Full Length SSAT Middle Level Mathematics Practice Test

The correct answer is $N \ + \ 4$
Mary has $N$ books.
Lucy has $7$ more books than Mary.
Then, Lucy has $N \ + \ 7$ books.
If Lucy gives Mary $3$ books, Lucy will have:
$N \ + \ 7 \ - \ 3 = N \ + \ 4$

The correct answer is $90$
If $20$ percent of a number is $45$, then the number is:
$20\%$ of $x = 45 →$
$0.20 = 40 →$
$x= \frac{45}{0.20} = 225$
$45$ percent of $225$ is:
$40\%$ of $225 = \frac{40}{100} \times 225 = 90$

The correct answer is $12$
If $\frac{5 \ x}{2} = 40$, then:
$5 \ x = 80 → x = 16$
$\frac{3 \ x}{4} =$
$\frac{3 \times 16}{4} =$
$\frac{48}{4} = 12$

The correct answer is $\frac{5}{15} \times 3$
$0.2 \times 2 = 0.4$, all options provided are equal to $0.4$ except option A.
$\frac{5}{15} \times 3 = 1$

The correct answer is $0.2 \ × \ 30 = 6$
$\frac{1}{5}$ of $30$ is $6$.
Let’s review the options provided:
A. $0.3 \ ×\ 6 = 1.8$
B. $0.3 \ ×\ 5 = 1.5$
C. $0.2 \ × \ 30 = 6$
D. $0.2 \ × \ 35 = 7$
E. $0.2 \ × \ 39.5 = 7.9$

The correct answer is $30$
The sum of supplement angles is $180$.
Let $x$ be that angle.
Therefore, $x \ + \ 5\ x = 180$
$6\ x = 180$, divide both sides by $6: \ x = 30$

The correct answer is $160$ degrees
$x = 30 \ +\ 130 = 160$ degrees

The correct answer is $40\%$
Use the formula for Percent of Change
$\frac{New \ Value-Old \ Value}{Old \ Value} \times 100\%$
$\frac{18 \ -\ 30}{30} \times 100\% = \ – \ 40\%$ (negative sign here means that the new price is less than old price)

The correct answer is $264$ cm$^2$
The perimeter of the trapezoid is $60$.
Therefore, the missing side (height) is:
$= 60 \ – \ 16 \ – \ 12 \ – \ 10 = 22$
Area of the trapezoid:
A $= \frac{1}{2} \ h \ (b1 \ + \ b2) = \frac{1}{2} \ (22) \ (12 \ + \ 10) =264$

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:
$\sqrt{32} \times \sqrt{32} = 32$

The correct answer is $7$
Simplify and solve for $x$ in the equation.
$3 \ (x \ + \ 2) = 2 \ (x \ − \ 6) \ + \ 24 →$
$3 \ x \ + \ 6 = 2 \ x \ − \ 12 \ + \ 24$
$3 \ x \ + \ 3 = 2 \ x \ – \ 12$
Subtract $2 \ x$ from both sides:
$x \ + \ 3 = – \ 4$, Add $4$ to both sides:
$x = 7$ 

The correct answer is $10$
If the score of Ashly was $40$, therefore the score of Jennifer is $20$.
Since, the score of Ashly was half as that of Jennifer, therefore, the score of Ashly is $10$.

The correct answer is $5$
Let $x$ be the number.
Then: $4 \ x \ +\ 4=24$
Solve for $x: \ 4 \ x \ + \ 4 =24→$
$4 \ x=24 \ - \ 4=20→$
$x=20 \div 4=5$

The correct answer is $28$
Five years ago, Emily was three times as old as John.
John is $12$ years now. Therefore, $5$ years ago John was $7$ years.
Five years ago, Emily was:
A $= 3 \times 7=21$
Now Emily is $28$ years old:
$21 \ +\ 7 = 28$

The correct answer is $14$
Let $x$ be the number.
Write the equation and solve for $x$.
$\frac{1}{3} \times 12= \frac{2}{7}$.
$x ⇒ \frac{1 \times 12}{3} = \frac{2 \ x}{7}$ , use cross multiplication to solve for $x$.
$12 \times 7 = 2 \ x \times 3 ⇒$
$84 = 6 \ x ⇒ x = 14$

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

The correct answer is $3$
Let $x$ be the number.
Write the equation and solve for $x$.
$(18 \ – \ x) \ ÷ \ x = 6$
Multiply both sides by $x$.
$(18 \ – \ x) = 6 \ x$, then add x both sides.
$18 = 6 \ x$, now divide both sides by $6$.
$x = 3$

The correct answer is $60.66$
average $= \frac{sum \ of \ terms}{number \ of \ terms}$
The sum of the weight of all girls is:
$12 \ ×\ 54 = 648$ kg
The sum of the weight of all boys is:
$24 \ × \ 64 = 1,536$ kg
The sum of the weight of all students is:
$648\ + \ 1,536 = 2,184$ kg
Average $= \frac{2,184}{36} = 60.66$

The correct answer is $21$
In a group of $3$ books, the average number of pages is $20$.
Therefore, the sum of pages in all $3$ books is $(3 \ × \ 20 = 54)$.
Ava adds a book with $24$ pages to the group.
Then, the sum of pages in all $4$ books is:
$(3 \ × \ 20 \ +\ 24 =84 )$.
The new average number of pages per book is:
$\frac{84}{4}=21$

The correct answer is $6$
Solve for $x$ in the equation.
$3(x \ +\ 2) = 24→$
$3 \ x \ + \ 6=24→$
$3 \ x=24 \ - \ 6=18→$
$x = 18 \div 3=6$

The correct answer is $\frac{2}{3} \ > \ 0.6$
Only option D is correct.
$\frac{2}{3} =0.66→$
$0.6 \ < \ \frac{2}{3}$

The correct answer is $14$
$\frac{2}{3} \ × \ 21= \frac{42}{3} =14$

The correct answer is $100$ cm
One lite $=1000$ cm$^{3} → 4$ liters $= 4,000$ cm$^{3}$
$4,000=10 \times 4 \times$ h $→$ h $=\frac{4000}{4}=100$ cm

The correct answer is $35$
Choices A, C, D, and E are incorrect because $80\%$ of each of the numbers is a non-whole number.
A. $49$     $80\%$ of $49 = 0.80 \ × \ 49=39.2$
B. $35$     $80\%$ of $35=0.80 \ × \ 35=28$
C. $32$     $80\%$ of $32=0.80 \ × \ 32=25.6$
D. $12$     $80\%$ of $12=0.80 \ × \ 12=9.6$
E. $8$       $80\%$ of $8=0.80 \ × \ 8=6.4$

The correct answer is $25$
The red box is $30\%$ greater than the blue box.
Let $x$ be the capacity of the blue box. Then:
$x \ + \ 30\%$ of $x=50→$
$1.3 \ x=50→$
$x=\frac{50}{1.3}=25$

The correct answer is $25$
The red box is $30\%$ greater than the blue box.
Let $x$ be the capacity of the blue box. Then:
$x \ + \ 30\%$ of $x=50→$
$1.3 \ x=50→$
$x=\frac{50}{1.3}=25$

The correct answer is $\frac{1}{6}$
From the options provided, only C $(\frac{1}{6})$ is less than $\frac{1}{3}$.

The correct answer is $18$
Four people can paint $5$ houses in $15$ days.
It means that for painting $10$ houses in $6$ days we need $9$ people.
To paint $10$ houses in $6$ days, $18$ people are needed.

The correct answer is $$\ 48$
$$\ 10 \ × \ 8=$\ 80$
Petrol use: $8 \ × \ 2=16$ liters
Petrol cost: $16 \ × \ $\ 2=$\ 32$
Money earned: $$\ 80 \ -\ $\ 32=$\ 48$

The correct answer is $3$
$N \ × \ (6 \ -\ 3)=9→$
$N \ ×\ 3=9→$
$N=3$

The correct answer is $$\ 4.69$
Ann earns $$20.00$ per hour now.
$$20.00$ per hour is $15$ percent more than her previous rate.
Let $x$ be her rate before her raise. Then:
$x \ +\ 0.15 \ x=20→$
$1.15 \ x=20→$
$x=\frac{20}{1.15}=17.39$
Alex earns $$25.40$ per hour now.
$$25.40$ per hour is $15$ percent more than his previous rate.
Let $x$ be Alex’s rate before his raise. Then:
$x \ + \ 0.15 \ x=25.40→$
$1.15\ x=25.40→$
$x=\frac{25.40}{1.15}=22.08$
Ann earned $$\ 4.69$ more per hour than John before their raises.

The correct answer is $50^°$
$\alpha =180^° \ -\ 105^°=75^°$
$\beta =180^° \ - \ 125^°=55^°$
The sum of all angles in a triangle is $180$ degrees. Then:
$x \ + \ \alpha \ + \ \beta=$
$180^°→x=180^° \ - \ 75^° \ - \ 55^°=50^°$

The correct answer is $9$
The width of a rectangle is $2 \ x$ and its length is $3 \ x$.
Therefore, the perimeter of the rectangle is $10 \ x$.
Perimeter of a rectangle $=2$(width $+$ length) $=2 \ (2 \ x \ + \ 3\ x)=2 \ (5\ x)=10\ x$
The perimeter of the rectangle is $90$. Then:
$10 \ x=90→x=9$

The correct answer is $0.01$
$0.35$ equals $35$M.
Then: $35$ M $=0.35→$
M $= \frac{0.35}{35}=0.01$

The correct answer is $40$
The length of the rectangle is $16$.
Then, its width is $4$.
$16 \ ÷ \ 4 = 4$
Perimeter of a rectangle $= 2 \ ×$ width $+ \ 2\ ×$ length $=2 \ × \ 4 \ + \ 2 \ × \ 16=$
$8 \ + \ 32=40$

The correct answer is $24$
If $x∎y=4 \ x \ + \ y \ - \ 3$, Then:
$3∎15=4(3) \ + \ 15 \ -\ 3=12 \ + \ 15 \ - \ 3=24$

The correct answer is $6 \ x \ +\ 17$
$z=2 \ x \ + \ 5$, then:
$3 \ z=3(2 \ x \ + \ 5)=6 \ x \ + \ 15$
$3 \ z \ + \ 2=6 \ x \ +\ 15 \ + \ 2= 6 \ x \ +\ 17$

The correct answer is $25$
$\frac{1}{8} =0.125→$ C $=5$
$\frac{1}{20}=0.05→$ D $=5→$ C $\times$ D $=5 \ ×\ 5=25$

The correct answer is $x \ × \ 4$
$36=x \ × \ 4→$
$x=36 \ ÷ \ 4=9$
$x$ equals to $9$.
Let’s review the options provided:
A. $x \ +\ 3→ 9 \ +\ 4=13$                         $36$ is not divisible by $13$.
B. $2 \ x \ + \ 10→2 \ ×\ 9 \ + \ 10=28$         $36$ is not divisible by $28$.
C. $x \ - \ 16→9 \ -\ 16=7$                       $36$ is not divisible by $7$.
D. $x \ × \ 4→9 \ × \ 4=36$                        $36$ is divisible by $36$.
E. $x \ + \ 1→9 \ +\ 1=10$                         $36$ is not divisible by $10$.

The correct answer is $12$
The area of the floor is:
$4$ cm $\times \ 18$ cm $=72$ cm
The number is tiles needed $= 72\div 6 = 12$

The correct answer is $- \ 14$
Use cross product to solve for $x$.
$\frac{x}{x \ - \ 4}= \frac{2}{3}→$
$3 \ × \ x=2 \ × \ (x \ - \ 4)→$
$3 \ x=2 \ x \ - \ 8=  - \ 8→$
$x \ - \ 6= - \ 8\ - \ 6=  - \ 14$

The correct answer is $\frac{1}{9}$
Number of biology book:
$20$, total number of books;
$20 \ +\ 85 \ + \ 75=180$
the ratio of the number of biology books to the total number of books is:
$\frac{20}{180}=\frac{1}{9}$

The correct answer is $$\ 675$
Let $x$ be all expenses, then:
$\frac{20}{100} \ x=$\ 500 →$
$x=\frac{100 \ × \ $\ 500}{20}=$\ 2500$
He spent for his rent:
$\frac{27}{100} \ × \ $\ 2500=$\ 675$

The correct answer is $0.2 \ x \ +\ 5,000$
$x$ is the number of all sales profit and $2\%$ of it is:
$2\% \ × \ x=0.02 \ x$
Employee’s revenue:
$0.2 \ x \ +\ 5,000$

The correct answer is $1,650$
$4,000 \ + \ A \ - \ 250=5,400→$
$4,000 \ +\ A=5,400 \ + \ 250 \ =5,650→$
$A=5,650 \ - \ 4,000=1,650$

The correct answer is $\frac{1}{4}$
$4 \ ×\ M\ + \ 6=7→$
$4 \ × \ M=7 \ -\ 6=1→$
$M=\frac{1}{4}$

The correct answer is $5$
The angles on a straight line add up to $180$ degrees. Then:
$x \ +\ 55 \ + \ y \ + \ 2 \ x \ +\ y=180$
Then: $3 \ x \ + \ 2 \ y=180 \ -\ 55→$
$3(45) \ + \ 2 \ y=125→$
$2 \ y=135 \ -\ 125=10→$
$y=5$

The correct answer is $98$
The ratio of lions to tigers is $6$ to $3$ at the zoo.
Therefore, total number of lions and tigers must be divisible by $9$.
$6 \ + \ 3=9$
From the numbers provided, only $98$ is not divisible by $9$.

The correct answer is $0.524$
$\frac{52.4}{100}=0.524$

The correct answer is $33$
let $x$ be the number of gallons of water the container holds when it is full.
Then: $\frac{3}{21} \ x=4.5→$
$x=\frac{21 \ × \ 4.5}{3}=33$

The correct answer is Greater than $5$
If $x$ is greater than $15$, then $\frac{1}{3}$ of $x$ must be greater than:
$\frac{1}{3} \ × \ 15=5$.