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:
\(\frac{1}{3} \ × \ 15=5\).