Full Length SSAT Upper Level Math Practice Test

The correct answer is $35$
$\frac{30}{A} \ + \ 3=9 → \frac{30}{A}=9 \ - \ 3=6$
→$30=6 \ A → A=\frac{30}{6}=5$
$30 \ + \ A=30 \ + \ 5=35$

The correct answer is $600$
Number of rotates in $16$ second equals to: $\frac{450 \ × \ 16}{12}=600$

The correct answer is $16$
The area of the floor is:$4$ cm $× \ 20$ cm $= 80$ cm$^2$
The number of tiles needed $= 80 \ ÷ \ 5 = 16$

The correct answer is $9$
The digit in tens place is $2$.
The digit in the thousandths place is $7$.
Therefore;
$2 \ + \ 7=9$ 

The correct answer is number of books sold in April is was $\frac{1}{2}$the number of books in sold in July.
A:Number of books sold in April is: $380$
Number of books sold in July is: $760→ \frac{ 380}{760}=\frac{38}{76}=\frac{1}{2}$
B:number of books sold in July is: $760$
Half the number of books sold in May is:$\frac{1140}{2}=570 → 760 \ >570$
C:number of books sold in June is: $190$
Half the number of books sold in April is:$380 \ × \ 2=760 → 760 \ > \ 190$
D:$380 \ + \ 190=570 \ < \ 760$
E:$380 \ < \ 760$

The correct answer is $6$
Number of packs equal to: $\frac{24}{4}=6$
Therefore, the school must purchase $6$ packs.

The correct answer is $2,541$
$15.246 \ ÷ \ 0.006=\frac{\frac{15,246}{1,000}}{{\frac{6}{1,000}}}=\frac{15,246}{6}=2,541$

The correct answer is $23$
The amount of money that Alex earns for one hour: $\frac{$\ 460}{20}=$\ 23$
Number of additional hours that he needs to work in order to make enough money is:
$\frac{$\ 630 \ - \ $\ 460}{2.5 \ × \ $\ 23}≅3$
Number of total hours is: $20 \ + \ 3=23$

The correct answer is $35$
First, find the number.
Let $x$ be the number. Write the equation and solve for $x$.
$120\%$ of a number is $60$, then:
$1.2 \ × \ x=→x=60 \ ÷ \ 1.2=50$
$70\%$ of $50$ is:$0.7 \ × \ 50=35$

The correct answer is $4.68$
$\frac{1 \ \frac{5}{2} \ + \ \frac{3}{5}}{4 \ \frac{3}{2} \ - \ \frac{15}{4}} = \frac{\frac{7}{2} \ + \ \frac{3}{5}}{\frac{11}{2} \ - \ \frac{15}{4}} = \frac{\frac{35 \ + \ 6}{10}}{\frac{22 \ - \ 15}{4}}$
$\frac{\frac{41}{10}}{\frac{7}{4}} = \frac{41 \times 2}{7 \times 5} = \frac{164}{35} \cong 4.68$

The correct answer is $70$
Average $=\frac{sum \ of \ terms }{number \ of \ terms}$
The sum of the weight of all girls is: $12 \ × \ 62 = 744$ kg
The sum of the weight of all boys is: $24 \ × \ 74 = 1776$ kg
The sum of the weight of all students is: $744 \ + \ 1776 =2520$ kg
The average weight of the $36$ students: $\frac{2520}{36}=70$

The correct answer is $7$
$2 \ ≤ \ x \ < \ 6$→ Multiply all sides of the inequality by $2$. Then:
$2 \ × \ 2 \ ≤ \ 2 \ × \ x \ < \ 2 \ × \ 6 → 4 \ ≤ \ 2 \ x \ < \ 12$
All $3$ to all sides. Then: →$4 \ + \ 3 \ ≤ \ 2\ x \ + \ 3 \ < \ 12 \ + \ 3→ 7 \ ≤ \ 2 \ x \ + \ 3 \ < \ 15$
Minimum value of $2 \ x \ + \ 3$ is $7$

The correct answer is $42.5$
$8.5 \ ÷ \ 0.20=\frac{8.5}{0.20}=\frac{\frac{{85}}{10}}{\frac{20}{100}}=\frac{85 \ × \ 100}{20 \ × \ 10}=\frac{85}{20} \ × \frac{100}{10}=4.25 \ × \ 10=42.5$

The correct answer is $5$
$4∎9=\sqrt{4^2 \ + \ 9}=\sqrt{16 \ + \ 9}=\sqrt{25}=5$

The correct answer is $2000$
Let $x$ be the capacity of one tank. Then, $\frac{1}{2} x=250→ x=250 \ × \ 2=500$ Liters
The amount of water in four tanks is equal to: $4 \ × \ 500=2000$ Liters

The correct answer is $$\ 10$
Let $x$ be the cost of one-kilogram orange, then:
$3 \ x \ + \ (2 \ × \ 3.2)=36.4→$
$3 \ x \ + \ 6.4=36.4→$
$3 \ x=36.4 \ - \ 6.4→$
$3 \ x=30→$
$x=\frac{30}{3}=$\ 10$

The correct answer is $138$ minutes
Let $b$ be the amount of time Mary can do the job, then,
$\frac{1}{a} \ + \ \frac{1}{b}=\frac{1}{100}→$
$\frac{1}{360} \ + \ \frac{1}{b}=\frac{1}{100}→$
$\frac{1}{b}=\frac{1}{100} \ - \ \frac{1}{360}=\frac{3.6 \ - \ 1}{360}=\frac{2.6}{360}=\frac{1}{138}$
Then: $b=138$ minutes

The correct answer is $145$ degrees
All angles in a triangle sum up to $180$ degrees. Then:
$x=35 \ + \ 110=145$

The correct answer is $- \ 15$
The smallest number is $- \ 12$.
To find the largest possible value of one of the other five integers, we need to choose the smallest possible integers for four of them.
Let $x$ be the largest number.
Then: $- \ 65=(- \ 12) \ + \ (- \ 11) \ + \ (- \ 10) \ + \ (- \ 9) \ + \ (- \ 8) \ + \ x→$
$- \ 65=- \ 50 \ + \ x→$
$x=- \ 65 \ + \ 50=- \ 15$

The correct answer is $6$ 
Let’s review the choices provided.
A. $4$. In $4$ years, David will be $46$ and Ava will be $10$.
$46$ is not $4$ times $10$.
B. $6$. In $6$ years, David will be $48$ and Ava will be $12$.
$48$ is $4$ times $12$!
C. $8$. In $8$ years, David will be $80$ and Ava will be $14$.
$50$ is not $4$ times $14$.
D. $10$. In $10$ years, David will be $52$ and Ava will be $16$.
$52$ is not $4$ times $16$.
E. $14$. In $14$ years, David will be $56$ and Ava will be $20$.
$56$ is not $4$ times $20$.

The correct answer is $40$
Choices A, B, D and E are incorrect because $60\%$ of each of the numbers is non-whole number.
A. $26$, $60\%$ of $26 = 0.60 \ × \ 26=15.6$
B. $32$, $60\%$ of $32=0.60 \ × \ 32=19.2$
C. $40$, $60\%$ of $40=0.60 \ × \ 40=24$
D. $41$, $60\%$ of $41=0.60 \ × \ 41=24.6$
E. $16$, $60\%$ of $16=0.60 \ × \ 16=9.6$

The correct answer is $- \ \frac{1}{3}$
The equation of a line in slope intercept form is:
$y=m \ x \ + \ b$
Solve for $y$.
$6 \ x \ - \ 2 \ y=16 ⇒$
$- \ 2 \ y=16 \ - \ 6 \ x ⇒$
$y=(16 \ - \ 6 \ x) \ ÷ \ (- \ 2) ⇒$
$y=3 \ x \ - \ 8$
The slope is $3$.
The slope of the line perpendicular to this line is:
$m_{1} \ × \ m_{2} = - \ 1 ⇒ 3 \ × \ m_{2} = - \ 1 ⇒$
$m_{2} = - \ \frac{1}{3}$

The correct answer is $\frac{90 \ x \ + \ 750}{x}$
The amount of money for $x$ bookshelf is: $90 \ x$
Then, the total cost of all bookshelves is equal to: $90 \ x \ + \ 750$
The total cost, in dollar, per bookshelf is: $\frac{Total \ cost}{number \ of \ items}=\frac{90 \ x \ + \ 750}{x}$

The correct answer is $288$ cm$^3$
If the length of the box is $24$, then the width of the box is one fourth of it, $6$, and the height of the box is $2$ (one third of the width).
The volume of the box is:
V $=$ (length) (width) (height) $= (24) \ (6) \ (2) =288$ cm$^3$

The correct answer is $42$ miles
Use the information provided in the question to draw the shape.
Use Pythagorean Theorem:
$a^2 \ + \ b^2 = c^2$
$60^2 \ + \ 120^2 = c^2 ⇒$
$3600 \ + \ 14400 = c^2 ⇒$
$18000 = c^2 ⇒$
$c =42$

The correct answer is $42$ miles
Use the information provided in the question to draw the shape.
Use Pythagorean Theorem:
$a^2 \ + \ b^2 = c^2$
$60^2 \ + \ 120^2 = c^2 ⇒$
$3600 \ + \ 14400 = c^2 ⇒$
$18000 = c^2 ⇒$
$c =42$

The correct answer is $1$
$\frac{13 \ + \ 11}{2}=\frac{24}{2}=12$ Then:
$12 \ - \ 11=1$

The correct answer is $385$
$\frac{84752}{202} \cong 385.2363 \cong 385$

The correct answer is $80$ liters
The Area that one liter of paint is required: $45$ cm $× \ 100$ cm = $4,500$ cm$^2$
Remember: $1$ m$^2 = 10,000$ cm$^2 \ (100 \ × \ 100 = 10,000)$, then, $4,500$ cm$^2 = 0.45$ m$^2$
Number of liters of paint we need: $\frac{36}{0.45}=80$ liters

The correct answer is $6$
Let’s review the choices provided:
A. $x=2→$ The perimeter of the figure is: $2 \ + \ 4 \ + \ 2 \ + \ 2 \ + \ 2=12≠ 20$
B. $x=3→$ The perimeter of the figure is: $2 \ + \ 4 \ +\ 2 \ + \ 3 \ + \ 3=14≠20$
C. $x=6→$ The perimeter of the figure is: $2 \ + \ 4 \ + \ 2 \ + \ 6 \ + \ 6=20=20$
D. $x=9→$ The perimeter of the figure is: $2 \ + \ 4 \ + \ 2 \ + \ 9 \ + \ 9=26≠20$
E. $x=12→$ The perimeter of the figure is: $2 \ +\ 4 \ + \ 2 \ + \ 12 \ + \ 12=32≠20$

The correct answer is $14 \ - \ k$
Will’s mark is $k$ less than John’s mark.
Then, from the choices provided Will’s mark can only be $14 \ - \ k$

The correct answer is $4$ hours and $32$ minutes
Number of times that the driver rests $=\frac{24}{6}=4$
Driver’s rest time $= 1$ hour and $8$ minutes $= 68$ minutes
Then, $4 \ × \ 68$ minutes $=272$ minutes
$1$ hour $= 60$ minutes $→ 272$ minutes $= 4$ hours and $32$ minutes

The correct answer is $$\ 600$
Let $x$ be the original price.
If the price of the sofa is decreased by $25\%$ to $$450$, then:
$75\%$ of $x=450 ⇒$
$0.75 \ x=450 ⇒$
$x=450 \ ÷ \ 0.75=$\ 600$

The correct answer is $6 \ × \ \frac{1}{6}$
Let’s review the options provided:
A. $12 \ × \ \frac{1}{2}=\frac{12}{2}=6=6$
B. $24 \ × \ \frac{1}{4}=\frac{24}{4}=6=6$
C. $4 \ × \ \frac{3}{2}=\frac{12}{2}=6=6$
D. $6 \ × \ \frac{5}{5}=\frac{30}{5}=6=6$
E. $6 \ × \ \frac{1}{6}=\frac{6}{6}=1≠6$

The correct answer is $40,500$
Number of Mathematics book:
$0.25 \ × \ 900=225$
Number of English books:
$0.20 \ × \ 900=180$
Product of number of Mathematics and number of English books:
$225 \ × \ 180=40,500$

The correct answer is $108^°, 54^°$
The angle $\alpha$ is:
$0.3 \ × \ 360=108^°$
The angle $β$ is:
$0.15 \ × \ 360=54^°$

The correct answer is $1.5$
$6 \ y \ + \ 6 \ < \ 24→$
$6 \ y \ < \ 24 \ - \ 6→$
$6 \ y \ < \ 18→y \ < \ 3$
The only choice that is less than $3$ is B.

The correct answer is $24$
$x \ + \ 1=1 \ + \ 1 \ + \ 1→x=2$
$y \ + \ 6 \ + \ 2=5 \ + \ 4→y \ + \ 8=9→y=1$
Then, the perimeter is:
$1 \ + \ 5 \ + \ 1 \ + \ 4 \ + \ 1 \ + \ 2 \ + \ 1 \ + \ 6 \ + \ 2 \ + \ 1=24$

The correct answer is $45$
Since, E is the midpoint of AB, then the area of all triangles DAE, DEF, CFE and CBE are equal.
Let $x$ be the area of one of the triangle, then:
$4\ x=90→x=22.5$
The area of DEC $=2 \ x=2 \ (22.5)=45$

The correct answer is: it cannot be determined from the information given
We have two equations and three unknown variables, therefore $x$ cannot be obtained.

The correct answer is $25$
The capacity of a red box is $20\%$ bigger than the capacity of a blue box and it can hold $30$ books.
Therefore, we want to find a number that $20\%$ bigger than that number is $30$.
Let $x$ be that number.
Then: $1.20 \ × \ x=30$, Divide both sides of the equation by $1.2$.
Then:
$x=\frac{30}{1.20}=25$

The correct answer is $40.46$ liters
Amount of available petrol in tank:
$70.5 \ - \ 4.65 \ - \ 35.7 \ + \ 10.31=40.46$ liters

The correct answer is $34$
Perimeter of figure A is: $2 \ π \ r=2 \ π \ \frac{12}{2}=12 \ π=12 \ × \ 3=36$
Area of figure B is: $4 \ × \ 8=32$
Average $=\frac{36 \ + \ 32}{2}=\frac{68}{2}=34$

The correct answer is $3$
Let’s review the choices provided:
A. $x=\frac{1}{2}→ \frac{4}{7} \ + \ \frac{1}{2}=\frac{8 \ + \ 7}{14}=\frac{15}{14} \cong 1.071 \ < \ 3$
B. $x=3→ \frac{5}{9} \ + \ 3=\frac{4 \ + \ 21}{7}=\frac{25}{7} \cong 3.6 \ >\ 3$
C. $x=\frac{4}{3}→ \frac{4}{7} \ + \frac{4}{3}=\frac{12 \ +\ 28}{21}=\frac{40}{21} \cong 1.91 \ < \ 3$
D. $x=\frac{4}{6}→ \frac{4}{7} \ + \ \frac{4}{6}=\frac{24 \ + \ 28}{42}=\frac{52}{42} \cong 1.238 \ < \ 3$
E. $x=\frac{2}{5}→ \frac{4}{7} \ + \ \frac{2}{5}=\frac{20 \ + \ 14}{35}=\frac{34}{35} \cong 0.9 \ <\ 3$

The correct answer is $4 \times a \times b$
Let put some values for $a$ and $b$.
If $a=9$ and $b=2 →a \ × \ b=18 →$
$\frac{18}{3}=6→18$ is divisible by $3$ then;
A. $a \ + \ b=9 \ + \ 2=11$ is not divisible by $3$
B. $3 \ a \ - \ b=(3 \ × \ 9) \ - \ 2=27 \ - \ 2=25$ is not divisible by $3$
If $a=11$ and $b=3 →a \ × \ b=33 →$
$\frac{33}{3}=11$ is divisible by $3$ then;
C. $a \ - \ 3 \ b=11 \ - \ (3 \ × \ 3)=11 \ - \ 9 =2$ is not divisible by $3$
D. $\frac{a}{b}=\frac{11}{3}$ is not divisible by $3$
E. $4 \ × \ 11 \ × \ 3=132$
$132$ is divisible by $3$.
If you try any other numbers for $a$ and $b$, you will get the same result.

The correct answer is $30$
The angles on a straight line add up to $180$ degrees.
Let’s review the choices provided:
A. $y=10→ x \ + \ 45 \ + \ y\ + \ 2 \ x \ + \ y=25 \ + \ 45 \ + \ 10 \ + \ 2 \ (25) \ + \ 10=140≠180$
B. $y=25→ x \ + \ 45 \ + \ y\ + \ 2 \ x \ + \ y=25 \ + \ 45 \ + \ 25 \ + \ 2 \ (25) \ + \ 25=170≠180$
C. $y=30→ x \ + \ 45\ + \ y \ +\ 2 \ x \ + \ y=25 \ + \ 45 \ + \ 30 \ + \ 2 \ (25) \ + \ 30=180$
D. $y=35→ x \ +\ 45 \ + \ y \ +\ 2 \ x \ + \ y=25 \ + \ 45 \ + \ 35 \ + \ 2 \ (25) \ + \ 35=190≠180$
E. $y=40→ x \ + \ 45 \ + \ y \ + \ 2 \ x \ + \ y=25 \ + \ 45 \ +\ 40 \ + \ 2 \ (25) \ + \ 40=200≠180$

The correct answer is $\frac{8}{20}$
Set of numbers that are not composite between $1$ and $20$:
A $= \left\{2, 3, 5, 7, 11, 13, 17, 19, \right\}$
Probability $=\frac{number \ of \ desired \ outcomes}{number \ of \ total \ outcomes} = \frac{8}{20}$ 

The correct answer is $15$
$\frac{3}{4} \ × \ 20=\frac{60}{4}=15$

The correct answer is $\frac{800}{6} \ + \ \frac{50}{6} \ + \ \frac{5}{6}$
$855 \ ÷ \ 6=\frac{855}{6}=\frac{800 \ + \ 50 \ + \ 5}{6}=\frac{800}{6} \ + \ \frac{50}{6} \ + \ \frac{5}{6}$

The correct answer is $29$
Find the difference of each pairs of numbers:
$1 \ , 2, 4, 7, 11, 16, 22$, ___, $37$
The difference of $1$ and $2$ is $1, \ 2$ 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 next number should be $7$.
The number is $22 \ + \ 7 = 29$

The correct answer is $444 \frac{5}{7}$
$450 \ - \ 5 \ \frac{4}{14}=(449 \ - \ 5) \ + \ (\frac{14}{14} \ - \ \frac{4}{14})= 444 \frac{10}{14} =444 \frac {5}{7}$