GED Math Practice Test 3

Here is another GED Math practice test that allows the use of a calculator. The majority of the GED 2014 Math questions do allow the use of a calculator. As you work through these problems, be sure to review the explanations for any wrong answers. It is very important to learn from your mistakes!

Directions: Solve each problem. You may use your calculator as needed. You may also refer to the formula sheet at the bottom of the page.

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Question 1
Marissa has built a new pool to replace her old one. The old pool is 5 feet long, 4 feet wide, and 2 feet high. It is currently half full. The new pool measures 5ft x 5ft x 4ft. If Marissa pours all of the water currently in the old pool into the new one, what fraction of the new pool will be filled?

A
1/8
B
1/6
C
1/5
D
1/4
Question 1 Explanation: 
Volume of a rectangular solid = length x width x height.
Using this formula, the volume of the old pool is 5 x 4 x 2 = 40 ft3 .
The pool is half full which mean it currently holds 40/2 = 20 ft3 of water.
The volume of the second pool is 5 x 5 x 4 = 100 ft3 .
To find the fraction of the water to the total volume, divide the amount of water added to the pool by its total capacity. 20/100 = 1/5.
Question 2
In the figure provided, a=b. Which of the following must also be true?

Triangle Problem

A
z = a
B
x = y
C
x = y + z
D
y = z
Question 2 Explanation: 
Angles a and y form a straight line and are therefore supplementary. Supplementary angles together equal 180 degrees.
Therefore y = 180 - a.
Angles b and z form a straight line and are, therefore, also supplementary. Supplementary angles = 180 degrees.
Therefore z = 180 - b.
Since a = b, 180 - a = 180 - b.
Therefore, y must equal z.
Question 3
If x is the set of prime numbers and y is the set of all two-digit even integers, how many numbers are common to both sets?

A
0
B
1
C
2
D
3
Question 3 Explanation: 
All even integers are divisible by the number 2. The only even prime number is 2, which is not two-digits. Therefore, no number in set y would be prime, because there are no two-digit even prime numbers.
Question 4
The table provided shows the number of ice cream possibilities at a certain ice cream store. All ice cream sold has exactly one flavor and one treat. If a chocolate ice cream is picked at random, what is the probability that it will have blue swirls?

Ice Cream Possibilities

A
1/3
B
1/4
C
5/12
D
5/14
Question 4 Explanation: 
According to the table, there are 3 chocolate ice creams without nuts, 5 with nuts, and 4 with blue swirls. So there are a total of 3+5+4 = 12 chocolate ice creams. Since 4 of these chocolate ice creams have the successful outcome (blue swirls) the probability of randomly choosing this will be 4/12 = 1/3.
Question 5
What is the value of b in the figure provided?

Angles

A
20
B
35
C
40
D
55
Question 5 Explanation: 
The angle measuring 40, the angle measuring 120, and the angle between them all form a straight line. They are therefore supplementary angles whose sum = 180.

Find the missing angle: 180-120-40=20. That angle with the 40-degree angle next to it make up an angle of the large triangle. This angle measures 40+20 = 60. The sum of the interior angles of a triangle is 180. Solve for b. 180-65-60 = 55.
Question 6
Charlie lives halfway between Chicago and Hoopertown. Amanda lives halfway between Charlie and Chicago. Raymond lives between Charlie and Hoopertown. All three houses lie on a straight line from Chicago to Hoopertown. If Raymond lives 15 miles from Amanda and 23 miles from Chicago, how far does he live from Hoopertown?

A
5 Miles
B
7 Miles
C
9 Miles
D
12 Miles
Question 6 Explanation: 
The given information tells us that Raymond lives 15 miles from Amanda and 23 miles from Chicago. Subtract these quantities to find the distance from Amanda’s house to Chicago: 23-15=8 miles. Amanda lives halfway between Charlie and Chicago, so the distance between her house and Charlie’s is 8 miles. The distance from Charlie’s house to Chicago is 8+8=16 miles. If Charlie lives 16 miles from Chicago and Raymond lives 23 miles from Chicago, then the distance between their houses must be 23-16=7. Since Charlie’s house is equidistant between Chicago and Hoopertown, the distance from Charlie’s to Hoopertown must also be 16 miles. Raymond lives 7 miles from Charlie so the distance from Raymond’s house to Hoopertown is 16-7=9 miles.
Question 7
What is the slope of line c?

Slope

A
-7/5
B
-5/7
C
5/7
D
7/5
Question 7 Explanation: 
Slope of a line is found by the following formula:
rise/run = (y2-y1)/(x2-x1).
The line in the figure passes through points (0,5) and (7,0).
Therefore x1= 0, x2=7, y1=5, and y2=0.
Plugging these values into the given formula yields (0-5)/(7-0) = -5/7.
Question 8
Which of the following equations represents y in terms of x for all ordered pairs listed?

Ordered pairs

A
y = 4x/3
B
y = 2x + 3
C
y = x + 5
D
y = 3x2
Question 8 Explanation: 
Plug values of x into each answer choice to see which equation yields the corresponding y values for all ordered pairs in the table. Only (B) y=2x+3 works for all ordered pairs:
y=2(2)+3 = 4+3 = 7
y=2(3)+3 = 6+3 = 9
y=2(4)+3 = 8+3 = 11.
Question 9
If x is a negative integer and y is a positive integer, which of the following expressions must be positive?

A
xy
B
y - x
C
y/x
D
x/y
Question 9 Explanation: 
Properties of integers tell us that subtracting a negative integer is the same as adding its opposite. Since x is a negative number, its opposite is a positive number. y is also positive. Adding two positive numbers yields a positive result.

Alternate Solution: Plug values for x and y into each answer choice. See which expression yields a positive value.
Example: y = 4, x = -2
y-x = 4 - (-2)
= 4+2 = 6.
y-x produces a positive value.
Question 10
The wheel provided has 8 spokes. If e = 50, f = 25 and c = 75, what is the valued of h?

Wheel

A
45
B
40
C
35
D
30
Question 10 Explanation: 
Vertical angles have the same measure so:
a = e, b = f, c = g, and d = h.
The given information states that e = 50, f = 25 and c = 75. Therefore, we have the measures of angles a, b, and g. The only angles missing are d and h. We know they are equal, so we may use the same variable x to represent their angle measure.

There are 360 degrees in a circle. So the sum of all 8 angles will equal 360. Substituting known values gives us:
2(50) + 2(25) + 2(75) + 2x = 360.
Simplify to 100 + 50 + 150 + 2x = 360.
300 + 2x = 360.
Subtracting 300 from both sides yields 2x = 60.
Dividing both sides by 2 gives the value of x = 30. So both h and d = 30.
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