Full Length GED Mathematical Reasoning Practice Test

The correct answer is $–\ 122$
Use PEMDAS (order of operation):
$[6\ ×\ (–\ 24)\ +\ 8]\ –\ (–\ 4)\ +\ [4\ ×\ 5]\ ÷\ 2 = [–\ 144\ +\ 8]\ –\ (–\ 4)\ +\ [20]\ ÷\ 2 =$
$[–\ 144\ +\ 8]\ –\ (–\ 4)\ +\ 10 =$
$[–\ 136]\ –\ (–\ 4) \ +\ 10 = [–\ 136]\ +\ 4\ +\ 10 = \ –\ 122$

The correct answer is $4\ x^2\ +\ 2\ x\ y \ - \ 2 \ y^2$
Use FOIL method.
$(2\ x\ +\ 2\ y)\ (2\ x\ -\ y) = 4\ x^2\ -\ 2\ x\ y\ +\ 4\ x\ y\ -\ 2\ y^2=4\ x^2\ +\ 2\ x\ y\ -\ 2\ y^2$

The correct answer is $91$
To solve absolute values equations, write two equations.
$x\ -\ 10$ could be positive $3$, or negative $3$. Therefore,
$x\ -\ 10=3 ⇒ x=13$
$x\ -\ 10=-\ 3 ⇒ x=7$
Find the product of solutions: $7\ ×\ 13 = 91$

The correct answer is $-\frac{1}{2}$
The equation of a line in slope intercept form is: $y=m\ x\ +\ b$
Solve for $y$.
$4\ x\ -\ 2\ y=12 ⇒ -\ 2\ y=12\ -\ 4\ x ⇒ y=(12\ -\ 4\ x)\ ÷\ (-\ 2)$ ⇒
$y=2\ x\ -\ 6$
The slope of this line is $2$.
The product of the slopes of two perpendicular lines is $-\ 1$.
Therefore, the slope of a line that is perpendicular to this line is:
$m_1\ ×\ m_2 = -\ 1 ⇒ 2\ ×\ m_2 = -\ 1 ⇒ m_2 = \ -\frac{1}{2}$

The correct answer is $36$
Plug in the value of$x$ and $y$.
$x=3$ and $y=-\ 2$
$5\ (x\ -\ 2\ y)\ +\ (2\ -\ x)^2= 5\ (3\ -\ 2\ (-\ 2))\ +\ (2\ -\ 3)^2=5\ (3\ +\ 4)\ +\ (-\ 1)^2 =36$

The correct answer is $10$
Let $x$ be the number. Write the equation and solve for $x$.
$40\%$ of $x=4⇒ 0.40\ x=4 ⇒ x=4\ ÷\ 0.40=10$

The correct answer is $3$
$A$ is $4$ times of $B$, then: $A$ = $4\ B$ ⇒ $(A = 12)\ 12 = 4\ ×\ B ⇒ B = 12\ ÷\ 4 = 3$

The correct answer is $6$ hours
The distance between Jason and Joe is $9$ miles.
Jason running at $5.5$ miles per hour and Joe is running at the speed of $7$ miles per hour.
Therefore, every hour the distance is $1.5$ miles less. $9\ ÷\ 1.5 = 6$

The correct answer is $80\%$ 
The failing rate is $11$ out of $55 = \frac{11}{55}$
Change the fraction to percent:
$\frac{11}{55} ×\ 100\%=20\%$
$20$ percent of students failed. Therefore, $80$ percent of students passed the exam.

The correct answer is $729$ 
$3^6 = 3\ ×\ 3\ ×\ 3\ ×\ 3\ ×\ 3\ ×\ 3 = 729$

Solve for $x$.
$-\ 2\ ≤\ 2\ x\ -\ 4\ <\ 8$ ⇒ (add $4$ all sides) $-\ 2\ +\ 4\ ≤\ 2\ x\ -\ 4\ +\ 4\ <\ 8\ +\ 4$ ⇒
$2\ ≤\ 2\ x\ <\ 12$ ⇒ (divide all sides by $2$) $1\ ≤\ x\ <\ 6$
$x$ is between $1$ and $6$

The correct answer is $28$
Let $x$ be the width of the rectangle. Use Pythagorean Theorem:
$a^2\ +\ b^2 = c^2$
$x^2\ +\ 8^2 = 10^2 ⇒ x^2\ +\ 64 = 100 ⇒ x^2 = 100\ –\ 64 = 36 ⇒ x = 6$
Perimeter of the rectangle $= 2$ (length $+$ width) $= 2\ (8\ +\ 6) = 2\ (14) = 28$

The correct answer is $70$ cm$^2$ 
The perimeter of the trapezoid is $36$ cm.
Therefore, the missing side (height) is $= 36\ –\ 8\ –\ 12\ –\ 6 = 10$
Area of a trapezoid: A = $\frac{1}{2}\ h\ (b_1\ +\ b_2) = \frac{1}{2}\ (10)\ (6\ +\ 8) = 70$

The correct answer is $\frac{1}{4}$
The probability of choosing a Hearts is $\frac{13}{52} =\frac{1}{4}$

The correct answer is $\frac{2}{3} ,\ 67\%,\ 0.68,\ \frac{4}{5}$
$\frac{2}{3} = 0.666…$
$0.68$
$67\% = 0.67$
$\frac{4}{5} = 0.80$
Therefore
$\frac{2}{3}\ <\ 67\%\ <\ 0.68\ <\ \frac{4}{5}$

The correct answer is $87.5$
average (mean) $=\frac{sum\ of\ terms}{number\ of\ terms} ⇒ 88 =\frac{sum\ of\ terms}{50} ⇒ sum = 88\ ×\ 50 = 4400$
The difference of $94$ and $69$ is $25$. Therefore, $25$ should be subtracted from the sum.
$4400\ –\ 25 = 4375$
mean $=\frac{sum\ of\ terms}{number\ of\ terms}$ ⇒ mean =$\frac{4375}{50} = 87.5$

The correct answer is $\frac{5}{36}$
To get a sum of $6$ for two dice, we should get $3$ and $3$, or $2$ and $4$, or $4$ and $2$, or $1$ and $5$, or $5$ and $1$.
Therefore, there are $5$ options.
Since, we have $6\ ×\ 6 = 36$ total options, the probability of getting a sum of $6$ is $5$ out of $36$ or $\frac{5}{36}$.

The correct answer is $8$
Use formula of rectangle prism volume.
V $=$ (length) (width) (height) ⇒ $2000 = (25)\ (10)$ (height) ⇒
height $= 2000\ ÷\ 250 = 8$

The correct answer is $60$
To find the number of possible outfit combinations, multiply the number of options for each factor:
$3\ ×\ 5\ ×\ 4 = 60$

The correct answer is $24$
$4\ ÷\ \frac{1}{6} = 24$

The correct answer is $32$
The diagonal of the square is $8$. Let $x$ be the side.
Use Pythagorean Theorem: $a^2\ +\ b^2 = c^2$
$x^2\ +\ x^2 = 8^2 ⇒ 2\ x^2 = 8^2 ⇒ 2\ x^2 = 64 ⇒x^2 = 32 ⇒\ x= \sqrt{32}$
The area of the square is:
$\sqrt{32}\ ×\ \sqrt{32} = 32$

The correct answer is $\frac{1}{4}$
Probability $=\frac{number \ of\  desired\  outcomes}{number \ of\  total\  outcomes} = \frac{18}{12\ +\ 18\ +\ 18\ +\ 24} = \frac{18}{72} = \frac{1}{4}$

The correct answer is $30$
Find the difference of each pairs of numbers:
$2,\ 3,\ 5,\ 8,\ 12,\ 17,\ 23,$ ___$,\ 38$
The difference of $2$ and $3$ is $1,\ 3$ and $5$ is $2,\ 5$ and $8$ is $3,\ 8$ and $12$ is $4,\ 12$ and $17$ is $5,\ 17$ and $23$ is $6,\ 23$ and next number should be $7$. The number is $23\ +\ 7 = 30$

The correct answer is $10$ meters
The width of the rectangle is twice its length. Let $x$ be the length. Then, width$=2\ x$
Perimeter of the rectangle is $2$ (width $+$ length) $= 2\ (2\ x\ +\ x)=60 ⇒ 6\ x=60 ⇒ x=10$
The length of the rectangle is $10$ meters.

The correct answer is $16$
average $=\frac{sum\ of\ terms}{number\ of\ terms}$ ⇒ (average of $6$ numbers) $12 = \frac{sum\ of\ numbers}{6}$ ⇒sum of $6$ numbers is
$12\ ×\ 6 = 72$
(average of $4$ numbers) $10 =\frac{sum\ of\ numbers}{4}$ ⇒sum of $4$ numbers is $10\ ×\ 4 = 40$
sum of $6$ numbers $–$ sum of $4$ numbers $=$ sum of $2$ numbers
$72\ –\ 40 = 32$
average of $2$ numbers $=\frac{32}{2} = 16$

The correct answer is $-\ 2$
Solving Systems of Equations by Elimination
Multiply the first equation by $(–2)$, then add it to the second equation.
$\cfrac{\begin{align}-\ 2\ (2\ x\ +\ 5\ y= 11) \\ \ 4\ x\ -\ 2\ y=-\ 14 \end{align}}{}$ $⇒-\ 4\ x\ -\ 10\ y= -\ 22\\4\ x\ -\ 2\ y=-\ 14 ⇒ -\ 12\ y= -\ 36 ⇒ y= 3$
Plug in the value of $y$ into one of the equations and solve for $x$.
$2\ x\ +\ 5\ (3)= 11 ⇒ 2\ x\ +\ 15= 11 ⇒ 2\ x= -\ 4 ⇒ x= -\ 2$

The correct answer is $27$
Solve for the sum of five numbers.
average $=\frac{sum\ of\ terms}{number\ of\ terms} ⇒ 24 = \frac{sum\ of\ 5\ numbers}{5}$ ⇒ sum of $5$ numbers $= 24\ ×\ 5 = 120$
The sum of $5$ numbers is $120$. If a sixth number $42$ is added, then the sum of $6$ numbers is
$120\ +\ 42 = 162$
average $=\frac{sum\ of\ terms}{number\ of\ terms} =\frac{162}{6} = 27$

The correct answer is $12$
The ratio of boys to girls is $4:7$. Therefore, there are $4$ boys out of $11$ students.
To find the answer, first, divide the total number of students by $11$, then multiply the result by $4$.
$44\ ÷\ 11 = 4 ⇒ 4\ ×\ 4 = 16$
There are $16$ boys and $28\ (44\ –\ 16)$ girls. So, $12$ more boys should be enrolled to make the ratio $1:1$

The correct answer is $\frac{1}{22}$
$2,500$ out of $55,000$ equals to $\frac{2500}{55000} =\frac{25}{550} =\frac{1}{22}$

The correct answer is $120\ x\ +\ 14,000\ ≤\ 20,000$
Let $x$ be the number of new shoes the team can purchase. Therefore, the team can purchase $120\ x$.
The team had $$20,000$ and spent $$14000$. Now the team can spend on new shoes $$6000$ at most.
Now, write the inequality:
$120\ x\ +\ 14,000\ ≤\ 20,000$

The correct answer is $60$
Jason needs an $75\%$ average to pass for five exams. Therefore,
the sum of $5$ exams must be at lease $5\ ×\ 75 = 375$
The sum of $4$ exams is:
$68\ +\ 72\ +\ 85\ +\ 90 = 315$.
The minimum score Jason can earn on his fifth and final test to pass is:
$375\ –\ 315 = 60$

The correct answer is $\frac{1}{4}$
Isolate and solve for $x$.
$\frac{2}{3}\ x\ +\ \frac{1}{6}= \frac{1}{3} ⇒ \frac{2}{3}\ x= \frac{1}{3}\ -\frac{1}{6} =\frac{1}{6} ⇒ \frac{2}{3}\ x=\frac{1}{6}$
Multiply both sides by the reciprocal of the coefficient of $x$.
$(\frac{3}{2})\ \frac{2}{3}\ x= \frac{1}{6}\ (\frac{3}{2}) ⇒ x= \frac{3}{12}=\frac{1}{4}$

The correct answer is $$840$
Use simple interest formula:
$I=$prt
$(I =$ interest, $p =$ principal, $r =$ rate, $t =$ time)
$I=(12000)\ (0.035)\ (2)=840$

The correct answer is $48\ x^8\ y^6$
Simplify.
$6\ x^2\ y^3\ (2\ x^2\ y)^3= 6\ x^2\ y^3\ (8\ x^6\ y^3 ) = 48\ x^8\ y^6$

The correct answer is $66\ π\ i n^2$
Surface Area of a cylinder $= 2\ π\ r\ (r\ +\ h)$,
The radius of the cylinder is $3\ (6\ ÷\ 2)$ inches and its height is $8$ inches. Therefore,
Surface Area of a cylinder $= 2\ π\ (3)\ (3\ +\ 8) = 66\ π$

The correct answer is $\frac{125}{512}$
The square of a number is $\frac{25}{64}$, then the number is the square root of $\frac{25}{64}$
$\sqrt{\frac{25}{64}}=\frac{5}{8}$
The cube of the number is:
$(\frac{5}{8})^3 =\frac{125}{512}$

The correct answer is $28$
Write the numbers in order:
$2,\ 19,\ 27,\ 28,\ 35,\ 44,\ 67$
The Median is the number in the middle. So, the median is $28$.

The correct answer is $170$
Use the information provided in the question to draw the shape.
Use Pythagorean Theorem: $a^2\ +\ b^2 = c^2$
$80^2\ +\ 150^2 = c^2 ⇒ 6400\ +\ 22500 = c^2 ⇒ 28900 = c^2 ⇒ c = 170$

The correct answer is $40$
Plug in $104$ for F and then solve for $C$.
$C = \frac{5}{9}\ (F\ –\ 32) ⇒ C = \frac{5}{9}\ (104\ –\ 32) ⇒ C = \frac{5}{9}\ (72) = 40$

The correct answer is $45$
First, find the number.
Let $x$ be the number. Write the equation and solve for $x$.
$150\%$ of a number is $75$, then:
$1.5\ ×\ x=75 ⇒ x=75\ ÷\ 1.5=50$
$90\%$ of $50$ is:
$0.9\ × \ 50 = 45$

The correct answer is $2$
Solve for $y$.
$4\ x\ -\ 2\ y=6 ⇒ -\ 2\ y=6\ -\ 4\ x ⇒ y=2\ x\ -\ 3$
The slope of the line is $2$.

The correct answer is $120$ cm$^3$
Volume of a box = length $×$ width $×$ height $= 4\ ×\ 5\ ×\ 6 = 120$

The correct answer is $4\ x^4\ +\ 4\ x^3\ -\ 12\ x^2$
$(6\ x^3\ -\ 8\ x^2\ +\ 2\ x^4 )\ -\ (4\ x^2\ -\ 2\ x^4\ +\ 2\ x^3 ) ⇒ (6\ x^3\ -\ 8\ x^2\ +\ 2\ x^4 )\ -\ 4\ x^2\ +\ 2\ x^4\ -\ 2\ x^3 ⇒ 4\ x^4\ +\ 4\ x^3\ -\ 12\ x^2$

The correct answer is $38\%$
the population is increased by $15\%$ and $20\%$. $15\%$ increase changes the population to $115\%$ of original population.
For the second increase, multiply the result by $120\%$.
$(1.15)\ ×\ (1.20) = 1.38 = 138\%$
$38$ percent of the population is increased after two years.

The correct answer is $60,000$
Three times of $24,000$ is $72,000$. One-sixth of them canceled their tickets.
One-sixth of $72,000$ equals $12,000\ (\frac{1}{6}\ ×\ 72000 = 12000)$.
$60,000\ (72000\ –\ 12000 = 60000)$ fans are attending this week

The correct answer is $97.6$
The area of the square is $595.36$. Therefore, the side of the square is the square root of the area.
$\sqrt{595.36}=24.4$
Four times the side of the square is the perimeter:
$4\ × \ 24.4 = 97.6$