 5 papers
in 30 minutes. How much faster does she have to work to grade the remaining
papers in the allotted time?
o
20%
o
10%
o
15%
o
25%
o
30%
9.
A sailor judges the distance to a lighthouse by holding a ruler
at arm's length and measuring the apparent height of the lighthouse. He knows
that the lighthouse is actually 60 feet tall. If it appears to be 3 inches tall
when the ruler is held 2 feet from his eye, how far away is it?
o
240
feet
o
60
feet
o
120
feet
o
480
feet
o
960
feet
10. If x2 - 4 = 45, then x could be equal to
o
9
o
-7
o
5
o
-4
o
3
11. Determine the volume
of a rectangular box with a length of 5 inches, a height of 7 inches, and a
width of 9 inches.
o
315
in.3
o
445.095
in.3
o
45
in.3
o
35
in.3
o
21
in.3
12.What is the greatest integer value of y for which 5y - 20 < 0?
o
5
o
1
o
4
o
2
o
3
13.Which equation is represented by the graph
shown below?
o
y = -5/3x - 2
o
y = 5/3x + 2
o
y = -5/3x + 2
o
y = 5/3x - 2
o
y = 5x + 2
14.The right circular cylinder shown in the
figure above has a height of 10 units and a radius of 1 unit. Points O and P
are the centers of the top and bottom surfaces, respectively. A slice is cut
from the cylinder as shown, so that the angle at the top, O, is 60 degrees, and
the angle at the bottom, P, is 60 degrees. What is the volume of the slice?
o
31.4
units
o
10.47
units
o
7.85
units
o
5.23
units
o
15.7
units
15.For the number set {7, 12, 5, 16, 23, 44, 18,
9, Z}, which of the following values could be equal to Z if Z is the median
of the set?
o
14
o
12
o
17
o
11
o
21
Answers: Sorry if my answers are very detailed or elementary. I want the others to fully understand the concept and how to get the correct answers.
. If 10x + 2 = 7, what is the value of 2x?
o -0.5
o 0.5
o 1
o 5
o 10
Answer: 1
Solution:
10x + 2 = 7
Solve for x
10x + 2 = 7
10x + 2 – 2 = 7 – 2
10x = 5
x = 5/10
x = ½
Since we are looking
for 2x ==> 2x = 2 (1/2) = 1
2. A long distance runner does a first lap around a track in exactly 50 seconds. As she tires, each subsequent lap takes 20% longer than the previous one. How long does she take to run 3 laps?
o 182 seconds
o 160 seconds
o 180 seconds
o 72 seconds
o 150 seconds
Answer: 182 seconds
Solution
First lap = 50 seconds
Each subsequent lap
takes 20% longer than the previous one
Second lap = 50 + (50 x 20%) = 50 + (50 x 0.20) = 50 + 10 = 60 seconds
Third lap = 60 + (60 x
20%) = 60 + (60 x0.20) = 60 + 12 = 72 seconds
Total = 50 + 60 + 72 =
182 seconds
3. A number N is multiplied by 3. The result is the same as when N is divided by 3. What is the value of N?
o -1
o 0
o 3
o 1
o -3
Answer: 0
Solution:
N x 3 = N/3
Solve for N
3N = N/3
Multiply by 3 to get
rid of the denominator in the 2nd term
3( 3N = N/3)
9N = N
Let’s substitute the
possible answers in the equation.
If N = -1, then 9(-1) = -1 ==> -9 = -1 ===> cannot
be
If N = 0, then
9(0) = 0 ==> 0 = 0 ===> can be
If N = 3, then
9(3) = 3 ==> 27 = 3 ===> cannot be
If N = 1, then
9(1) = 1 ==> 9 = 1 ===> cannot be
If N = -3, then 9(-3) = -3 ==> -27 = -3 ===>
cannot be
Only N = 0 satisfies the equation.
4. Which of the following equations satisfies the five sets of numbers shown in the above table?
o y = 2x
o y = x3 + 4
o y = 2x2 = 7
o y = 3x + 1
o y = 6x
Answer: y = x3 + 4
Solution:
You can solve this by
substituting the value of x in every equation and check if you can get the
correct values of y. But this process takes time and you will lose a lot of
time for only one item. The best thing to do is get the y - intercept. This is the value of y when x = 0. By glancing and
mentally calculating, only y = x3 +
4 satisfies the given table because you will get
y = 4 when x = 0, that is, y = 0^3 + 4 =
0 + 4 = 4. For the other equations ==>for y = 2x you will get y = 0; y = 2x2 =
7 cannot be 4 because it is already 7; y = 3x + 1 will give you y = 1 since y = (3x0)+1 = 0 + 1 = 1; and y = 6x will give you y =
0.
5. John buys 100 shares of stock at $100 per share. The price goes up by 10% and he sells 50 shares. Then, prices drop by 10% and he sells his remaining 50 shares. How much did he get for the last 50?
o $5050
o $4900
o $5000
o $5500
o $4950
Answer: $4950
Solution:
1. Get the price per
share when it goes up by 10%
Original price x 10%
===> 100 + 100 (10%) = 100 + (100 x 0.10) = 100 + 10 = $110 ==> price after the increase
2. Get the price per
share when it goes down by 10%
Remember to get the price after the increase and not the original price as basis.
Current price = price
after the increase – (price after the increase x 10%)
Current price = 110 –
(110 x 10%) = 110 – (110 x 0.10) = 110 –
(11) = $99
3. Multiply the
remaining stocks with the current price
50 x 99 = $4950
6. The sides of a triangle are equal to integral numbers of units. Two sides are 4 and 6 units long, respectively; what is the minimum value for the triangle's perimeter?
o 11 units
o 13 units
o 10 units
o 9 units
o 12 units
Answer: 13 units
Solution:
1. Recall how to
compute Perimeter = side A + side B + side C
2. Remember that the
sum of the 2 shorter sides must be greater than the third side.
3. Since we are
looking for the minimum value of the perimeter, we assume that 6 is the longest
side of the triangle.
4. Since the third
side x + 4 must be greater than 6, x
should be greater than 2 ( 6 - 4 = 2). But since all the sides are integral
numbers (whole number, no fraction is allowed), the closest number is 3 units.
5. Our Perimeter is 4
+ 6 + 3 = 13
units.
7.
Herbert plans to use the earnings from his lemonade stand according to the table above, for the first month of operations. If he buys $70 worth of lemons, how much profit does he take home?
o $15
o $30
o $20
o $35.50
o $40
Answer: $30
Solution:
1. Recall how to
compute percentages.
2. Note that Lemons
which cost $70 is 35% of Expenses.
3. What is the value
of the expenses then? Let E = Expenses
4. 70 is 35% of E
==> 70 = 35%E ==> 70 = 0.35E ==> 70/0.35 = E ==> E = 200
Our Expenses is $ 200
5. Profit is 15% of
Expenses ==> P = 15%E ==> P = 0.15E ==> P = 0.15(200) ==> P = 30
8. A teacher has 3 hours to grade all the papers submitted by the 35 students in her class. She gets through the first 5 papers in 30 minutes. How much faster does she have to work to grade the remaining papers in the allotted time?
o 20%
o 10%
o 15%
o 25%
o 30%
Answer: 20%
Solution:
1. Convert the hours
into minutes. 3 hours = 3 (60 minutes/hour) = 180 minutes
2. There are 35
students and 35 papers to grade. She already finished 5 papers in 30 minutes.
3. Remaining papers =
35 – 5 = 30 papers.
4. Remaining time =
160 – 30 = 150 minutes
5. She has to finish
the 30 papers in 150 minutes.
6. Her speed should be
30/150 = 0.20 x 100% = 20%
9.
A sailor judges the distance to a lighthouse by holding a ruler at arm's length and measuring the apparent height of the lighthouse. He knows that the lighthouse is actually 60 feet tall. If it appears to be 3 inches tall when the ruler is held 2 feet from his eye, how far away is it?
o 240 feet
o 60 feet
o 120 feet
o 480 feet
o 960 feet
Answer: 480 feet
Solution:
1. Gather our given.
Lighthouse = 60 ft. Ruler = 3 inches =
3 inches/12 inches/foot = 0.25 ft.
Distance of ruler to the eye = 2 ft. Distance of lighthouse to the eye = x
2. Use proportion
3. 60/x = 0.25/2 ===> 2x( 60/x = 0.25/2) ===> 120 = 0.25x ==>
x = 120/0.25 = 480 ft.
10. If x2 - 4 = 45, then x could be equal to
o 9
o -7
o 5
o -4
o 3
Answer: -7
Solution:
x2 - 4 = 45
x2 = 45 + 4
x2 = 49
x = sqrt of 49
x = 7 and -7
Since there is no 7 in the choices,
the answer is – 7
To check: (-7)^2 – 4 = 45 ===> 49 – 4 = 45 ===>
45 = 45
11. Determine the volume of a rectangular box with a length of 5 inches, a height of 7 inches, and a width of 9 inches.
o 315 in.3
o 445.095 in.3
o 45 in.3
o 35 in.3
o 21 in.3
Answer: 315 in.3
Solution:
1. Recall how to
compute the volume of a rectangle.
Volume = length x height x width
2. The unit of
measure MUST be the SAME. If not the same, convert them to the same unit of measure
(inches, feet, cm, m, etc.)
3. Since our units are
the same. V = 5 x 7 x 9 = 315 in.3
12.What is the greatest integer value of y for which 5y - 20 < 0?
o 5
o 1
o 4
o 2
o 3
Answer: 3
Solution;
5y – 20 < 0
5y < 20
y < 20/5
y < 4
Since y must be the
largest integer less than 4, the answer is 3.
13.Which equation is represented by the graph shown below?
o y = -5/3x - 2
o y = 5/3x + 2
o y = -5/3x + 2
o y = 5/3x - 2
o y = 5x + 2
Answer: y = -5/3x + 2
Solution:
1. You can get the
answer by computing the equation with 2 points on the graph. But this is not
the best thing to do because it requires a lot of time. Anyway, we shall do
this for the sake of discussion and recall. We can use the point slope form
==> y = mx + b, where m is the slope and b is the y-intercept.
1a. By looking at the
graph, we already know that the y-intercept
(the value of y when x = 0) is 2.
We can now substitute it into our equation==> y = mx + 2
1b. We need to
calculate m to complete our equation. The formula for finding the slope is m =
(y1 – y2)/ (x2 – x1). Our points
are (x1, y1) = (0,2) ; (x2,y2) = (3, -3)
M = ( -3 – 2)/(3-0) = -5/3
1c. Our equation,
therefore, is y =mx +b ==> y = -5/3x + 2
2. Although we get the correct
answer, step 1 is not the best thing to do since it requires a lot of time to
compute for just one item. The best approach is directly observing the graph.
2a. By observation, we know that the
slope is negative.
2b. Eliminate the equation with
positive slope. That leaves us to 2 choices ==> y = -5/3x – 2 and
y = -5/3x + 2
2c. Find the y-intercept. We see
that it is 2.
2d. Our correct answer is y = -5/3x + 2
14.The right circular cylinder shown in the figure above has a height of 10 units and a radius of 1 unit. Points O and P are the centers of the top and bottom surfaces, respectively. A slice is cut from the cylinder as shown, so that the angle at the top, O, is 60 degrees, and the angle at the bottom, P, is 60 degrees. What is the volume of the slice?
o 31.4 units
o 10.47 units
o 7.85 units
o 5.23 units
o 15.7 units
Answer: 5.23 units
Solution:
1. We need to remember
the formula for the volume of a cylinder.
V = h x pi x radius squared, where h is
the height of the cylinder (or altitude).
2. To remember the
formula for the volume of the cylinder, it is MORE EASY to remember if you know
the area of a circle. The area of the circle is pi x radius squared. The volume of the cylinder is h x pi x radius squared, it means that you have only to multiply the height to the area
of the square to get the volume of the cylinder.
3. What if you forget
the formula for the area of square? Just
remember ==> pie are squared, although pie is a circle (o round). Pie are squared ==> pie is pi; are squared is radius squared (r2)
===> pi x r2 ==> area of square
4. Get back to our
problem. Since V = h x pi x r2 , we need the value of h, pi and r
and substitute them in our equation. We already know that h = 10 units; r = 1
unit; and pi = 3.14 (approximately)
V = 10 x 3.14 x (1)2
V = 31.40 units ==> the volume of the whole cylinder.
5. Our problem is to
find only the volume of the slice.
6. The degree angle of
the slice is 60 degrees. We know that the total degree of a circle is 360
degrees. This means that the slice is only 1/6 of the whole cylinder ( 60/360 =
1/6).
The volume of the
slice is, therefore, 1/6 x 31.40 =
31.40/ 6 = 5.23 units.
15.For the number set {7, 12, 5, 16, 23, 44, 18, 9, Z}, which of the following values could be equal to Z if Z is the median of the set?
o 14
o 12
o 17
o 11
o 21
Source: https://www.mometrix.com/academy/ged-math-practice-test/
Answer: 14
Solution:
1. We need to recall what
a median is. The Median is the "middle" of a sorted list of numbers.
2. Therefore, we need to sort the number to
find the median. Begin with the lowest to the highest.
Thus,
5 7 9 12 Z 16
18 23 44
3. From the above choices, 14 is the correct answer because all the rest cannot fit.
it so HARD!
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