GED Math Practice Test

The correct answer is $- \ 248$
Use PEMDAS (order of operation):
$[ 8 × (-32) + 12]$ $+$ $4$ $-$ $[ 8 \ ×\  2 ]$ $÷$ $2$ $=$ $[ - \ 256 \ +\  12]$ $+$ $4$ $-$ $[16]$ $÷$ $2$ $=$
$[ -\  256 \ + \  12]$ $+$ $4$ $-$ $[8]$ $=$ $[ - \  244]$ $+$ $4$ $-$ $[8]$ $=$ $[ - \ 244]$ $+$ $4$ $-$ $8$ $=$ $- \ 248$

The correct answer is $12\ x^2 \ -\ 5\ x\ y \ - \  2\ y^2$
Use FOIL method.
$(4\ x \  + \ y) \ (3\ x \ - \ 2\ y)= 12\ x^2 \ -\  8\ x\ y + 3\ x\ y - 2\ y^2 = 12\ x^2 - 5\ x\ y \ - \ 2 \ y^2$

The correct answer is $24$
To solve absolute values equations, write two equations 
$y-7$ could be positive $5$, or negative $5$. Therefore, 
$y-7$$=$ $5$ $⇒$ $y$ $=$ $12$
$y-7$$=$ $-5$ $⇒$ $y$ $=$ $2$
Find the product of solutions: $2$ $×$ $12$ $=$ $24$

The correct answer is $-\ \frac{2}{3}$
The equation of a line in slope intercept form is: $y = mx + b$
Solve for $y$.
$3\ x$ $-$ $2\ y$ $=$ $8$ $⇒$ $-\ 2\ y$ $=$ $8$ $-$ $3\ x$ $⇒$ $y$ $=$ $(8 \ -\  3\ x)$  $÷$ $(-\ 2)$ $⇒$
$y$ $=$ $1.5\ x \ -\  4$
The slope of this line is $1.5$.
The product of the slopes of two perpendicular lines is $-\ 1$. Therefore, the slope of a line that is perpendicular to this line is:
$𝑚_1 \ ×\  𝑚_ 2 = −\ 1 ⇒ 1.5 × 𝑚_2 = −\ 1 ⇒ 𝑚_2 = −\ \frac{2}{3}$

The correct answer is $-\ 27$
Plug in the value of $x$ and $y$.
 $x = 1$ and $y = 5$
$2$ $(x\ -\  3\ y)$ $+$ $(4 \ -\  y)$$(4 \ -\  y)$ $=$ $2$ $(1\ -\  3\ (5))$ $+$ $(4 \ -\  5)$ $(4 \ -\  5)$ $=$
$2$ $(1\ -\  15)$ $+$ $(-\ 1)$ $(-\ 1)$ $=$ $2$ $(-\ 14)$ $+$ $1$ $=$ $-\ 27$

The correct answer is $20$
Let $x$ be the number. Write the equation and solve for $x$.
$60$% of $x$ $=$ $12$ $⇒$ $0.6 \ x$ $=$ $12$ $⇒$ $x$ $=$ $12$ $÷$ $0.6$ $=$ $20$

The correct answer is $10$
$x$ is $1.5$ times of $y$, then $x = 1.5\ y$ $⇒$ ($x = 15$)   $15$ $=$ $1.5$ $×$ $y$ $⇒$
$y$ $=$ $15$ $÷$ $1.5$ $=$ $10$

The correct answer is $2$ hours
The distance between Alex and Jack is $12$ miles.
Jack running at $4$ miles per hour and  Alex is running at the speed of $10$ miles per hour.
Therefore, every hour the distance is $6$ miles less. $12$ $÷$ $6$ $=$ $2$

The correct answer is $80$%
The failing rate is $6$ out of $30$ $=$ $\frac{6}{30}$
Change the fraction to percent:
$\frac{6}{30}$ × $100$% $=$ $20$%
$20$ percent of students failed. Therefore, $80$ percent of students passed the exam.

The correct answer is $16$
$2^4$$=$ $2$$×$$2$$×$$2$$×$$2$$=$ $16$

The correct answer is  $2$ $≤$ $x$ $<$ $3$ 
Solve for $x$.
$2$ $≤$ $3x - 4$ $<$ $5$ $⇒$ (add 4 all sides) $2 + 4$ $≤$  $3x$ $<$ $5 + 4$ $⇒$
$6$ $≤$ $3x$ $<$ $9$ $⇒$ (divide all sides by $3$)  $2$ $≤$ $x$ $<$ $3$ 
$x$ is between $2$ and $3$ . 

The correct answer is $14$
Let $x$ be the width of the rectangle. Use Pythagorean Theorem:
$a^2 + b^2 = c^2$
$4^2 + x^2 = 5^2$ $⇒$ $x^2 + 16 = 25$ $⇒$ $x^2$ $=$ $25 - 16$ $=$ $9$  $⇒$  $x$ $=$ $3$
Perimeter of the rectangle $=$ $2$ (length + width) $=$ $2$ $(4 + 3 )$ $=$ $2$ $(7)$ $=$ $14$

The correct answer is $160$
The perimeter of the trapezoid is $50$ cm.
Therefore, the missing side (height) is $= 50 \ – \ 14 \  – \ 12 \ – \ 8 = 16$
Area of a trapezoid: A $= \frac{1}{2}\  h \ (b_1 \ +\  b_ 2) =  \frac{1}{2} \ (16) \ (12 \ + \ 8) = 160$

The correct answer is $\frac{1}{3}$
The probability of choosing a diamond is $\frac{21}{63}$ = $\frac{1}{3}$

The correct answer is : $\frac{1}{3}$$<$$0.35$$<$$36\%<65\%$
Change the numbers to decimal and then compare.
$\frac{1}{3}$ = $0.333...$
$0.35$
$36$% = $0.36$
$65$% = $0.65$
$0.333...$$<$$0.35$$<$$0.36$$<$$0.65$

The correct answer is $84.5$
average (mean) = $\frac{sum \ of \  terms}{number \ of \  terms}$$⇒$ $85$ = $\frac{sum \ of \  terms}{40}$$⇒$ sum = $85 × 40 = 3400$
The difference of $92$ and $72$ is $20$. Therefore, $20$ should be subtracted from the sum. 
$3400 - 20 = 3380$
mean = $\frac{sum \ of \  terms}{number \ of \  terms}$$⇒$ mean = $\frac{3380}{40}$ = $84.5$

The correct answer is $\frac{1}{6}$
To get a sum of $6$ or $8$ for two dice, we should get $3$ and $3$, or $2$ and $4$, or $1$ and $5$ or $3$ and $5$ or $2$ and $6$ or $4$ and $4$.
Therefore, there are $6$ options.
Since, we have $6 × 6 = 36$ total options, the probability of getting a sum of $6$ and $8$ is $6$ out of $36$ or $\frac{1}{6}$.

The correct answer is $10$
Use formula of rectangle prism volume
$V =$ (length) (width) (height) ⇒ $1500 = (20$) ($7.5$) (height) ⇒  height $=1500 \ ÷ \ 150 =  10$

The correct answer is $8$
To find the number of possible outfit combinations, multiply the number of options for each factor:
$4 × 1 × 2 = 8$

The correct answer is : $12$
$4 \ ÷ \ \frac{1}{3}$ = $12$

The correct answer is : $50$
The diagonal of the square is $10$. Let $x$ be the side.
Use Pythagorean Theorem: $a^2$ + $b^2$ = $c^2$
$x^2$ $+$ $x^2$ $=$ $10^2$ $⇒$ $2\ x^2$ $=$ $10^2$
 $⇒$  $x^2$ $=$ $50$ $⇒$ $x$ $=$ $\sqrt{50}$
The area of the square is: $\sqrt{50}$ $×$ $\sqrt{50}$ $=$ $50$

The correct answer is : $\frac{1}{5}$
Probability = $\frac{number \ of \  desired\ outcomes}{number \ of\  total \  outcomes}$ =  $\frac{12}{20 + 12 + 12 + 16}$ = $\frac{1}{5}$

The correct answer is $37$
Find the difference of each pairs of numbers:
$2$, $4$, $7$, $11$, $16$, $22$, $29$, ___, $46$
The difference of $2$ and $4$ is $2$, $4$ and $7$ is $3$, $7$ and $11$ is $4$, $11$ and $16$ is $5$,
$16$ and $22$ is $6$, $22$ and $29$ is $7$, $29$ and next number should be $8$. The number is $29$ + $8$ = $37$

The correct answer is $13.33$ 
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) $= 2 \ (2\ x  \ + \ x ) =  80 ⇒  6\ x = 80  ⇒  x  =  13.33$
The length of the rectangle is $13.33$ meters.

The correct answer is : $32$
average = $\frac{sum \ of \ terms}{number \ of \ terms}$ $⇒$ (average of $6$ numbers) $16$ =  $\frac{sum \ of \ terms}{6}$
$⇒$ sum  of $6$ numbers is $16 × 6 = 96$  (average of $4$ numbers) $8$ = $\frac{sum \ of \ numbers}{4}$
$⇒$ sum  of $4$ numbers is $4 × 8 = 32$ 
 sum  of $6$ numbers - sum  of $4$ numbers = sum  of $2$ numbers $⇒$ $96 - 32 = 64$ 
(average of $2$ numbers) = $\frac{64}{2}$ = $32$

The correct answer is $0$
Solving Systems of Equations by Elimination
Multiply the first equation by ($-3$), then add it to the first equation.
$-\ 3 \  (3\ x \ +\  y = 9$)
$x \ +\  3\ y = 3$
$⇒$ $-\ 9\ x \ -\  3\ y = -\ 27$   $⇒$ $-\ 8\ x = -\ 24$ $⇒$ $x = 3$
$x \ +\  3\ y = 3$
Plug in the value of $x$ into one of the equations and solve for $y$.
 $3\ (3$) + $y$ $=$ $9$ $⇒$ $y = 0$

The correct answer is $35$
Solve for the sum of four numbers.  
average = $\frac{sum \ of \  terms}{number \ of \  terms}$ $⇒$ $32$ =  $\frac{sum  \ of \  4 numbers}{4}$
$⇒$ sum  of  $4$ numbers = $32 \ ×\   4 = 128$  
The sum of $4$ numbers is $128$. If a fifth number $47$ is added, then the sum of $5$  numbers is $128 \ +\  47 = 175$
average = $\frac{sum  \ of \  terms}{number \ of \ terms} = \frac{175}{5}$ = $35$

The correct answer is $5$
Th ratio of boy to girls is $3: 7$. Therefore, there are $3$ boys out of $10$ students.
To find the answer, first divide the total number of students by $10$, then multiply the result by 4.
$30$ ÷ $10$ = $3$ ⇒ $3$ × $3$ = $9$
There are $9$ boys and $21$ ($30 - 9$) girls.
So, $5$ more boys should be enrolled to make the ratio $2:3$

The correct answer is $\frac{1}{6}$
$5000$ out of $30000$ equals to = $\frac{5000}{30000}$ = $\frac{5}{30}$ =  $\frac{1}{6}$

The correct answer is $150\ x + 38000 ≤ 50000$
Let $x$ be the number of new shoes the team can purchase. Therefore, the team can purchase $150\ x$.
The team had $$50000$ and spent $$38000$. Now the team can spend on new shoes $$12000$ at most.
Now, write the inequality:
$150\ x \  + \ 38000  ≤ 50000$

The correct answer is $65$
Jack needs an $70\%$ average to pass for four exams.
Therefore, the sum of $4$ exams must be at lease $4 \ × \ 70  = 280$The sum of $3$ exams is: $63$ $+$ $67$ $+$ $85$ $=$ $215$
The minimum score Jack can earn on his fifth and final test to pass is:
$280 \ -\  215 = 65$

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

The correct answer is $2160$
Use simple interest formula:
$I=prt$
($I =$ interest, $p =$ principal, $r =$ rate, $t =$ time)
$I = (18000$) ($0.03$) ($4$) = $2160$

The correct answer is $21\ x^5\  y^4$
Simplify. 
$3\  x\  y^2 \  (7\ x^4 \ y^2 ) = 21\ x^5 \  y^4$ 

The correct answer is $110\ π\ i n^2$
Surface Area of a cylinder $= 2\ π\ r\ (r\ +\ h)$,
The radius of the cylinder is $5\ (10 \ ÷\ 2)$ inches and its height is $6$ inches. Therefore, 
Surface Area of a cylinder $= 2\ π\ (5 )\ (5 \ +\ 6 ) = 110 \ π$

The correct answer is $\frac{512}{1331}$
The square of a number is $\frac{64}{121}$, then the number is the square root of $\frac{64}{121}$
$\sqrt{\frac{64}{121}}$ = $\frac{8}{11}$
The cube of the number is: ($\frac{8}{11}$)³ = $\frac{512}{1331}$

The correct answer is $12$
Write the numbers in order:
$2$,$4$,$12$,$14$,$21$
edian is the number in the middle. So, the median is $12$.

The correct answer is $100$ miles
Use the information provided in the question to draw the shape.
Use Pythagorean Theorem: $a^2 + b^2 = c^2$
$60^2 \ + \ 80^2 = c^2$ $⇒$ $3600 \ + \ 6400 = c^2$ $⇒$ $10000 = c^2$ $⇒$ $c = 100$ miles

The correct answer is $25.55$
Plug in $78$ for F and then solve for C.
C$= \frac{5}{9} (F \ -\  32) ⇒$ C$=\frac{5}{9}$($78 \ -\  32$) $⇒$ C$= \frac{5}{9}$($46$) $= 25.55$

The correct answer is $34$ 
First, find the number. Let $x$ be the number. Write the equation and solve for $x$.
$250$ % of a number is $100$, then:
$2.5 × x = 100$ $⇒$ $x =100 ÷ 2.5 = 40$  
$85$ % of $40$ is $34$ 

The correct answer is $1$
Solve for $y$ .
$3\ x \ -\  3\ y = 1$ $⇒$ $-\ 3\ y = 1 \ -\  3\ x$ $⇒ y = x \ - \ \frac{1}{3}$
The slope of the line is $1$.

The correct answer is $126$
Volume of a box = length × width × height = $3 × 6 × 7 = 126$ 

The correct answer is ($5\ x^4\  +\  3\ x^3$)
($3\ x \ + \ 4\ x^3 \ +\  3\ x^4) \ +\  (-\ x^3 \ -\ 3\ x\  + \ 2\ x^4$) $⇒$ $( 3 \ x^4\ + \ 4\ x^3\  +\  3\ x ) \ +\  ( 2\ x^4\  -\  x^3\  -\  3\ x$) $=$ ($5\ x^4 \ + \ 3\ x^3$)

The correct answer is $145\%$
the population is increased by $10\%$ and $12\%$ and $18\%$ . $10\%$ increase changes the population to $110\%$ of original population.
For the second increase, multiply the result by $112\%$.
For the third increase, multiply the result by $118\%$
($1.10) \ × \ (1.12) \ × \ ( 1.18) = 1.45 = 145\%$

The correct answer is $72000$
Three times of $30000$ is $90000$. One fifth of them cancelled their tickets.
One fifth of $90000$ equals $18000$.
$72000$  ($90000$ – $18000$ = $72000$) fans are attending this week

The correct answer is $88.4$
The area of the square is $488.41$. Therefore, the side of the square is a square root of the area.
$\sqrt{488.41} = 22.1$
Four times the side of the square is the perimeter:
$4 \ ×\  22.1 = 88.4$