Free Full Length SSAT Middle Level Mathematics Practice Test

The correct answer is $0.01$
$0.65$ equals $65$ M.
Then: $0.65=65$ M $→$
M $=\frac{0.65}{65}=0.01$

The correct answer is $7$ hours
Use distance formula:
Distance $=$ Rate $\times$ time $⇒$
$490 = 70 \ \times$ T, divide both sides by $70$.
$\frac{490}{ 70} =$ T $⇒$
T $= 7$ hours.

The correct answer is $$54$
Use simple interest formula:
I $=$ prt (I $=$ interest, p $=$ principal, r $=$ rate, t $=$ time)
t is for one year.
For $3$ months, t is $\frac{1}{4}$ or $0.25$
I $=(5,400) \ (0.04) \ (0.25)=$54$

The correct answer is $93.5$ D
To find the discount, multiply the number by
($100\% \ –$ rate of discount).
Therefore, for the first discount we get:
(D) ($100\% \ – \ 15\%$) = (D) $(0.85) = 0.85$ D
For increase of $10\%: \ (0.85$ D) $(100\% \ + \ 10\%) =$
$(0.85$ D) $(1.10) = 93.5$ D $=93.5$
$93.5\%$ of D

The correct answer is $20$
average $= \frac{sum \ of \ terms}{number \ of \ terms} ⇒$
$16 = \frac{11 \ + \ 14 \ + \ 19 \ + \ x}{4} ⇒$
$64 = 44 \ + \ x ⇒$
$x = 20$

The correct answer is $6$
Three times a certain number, increased by $18$, is equal to $36$.
Write an equation and solve.
$3 \ x \ + \ 18=36→$
$3 \ x=36 \ - \ 18=18→$
$x=\frac{18}{3}=6$

The correct answer is $N \ + \ 2$
Alex has $N$ toy cars.
John has $5$ more cars than Alex.
Therefore, Alex has $N \ + \ 5$ toy cars.
John gives Alex $3$ cars.
Now, Alex has $(N \ + \ 5 \ – \ 3) \ N \ + \ 2$ toy cars.

The correct answer is $520$ km
Add the first $5$ numbers.
$45 \ + \ 50 \ + \ 55 \ + \ 35 \ + \ 60 = 245$
To find the distance traveled in the next $5$ hours, multiply the average by number of hours.
Distance $=$ Average $\times$ Rate $= 55 \times 5 = 275$
Add both numbers.
$245 \ + \ 275 =520$ km

The correct answer is $27$
$\frac{x \ + \ 3}{6}=5→$
$x \ + \ 3=5 \ × \ 6=30→$
$x=30 \ - \ 3=27$

The correct answer is $108$
$20$ percent of a number is $120$.
Therefore, the number is $600$.
$0.20 \ x=120→$
$x=\frac{120}{0.20}=600$
$18$ percent of $600$ is $108$.
$0.18 \times 600=108$

The correct answer is $200\%$
Write the equation and solve for B:
$0.60$ A $=0.30$ B , divide both sides by $0.30$, then you will have $\frac{0.60}{0.30}$ A $=$ B, therefore:
B $= 2$ A, and B is $2$ times of A or it’s $200\%$ of A.

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 $$0.318$
One pound of cheese costs $$0.86$.
One pound $=16$ ounces
$16$ ounces of cheese costs $$0.86$.
Then, $1$ ounce of chees costs $(0.86 \ ÷ \ 16) \ $0.053$.
$6$ ounces of cheese costs $(6 \ × \ $0.053) \ $0.318$.

The correct answer is $13.5\%$
The question is this:
$450.40$ is what percent of $520$?
Use percent formula:
part $=\frac{ percent}{100} \ ×$ whole
$450.20 = \frac{percent}{100} \ × \ 520 ⇒$
$450.20 = \frac{percent \ ×\ 520}{100} ⇒$
$45020 =$ percent $× \ 520 ⇒$
percent $= \frac{45020}{520} = 86.5$
$450.20$ is $86.5\%$ of $520$.
Therefore, the discount is:
$100\% \ – \ 86.5\% = 13.5\%$

The correct answer is $30$
Let $x$ be the number.
Write the equation and solve for $x$.
$\frac{2}{3} \times 18= \frac{2}{5}$.
$x ⇒ \frac{2 \ × \ 18}{3}= \frac{2 \ x}{5}$
use cross multiplication to solve for $x$.
$5 \ × \ 36= 2 \ x \ × \ 3 ⇒$
$180=6 \ x ⇒ x=30$

The correct answer is $\frac{19}{20}$
If $15$ balls are removed from the bag at random, there will be five balls in the bag.
The probability of choosing a brown ball is $1$ out of $20$.
Therefore, the probability of not choosing a brown ball is $19$ out of $20$ and the probability of having not a brown ball after removing $19$ balls is the same.

The correct answer is $75\%$
The failing rate is $15$ out of $60 = \frac{15}{40}$
Change the fraction to percent:
$\frac{15}{60} \ × \ 100\%=25\%$
$25$ percent of students failed.
Therefore, $75$ percent of students passed the exam.

The correct answer is $8$
Let $x$ be the number.
Write the equation and solve for $x$.
$(40 \ – \ x) \ ÷ \ x = 4$, Multiply both sides by $x$.
$(40\ – \ x) = 4 \ x$, then add $x$ both sides.
$40 = 5 \ x$, now divide both sides by $5$.
$x = 8$

The correct answer is $0$
$N \ × \ \frac{2}{5} \ × \ 3=0$, then $N$ must be $0$. 

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

The correct answer is $9$
$4 \ x \ +\ 7=→43$
$4 \ x=43 \ - \ 7=36→$
$x=\frac{36}{4}=9$

The correct answer is $20$
Let $x$ be the number.
Write the equation and solve for $x$.
$30\%$ of $x=6⇒$
$0.30 \ x=6 ⇒$
$x=6 \ ÷ \ 0.30=20$

The correct answer is $I \ > \ 3000 \ x \ + \ 32000$
Let $x$ be the number of years.
Therefore, $$3,000$ per year equals $3000 \ x$.
starting from $$32,000$ annual salary means you should add that amount to $3000 \ x$.
Income more than that is:
$I \ > \ 3000 \ x \ + \ 32000$

The correct answer is $25\%$
$$\ 14$ is what percent of $$\ 56$?
$14 \ ÷ \ 56 = 0.25 = 25\%$

The correct answer is $13$
$\frac{z}{3} =3→$
$z=3 \ ×\ 3=9$
$z \ + \ 4=9 \ + \ 4=13$

The correct answer is $13$
$\frac{z}{3} =3→$
$z=3 \ ×\ 3=9$
$z \ + \ 4=9 \ + \ 4=13$

The correct answer is $143$
$\frac{x \ - \ 5}{6} \ + \ 5=28→$
$\frac{x \ - \ 5}{6}=28 \ - \ 5=23→$
$x \ - \ 5=23 \ × \ 6=138→$
$x=138 \ + \ 5=143$

The correct answer is $2.5$
The width of a rectangle is $4 \ x$ and its length is $6 \ x$.
Then, the perimeter of the rectangle is $20 \ x$.
Perimeter of a rectangle $= 2$ (width $+$ length) $=2 \ (4 \ x \ + \ 6 \ x)=20 \ x$
The perimeter of the rectangle is $50$. Then:
$20 \ x=50→x=2.5$

The correct answer is $x \ + \ 20$
John has $x$ dollars and he receives $$120$.
Therefore, he has $x \ + \ 120$.
He then buys a bicycle that costs $$100$.
Now, he has:
$x \ + \ 120 \ - \ 100= x \ + \ 20$

The correct answer is $$\ 500$
Use simple interest formula: I $=$ prt (I $=$ interest, p $=$ principal, r $=$ rate, t $=$ time)
I $= (4,000) \ (0.025) \ (5)=500$

The correct answer is $27\%$
David needs an $45\%$ average to pass for five exams.
Therefore, the sum of $4$ exams must be at least $4 \ ×\ 65 = 260$
The sum of $4$ exams is:
$62 \ + \ 70 \ + \ 75 \ + \ 80 = 287$.
The minimum score David can earn on his fifth and final test to pass is:
$287 \ – \ 260 = 27$

The correct answer is $8$ hours
The distance between Alex and Jack is $6$ miles.
Alex running at $4.5$ miles per hour and Jack is running at the speed of $6$ miles per hour.
Therefore, every hour the distance is $1.5$ miles less.
$12 \ ÷\ 1.5 = 8$

The correct answer is $18$
The formula for the area of the circle is:
A $=π \ r^2$
The area of the circle is $81 \ π$. Therefore:
A $=π \ r^2 ⇒$
$81 \ π = π \ r^2$
Divide both sides by $π$:
$81 = r^2 ⇒ r=9$
Diameter of a circle is $2 \times$ radius.
Then: Diameter $= 2 \ ×\ 9 = 18$

The correct answer is $15$
$3 \ ÷ \ \frac{1}{5} = 15$

The correct answer is $1$
$(8 \ - \ 6)\ × \ 4=8 \ + \ \Box$
Then:
$2 \ × \ 4=8 \ + \ \Box, \ 8 =8 \ +\ \Box$, then:
$\Box = 1$

The correct answer is $10 \ x \ + \ 6 \ y$
There are $y$ tables that can each seat $6$ people and there are $x$ tables that can each seat $10$ people.
Therefore, $6 \ y \ + \ 10 \ x$ people can be seated in the classroom.

The correct answer is $7$ 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) $= 2 \ (2 \ x \ + \ x)=42 ⇒$
$6 \ x=42 ⇒$
$x=7$
Length of the rectangle is $7$ meters.

The correct answer is $76.40$
average (mean) $= \frac{sum \ of \ terms}{number \ of \ terms} ⇒$
$77 = \frac{sum \ of\ terms}{42} ⇒$
sum $= 77 \ × \ 42 = 3234$
The difference of $92$ and $68$ is $24$.
Therefore, $24$ should be subtracted from the sum.
$3234 \ – \ 25 = 3209$
mean $= \frac{sum \ of \ terms}{number \ of \ terms} ⇒$
mean $= \frac{3209}{42} = 76.40$

The correct answer is $(250) \ (0.80) \ (0.80)$
To find the discount, multiply the number by ($100\% \ –$ rate of discount).
Therefore, for the first discount we get:
$(250) (100\% \ – \ 10\%) = (250) \ (0.80) = 200$
For the next $10\%$ discount: $(250) \ (0.80) \ (0.80)$

The correct answer is $40$
average $= \frac{sum \ of \ terms}{number \ of \ terms} ⇒$
(average of $8$ numbers) $16 = \frac{sum \ of \ numbers }{8} ⇒$
sum of $8$ numbers is:
$16 \ × \ 8 = 128$
(average of $6$ numbers) $8 = \frac{sum \ of \ numbers}{6} ⇒$
sum of $6$ numbers is $8 \ × \ 6 = 48$
sum of $8$ numbers $–$ sum of $6$ numbers $=$ sum of $2$ numbers
$128 \ – \ 48 = 80$ average of $2$ numbers $= \frac{80}{2} = 40$

The correct answer is $\frac{1}{5}$
The deck contains $13$ Hearts.
Then, the probability of choosing a Hearts is $\frac{13}{65}=\frac{1}{5}$

The correct answer is $\frac{1}{10}$
$4,500$ out of $45,000$ equals to $\frac{4500}{45000} = \frac{45}{450} = \frac{1}{10}$

The correct answer is $20$
$x \ + \ 3=6→$
$x=6 \ - \ 3=3$
$2 \ y \ -\ 2=10→$
$2 \ y=8→$
$y=4$
$x \ y \ +\ 8=3 \ × \ 4 \ + \ 8=20$

The correct answer is $\frac{1}{4}$
From the options provided, only $\frac{1}{4}$ is greater than $\frac{1}{6}$.

The correct answer is $19$
$x=7$, then:
$2 \ x \ + \ 5=2 \ ×\ 7 \ +\ 5=14 \ + \ 5=19$

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 $121$ cm$^2$
The perimeter of the trapezoid is $24$.
Therefore, the missing side (height) is:
$= 49 \ – \ 10 \ – \ 16 \ – \ 12 = 11$
Area of a trapezoid:
A $= \frac{1}{2} \ h \ (b1 \ + \ b2) =$
$\frac{1}{2} \ (11) \ (10 \ + \ 12) = 121$ cm $^2$

The correct answer is $26\%$
the population is increased by $10\%$ and $15\%$.
$10\%$ increase changes the population to $110\%$ of original population.
For the second increase, multiply the result by $115\%$.
$(1.10) \ × \ (1.15) = 1.26 = 126\%$
$26$ percent of the population is increased after two years.

The correct answer is $50$
Plug in $104$ for F and then solve for C.
C $= \frac{4}{8}$ (F $– \ 30) ⇒$
C $= \frac{4}{8} \ (110 \ –\ 30) ⇒$
C $= \frac{5}{8} \ (80) = 50$

The correct answer is $384$ cm$^3$
If the length of the box is $24$, then the width of the box is one third of it, $8$, and the height of the box is $2$ (one fourth of the width).
The volume of the box is:
Volume of a box $=$ (length) $×$ (wdth) $×$ (height)
$= (24) \ × \ (8) \ × \ (2) = 384$ cm$^3$

The correct answer is $15$
$2 \ x \ + \ 10=40→$
$2\ x=40 \ - \ 10=30→$
$x=\frac{30}{2}=15$