Full Length GED Mathematical Reasoning Practice Test

The correct answer is 286
$5 \ × \ 36 \ + \ 8 \ × \ 12 \ + \ 10 \ = \ 286$

The correct answer is $33$
Let x be the integer. Then:
$3\ x \ + \ 7 \ = \ 106$
reduce $7$ both sides: $3\ x \ = \ 99$
Divide both sides by $3$: $x \ = \ 33$

The correct answer is $(200) \ (0.90) \ (0.75)$
To find the discount, multiply the number by ($100$% – rate of discount).
Therefore, for the first discount we get: $(200) \ (100$% $– \ 10$%) $= \ (200) \ (0.90) \ = \ 180$
For the next $25%$ discount: $(200) \ (0.90) \ (0.75)$

The correct answer is $(5 \ , \ 3)$
A. $(4 , 1)$ : $3 \ (4) \ + \ 5 \ (1) \ = \ 17$
B. $(3 , 2)$ : $3 \ (3) \ + \ 5 \ (2) \ = \ 19$
C. $(4 , 3)$ : $3 \ (4) \ + \ 5 \ (3) \ = \ 27$
D. $(5 , 3)$ : $3 \ (5) \ + \ 5 \ (3) \ = \ 30$

The correct answer is $-\ 25$
Use PEMDAS (order of operation):
$7 \ + \ 4 \ × \ (–\ 3) \ – \ [5 \ + \ 11 × \ 5] \ ÷ \ 3 \ = \ 7 \ + \ 4 \ × \ (–\ 3) \ – \ [4 \ +  \ 55] \ ÷ \ 3 \ =$
$7 \ + \ 4 \ × \ (–\ 3) \ – \ [60] \ ÷ \ 3 \ = \ 7 \ + \ (-\ 12) \ – \ 20 \ = \ –\ 5 \ –\  20 = –\ 25$

The correct answer is $30$%
Use this formula: Percent of Change
$\frac{New\  Value \ - \ Old \ Value}{Old \ Value}$ $× \ 100$%
$\frac{21000 \ - \ 30000}{30000}$ $× \ 100$% $= \ 30$% and $\frac{14700 \ - \ 21000}{21000}$ $× \ 100$% $= \ 30$%

The correct answer is $360$
If the length of the box is $30$, then the width of the box is one-fifth of it, $6$
and the height of the box is $2$ (one-third of the width). The volume of the box is:
V $=$ lwh $=$ $(30) \ (6) \ (2) \ = \ 360$

The correct answer is $25$%
Write the equation and solve for B:
$0.20 \ A \ = \ 0.80 \ B$, divide both sides by $0.80$, then:
$\frac{0.20}{0.80} A \ = \ B$, therefore: 
$B = \frac{1}{4} A$, and $B$ is $\frac{1}{4}$ times of $A$ or it’s $25$% of $A$.

The correct answer is $70$
To find the number of possible outfit combinations, multiply the number of options for each factor:
$7 \ × \ 2 \ × \ 5 \  = \ 70$

The correct answer is $50$ feet 
The relationship among all sides of special right triangle
$30^\circ\ -\ 60^\circ\ -\ 90^\circ$ is provided in this triangle: 
In this triangle, the opposite side of $30^\circ$ angle is half of the hypotenuse. 
Draw the shape for this question: 
The latter is the hypotenuse. Therefore, the latter is $50$ ft.

The correct answer is $8$
Let $x$ be the number. Write the equation and solve for $x$.
$(48 \ – \ x) \ ÷ \ x \ = \ 5$
Multiply both sides by x.
$(48 \ – \ x) \ = \ 5\ x$, then add x both sides:
$48 \ = \ 6\ x$, now divide both sides by $6$:
$x \ = \ 8$

The correct answer is $36$
The sum of supplement angles is $180$ . Let $x$ be that angle.Therfore,
($x \ + \ 4\ x) \ = \ 180$
$5\ x \ = \ 180$, divide both sides by $5$: 
$x \ = \ 36$

The correct answer is $2 \ : \ 3$
The average speed of john is: $200 \ ÷ \ 5 \ = \ 40$ km
The average speed of Alice is: $240 \ ÷ \ 4 \ = \ 60$ km
Write the ratio and simplify.
$40 \ : \ 60$ ⇒ $2 \ : \ 3$

The correct answer is $18\%$
The percent of girls playing tennis is: $30\%$ × $60\%$ = $0.30$ × $0.60$ = $0.18$ = $18\%$

The correct answer is $0$
Solving Systems of Equations by Elimination
$2\ x \ - \ y \ = \ -\ 3$
$4\ x \ + \ 2\ y \ = \ 6$
Multiply the first equation by $2$, then add it to the second equation.
$2\ (2\ x \ - \ y \ = -\ 3$)
$4\ x \ + \ 2\ y \ = \ 6$             
$⇒$
$4\ x \ - \ 2\ y \ =  -\ 6$ 
$4\ x \ + \ 2\ y \ =  6⇒8\ x = 0 ⇒ x = 0$

The correct answer is $310$
Add the first $5$ numbers. $20$ + $45$ + $40$ + $35$ + $50$ = $190$
To find the distance traveled in the next $2$ hours, multiply the average by the number of hours.  
Distance = Average $×$ Rate = $60$ $×$ $2$ = $120$
Add both numbers.  $120$ + $190$ = $310$

The correct answer is $6$ hours and $24$ minutes
Use the distance formula: 
Distance $=$ Rate $×$ time $⇒$ $320$ = $50$ $×$ T , divide both sides by $50$ .  $320$ $÷$ $50$ $=$ T $⇒$ T $=$ $6.4$ hours.
Change hours to minutes for the decimal part. $0.4$ hours $=$ $0.4$ $×$ $60$ $=$ $24$ minutes

The correct answer is $9899$
Smallest  $3$–digit number is $100$ and biggest $4$–digit number is : $9999$

The correct answer is $1024$
$4^5$ $=$  $4$ $×$ $4$ $×$ $4$ $×$ $4$ $×$ $4$ $=$ $1024$

The correct answer is $5$
Use Pythagorean Theorem: $a^2$ $+$ $b^2$ $=$ $c^2$
$3^2$ $+$ $4^2$ $=$ $c^2$ $⇒$ $25$ $=$ $c^2$ $⇒$ $c$ $=$ $5$

The correct answer is $300$
The ratio of boy to girls is $3$:$5$ .
Therefore, there are $3$ boys out of $8$ students.
To find the answer, first divide the total number of students by $8$, then multiply the result by $3$
$800$ $÷$ $8$ $=$ $100$ $⇒$ $100$ $×$ $3$ $=$ $300$

The correct answer is $200$
Use percent formula$:$ 
Part $=$ $\frac{percent}{100}$ $×$ whole
$30$ $=$ $\frac{percent}{100}$ $×$ $15$ $⇒$ $30$ $=$ $\frac{percent × 15}{100}$ multiply both sides by $100$
$3000$ $=$  percent  $×$ $15$, divide both sides by $15$
percent $=$ $200$

The correct answer is $260$
Therefore, the missing side (height) is  $=$  $64$  $-$  $18$  $-$  $12$  $-$  $14$  $=$  $20$
 Area of a trapezoid: A $=\frac{1}{2} \  h \ (b_1 \ +\  b_2) = \frac{1}{2}\ (20)\  (12\ +\ 14) = 260$

The correct answer is $64$
Let $x$ be the number. Write the equation and solve for $x$
$\frac{2}{3}$ $×$ $24$ $=$ $\frac{1}{4}$ . $x$ $⇒$ $\frac{2 × 24}{3}$ $=$ $\frac{x}{4}$
use cross multiplication to solve for $x$.
$4$ $×$ $48$ $=$ $3\ x$ $⇒$ $192$  $=$ $3\ x$ $⇒$ $x$ $=$ $64$

The correct answer is $78$% 
To find the discount, multiply the number by ($100$% – rate of discount).
Therefore, for the first discount we get: (D) ($100\% – (25)\%)$= (D) ($0.75) = (0.75$ D)
For increase of $5\%: (0.75$ D) ($100\%  \ + \ 5\%)= (0.75$D) ($1.05$D) $=0.78$D $= (78\%)$of D

The correct answer is $14\ π$
Use the formula of area of circles.
Area $=$ $π$$r^2$ $⇒$ $49$$π$ $=$ $π$$r^2$ $⇒$ $49$ $=$  $r^2$  $⇒$ $r$ $=$ $7$
Radius of the circle is $7$. Now, use the circumference formula$:$
Circumference$=$ $2\ π\ r$ $=$ $2\ π\ (7)$ $=$ $14\ π$

The correct answer is $30$%
Use the formula for Percent of Change:
Part $=$ $\frac{New Value - Old Value}{Old Value}$ $×$ $100$% 
$\frac{35 - 50}{50}$ $×$ $100$% $=$ $-30$% (negative sign here means that the new price is less than old price).

The correct answer is: $I >$ $1900\ x$ $+$ $25000$
Let $x$ be the number of years. Therefore, $$1900$ per year equals $1900x$.
starting from $$25000$ annual salary means you should add that amount to $1900x$.
Income more than that is:
$I >$ $1900\ x$ $+$ $25000$

The correct answer is $150$
The question is this: $1.5$ is what percent of $1$$?$
Use percent formula:
$Part$ $=$ $\frac{percent}{100}$ $×$ whole
$1.5$ $=$ $\frac{percent × 1 }{100}$ $⇒$ $150$ $=$ percent $×$ 1 $⇒$ percent = $\frac{150}{1}$ = $150$ 

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

The correct answer is $6$
Some of prime numbers are: $2$, $3$, $5$, $7$, $11$, $13$
Find the product of two consecutive prime numbers:
$2$ $×$ $3$ = $6$ (bingo!)
$3$ $×$ $5$ = $15$ (not in the options)
$13$ $×$ $11$ $=$ $143$ (not in the options)

The correct answer is $26.2\%$
The question is this: $$620$ is what percent of $$840$ ?
Use percent formula:
$Part$ $=$ $\frac{percent}{100}$ $×$ whole
$620$ $=$ $\frac{percent}{100}$ $×$ $840$ $⇒$ $620$ $=$  $\frac{percent × 840}{100}$ $⇒$ $62000$ $=$ percent $×$ $840$ $⇒$
percent $=$ $\frac{62000}{840}$ $=$ $73.8$
$620$ is $73.8$% of $840$. Therefore, the discount is: $100$% $-$ $73.8$% $=$ $26.2$%

The correct answer is $20$
If the score of Mia was $80$, therefore the score of Ava is $40$.
Since the score of Emma was half that of Ava, therefore, the score of Emma is $20$.

The correct answer is $\frac{23}{24}$
If $23$ balls are removed from the bag at random, there will be one ball in the bag.
The probability of choosing a brown ball is $1$ out of $24$. Therefore, the probability of not choosing a brown ball is
 $23$ out of $24$ and the probability of having not a brown ball after removing $23$ balls is the same.

The correct answer is $38$
Let $x$ be the smallest number. Then, these are the numbers:
$x$ , $x$ $+$ $1$ , $x$ $+$ $2$ , $x$ $+$ $3$ , $x$ $+$ $4$
average =  $\frac{sum \ of \ terms }{number \ of  \ terms}$ $⇒$ $40$ = $\frac{sum \ of \ terms }{5}$ $⇒$ $40$ = $\frac{5\ x \ +\  10 }{5}$ $⇒$ 
$200 = 5\ x+ 10 ⇒  190 =  5\ x ⇒  x = 38$ 

The correct answer is $16$
The area of the floor is: $8$ cm × $32$ cm = $256$ cm$^2$
The number of tiles needed = $256$ $÷$ $16$ = $16$

The correct answer is $11.52$ kg
The weight of $14.4$ meters of this rope is: $14.4\  ×\  800$ $= 11520$g
$1$ kg $= 1000$ g, therefore,  $11520$ g $÷\  1000 = 11.52$ kg

The correct answer is $400$
$10$% of the volume of the solution is alcohol. Let $x$ be the volume of the solution. 
Then: $10$% of $x = 40$ ml $⇒$ $0.1\ x= 40$ $⇒$ $40$ $÷$ $0.1= 400$

The correct answer is $63.2$
average =  $\frac{sum \ of \  terms }{number \ of \ terms}$
The sum of the weight of all girls is:  $24$ $×$ $56$ = $1344$
The sum of the weight of all boys is: $36$ $×$  $68$ = $2448$ 
The sum of the weight of all students is: $2448$ $+$ $1344$ = $3792$
average = $\frac{3792 }{60}$= = $63.2$

The correct answer is : $500$
Let$x$ be the original price.
If the price of a laptop is decreased by $20$% to $$400$, then:
$80$% of $x$ = $400$ $⇒$ $0.8\ x$ = $400$ $⇒$ $x$ = $400$ $÷$ $0.8$ = $500$

The correct answer is : $11$
Write the numbers in order:
$3$,$10$,$11$,$14$,$20$
Since we have $5$ numbers ($5$ is odd), then the median is the number in the middle, which is $11$.

The correct answer is : $2813.44$
Surface Area of a cylinder $= 2\ π\ r \ (r \ + \ h)$ ,
The radius of the cylinder is $14$ inches and its height is $18$ inches. $π$ is about $3.14$. Then:
Surface Area of a cylinder = $( 2) \ (π)  (14$) ($14 \ + \  18) = 896 \ π = 2813.44$

The correct answer is: $46$
average = $\frac{sum \ of \ terms}{number \ of\  terms}$ $⇒$ $24$ $=$ $\frac{13 + 15 + 22 + x}{4}$ $⇒$ $96$ $=$ $50 + x$
$⇒$ $x =46$

The correct answer is :$1440$
Let $x$ be the original price.
If the price of the shoe is decreased by $50\%$ to $$720$, then:
$50$% of $x$ $=$ $720$ ⇒ $0.5\ x= 720$ $⇒$ $x$ $=$ $720\ ÷ \ 0.5= 1440$

$y\ ≤\ x\ +\ 4$
$2\ x\ +\ y\ ≤\ -\ 4$
A.Point $(–\ 4,\ –\ 4)$ is in the solution section. Let’s check the point in both inequalities. 
$–\ 4\ ≤\ –\ 4\ +\ 4$, It works
$2\ (–\ 4)\ +\ (–\ 4)\ ≤\ –\ 4 ⇒ –\ 12\ ≤\ –\ 4$, it works (this point works in both)
B.Let’s choose this point $(0,\ 0)$ 
$0\ ≤\ 0\ +\ 4$, It works
$2\ (0)\ +\ (0)\ ≤\ –\ 4$, That’s not true!
C. Let’s choose this point $(–\ 5,\ 0)$ 
$0\ ≤\ –\ 5\ +\ 4$, That’s not true!
D.Let’s choose this point $(0,\ 5)$ 
$5\ ≤\ 0\ +\ 4$, That’s not true!

The correct answer is: $3000$
Use simple interest formula:
$I  =p\ r\ t$
($I =$interest, $p =$ principal, $r =$ rate, $t =$ time) 
$I =$ $(20000)$($0.03)( 5)= 3000$