Free Full Length SSAT Upper Level Math Practice Test

The correct answer is \(6\) tenths
Digit \(6\) is in the tenths place.

The correct answer is \(0.64\)
\(0.04 \ × \ 16.00=\frac{4}{100} \ × \ \frac{16}{1}=\frac{64}{100}=0.64\)

The correct answer is \(3\)
Number of packs needed equals to: \(\frac{12}{4} = 3\).
Then Mary must purchase \(3\) packs.

The correct answer is \(- \ 4\)
\(x \ - \ 8=- \ 12→\)
\(x=- \ 10 \ + \ 8→\)
\(x=- \ 2\), Then; \(x \ × \ 2=- \ 2 \ × \ 2=- \ 4\)

The correct answer is \(9\) miles per hour
His average speed was: \(\frac{4.5}{0.5}=9\) miles per hour

The correct answer is approximately \(66\) hours
The time it takes to drive from city A to city B is:
\(\frac{3600}{54}=66.66\)

The correct answer is \(28\%\)
Number of males in the classroom is:
\(50 \ - \ 36=14\)
Then, the percentage of males in the classroom is:
\(\frac{14}{50} \ × \ 100=0.28 \ × \ 100=28\%\)

The correct answer is \(x \ - \ 40\).
The amount of flour is: \(x \ - \ 40\)

The correct answer is \(63\)
The perimeter of the quadrilateral is:
\(5 \ + \ 22 \ + \ 8 \ + \ 28=63\)

The correct answer is \(100\)
Let \(x\) be the fourth quarter rate, then:
\(\frac{90 \ + \ 82 \ + \ 80 \ + \ x}{4}=88\)
Multiply both sides of the above equation by \(4\). Then:
\(4 \ × \ (\frac{90 \ + \ 82 \ + \ 80 \ + \ x}{4})=4 \ × \ 88→\)
\(90 \ + \ 82 \ + \ 80 \ + \ x=352→\)
\(252 \ + \ x=352→\)
\(x=352 \ - \ 252=100\)

The correct answer is \($\ 28.08\)
For one person the total cost is: \($\ 9.36\)
Therefore, for three persons, the total cost is:
\(3 \ × \ $\ 9.36=$\ 28.08\)

The correct answer is \(\frac{1}{6}\)
The equation of a line in slope intercept form is:
\(y=m \ x \ + \ b\)
Solve for \(y\).
\(6 \ x \ + \ y=10 ⇒\)
\(y=- \ 6 \ x \ + \ 10\)
\(y=- \ 6 \ x \ + \ 10\)
The slope of this line is \(- \ 6\).
The slope of the line perpendicular to this line is:
\(m_{1} \ × \ m_{2} = - \ 1 ⇒\)
\(- \ 6 \ × \ m_{2} = - \ 1 ⇒\)
\(m_{2} = \frac{1}{6}\)

The correct answer is \(20\)
Let \(x\) be the number.
Write the equation and solve for \(x\).
\(\frac{2}{3} \ × \ 15= \frac{1}{2} \ x →\)
\(\frac{2 \ × \ 15}{3}= \frac{1 \ x}{2}\) , use cross multiplication to solve for \(x\).
\(2 \ × \ 30=1 \ x \ × \ 3 ⇒\)
\(60=3 \ x ⇒ x=20\)

The correct answer is \(72,000\)
Three times of \(32,000\) is \(96,000\).
One fourth of them cancelled their tickets.
One fourth of \(96,000\) equals \(24,000 \ (\frac{1}{4} \ × \ 96000 = 24000)\).
\(72,000 \ (96000 \ – \ 24000 = 72000)\) fans are attending this week

The correct answer is \(136\) miles
Use the information provided in the question to draw the shape.
Use Pythagorean Theorem: \(a^2 \ + \ b^2 = c^2\)
\(80^2 \ + \ 110^2 =c^2 ⇒\)
\(6400 \ + \ 12100 = c^2 ⇒\)
\(18500 = c^2 ⇒\)
\(c\cong136\) miles

The correct answer is \(0.97\)
Ratio of women to men in city A: \(\frac{570}{600}=0.95\)
Ratio of women to men in city B: \(\frac{291}{300}=0.97\)
Ratio of women to men in city C: \(\frac{665}{700}=0.95\)
Ratio of women to men in city D: \(\frac{528}{550}=0.96\)
\(0.97\) is the maximum ratio of woman to man in the four cities.

The correct answer is \(1.05\)
Percentage of men in city A \(= \frac{600}{1170} \ × \ 100=51.28\% \)
Percentage of women in city C \(= \frac{665}{1365} \ × \ 100=48.72\% \)
Percentage of men in city A to percentage of women in city C \(= \frac{51.28}{48.72}=1.05\)

The correct answer is \(I \ > \ 3000 \ x \ + \ 21000\)
Let \(x\) be the number of years.
Therefore, \($\ 3,000\) per year equals \(3000 \ x\).
Starting from \($\ 21,000\) annual salary means you should add that amount to \(3000 \ x\).
Income more than that is:
\(I \ > \ 3000 \ x \ + \ 21000\)

The correct answer is \(\frac{4}{5} \ x\)
\(\frac{x}{1 \ + \ 4 }=\frac{y}{9 \ - \ 5}→\)
\(\frac{x}{5}=\frac{y}{4}→\)
\(5 \ y=4 \ x→\)
\(y=\frac{4}{5} \ x\)

The correct answer is \(132\)
Let the number of women should be added to city D be \(x\), then:
\(\frac{528 \ + \ x}{550}=1.2→\)
\(528 \ + \ x=550 \ × \ 1.2=660→\)
\(x=132\)

The correct answer is \(8 : 12\)
The average speed of Jason is:
\(240 \ ÷ \ 6= 40\) km
The average speed of Emily is:
\(120 \ ÷ \ 2 = 60\) km
Write the ratio and simplify.
\( 40: 60 ⇒ 8 : 12\)

The correct answer is \(30\) cm
The length of MN is equal to:
\(4 \ x \ + \ 6 \ x=10 \ x\)
Then:
\(10 \ x=50→\)
\(x=\frac{50}{10}=5\)
The length of ON is equal to:
\(6 \ x=5 \ × \ 6=30\) cm

The correct answer is \(108.3\%\)
Perimeter of rectangle A is equal to:
\(2 \ × \ (9 \ + \ 3)=2 \ × \ 12=24\)
Perimeter of rectangle B is equal to:
\(2 \ × \ (9 \ + \ 4)=2 \ × \ 13=26\)
Therefore:
\(\frac{26}{24} \ × \ 100=1.083 \ × \ 100=108.3\%\)

The correct answer is \(x^3 \ \sqrt[4]{x}\)
\(\sqrt[4]{x^{13}} = \sqrt[4]{x^{12} \ × \ x}=\)
\(\sqrt[4]{x^{12}} \ ×\ \sqrt[4]{x}=x^{\frac{12}{4}} \ × \ \sqrt[4]{x}=\)
\(x^3 \ \sqrt[4]{x}\)

The correct answer is \(899\)
Smallest \(3\)–digit number is \(100\), and biggest \(3\)–digit number is \(999\).
The difference is: \(899\)

The correct answer is \(899\)
Smallest \(3\)–digit number is \(100\), and biggest \(3\)–digit number is \(999\).
The difference is: \(899\)

The correct answer is \(3.5 \ + \ \frac{7}{2}\)
A. \(\frac{1}{2} \ × \ \frac{1}{3}=\frac{1}{6}\) is not equal to whole number
B. \(\frac{1}{2} \ + \ \frac{1}{3}=\frac{3 \ + \ 2}{6}=\frac{5}{6}\) is not equal to whole number
C. \(\frac{12}{9}=\frac{4}{3}=1.3\) is not equal to whole number
D. \(3.5 \ + \frac{2}{3} =\frac{7}{3}=2.33\) is not equal to whole number
E. \(3.5 \ + \ \frac{7}{2}=3.5 \ + \ 3.5=7\) is a whole number

The correct answer is \(15\%\)
The question is this: 530.40 is what percent of 624?
Use percent formula: Part = percent/100 × whole
\(530.40 = \frac{percent}{100} \ × \ 624 →\)
\(530.40 = \frac{percent \ × \ 624}{100} →\)
\(53040 =\) percent \(× \ 624\)
Then, Percent \(= \frac{53040}{624} = 85\)
\(530.40\) is \(85%\) of \(624\).
Therefore, the discount is: \(100\% \ – \ 85\% = 15\%\)

The correct answer is \(14\ \frac{7}{9}\)
\(4 \ \frac{2}{3} \ × \ 3 \ \frac{ 1}{6}=\frac{14}{3} \ × \ \frac{19}{6}=\frac{14 \ × \ 19}{3 \ × \ 6}=\frac{266}{18}=\frac{133}{9}=14 \ \frac{7}{9}\)

The correct answer is \(4.620\)
\(0.30 \ × \ 15.4=\frac{30}{100} \ × \ \frac{154}{10}=\frac{30 \ × \ 154}{100 \ × \ 10}=\frac{4620}{1000}=4.620\)

The correct answer is \(8\)
Let \(x\) be the number, then;
\(\frac{2}{3} \ x=14→\)
\(x=\frac{3 \ × \ 14}{2}=21\)
Therefore: \(\frac{2}{5} \ x=\frac{2}{5} \ × \ 21=8\)

The correct answer is \($\ 750\)
Use simple interest formula: I \(=\) prt (I \(=\) interest, p \(=\) principal, r \(=\) rate, t \(=\) time)
I \(=(15000) \ (0.025) \ (2)=$\ 750\)

The correct answer is \(4\)
Number of boxes equal to:
\(\frac{144}{36}=\frac{16}{4}=4\)

The correct answer is \(10\) hours
Use distance formula: Distance \(=\) Rate \(×\) time \(⇒ 500 = 50 \ ×\) T, divide both sides by \(50\).
\(\frac{500}{50} =\) T \(⇒\) T \(= 10\) hours.
Change hours to minutes for the decimal part.
\(10\) hours \(= 10 \ × \ 60 = 600\) minutes

The correct answer is \(135\) degrees
The angle \(x\) and \(45\) are complementary angles.
Therefore: \(x \ + \ 45=180, 180^° \ - \ 45^°=135^°\)

The correct answer is \(7.5\) feet
Use formula of rectangle prism volume.
V \(=\) (length) (width) (height) \(⇒ 1800 = (20) \ (12)\) (height)
\(⇒\) height \(= 1800\ ÷ \ 240= 7.5\) feet

The correct answer is \(2.28\) m
The rate of construction company \(=\frac{25 \ cm}{1 \ min}=25\) cm/min
Height of the wall after \(30\) min \(= \frac{25 \ cm}{1 \ min} \ × \ 30\) min \(=570\) cm
Let \(x\) be the height of wall, then \(\frac{2}{5} \ x=570\) cm\(→\)
\(x=\frac{2 \ × \ 570}{5}→\)
\(x=228\) cm \(=2.28\) m

The correct answer is \(4\)
Let’s review the choices provided:
A. \(12 \ - \ 2=10→\frac{10}{2}=5≠2\)
B. \(12 \ - \ 3=9→\frac{9}{3}=3≠2\)
C. \(12 \ - \ 4=8→\frac{8}{4}=2=2\)
D. \(12 \ - \ 6=6→\frac{6}{6}=1≠2\)
E. \(12 \ - \ 12=0→\frac{0}{12}=0≠2\)

The correct answer is \(150\)
The ratio of boys 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 \(3\).
\(400 \ ÷ \ 8 = 50 ⇒\)
\(50 \ × \ 3 = 150\)

The correct answer is \(125\)
\(5\) cubed is: \(5 \ × \ 5 \ × \ 5=25 \ × \ 5=125\)

The correct answer is \(30\) Km/h
Speed of car A is: \(\frac{400}{8}=50\) Km/h
Speed of car B is: \(\frac{400}{5}=80\) Km/h
\(→80 \ - \ 50=30\) Km/h

The correct answer is \(56\)
\(y = 3 \ a \ b \ + \ 2 \ b^2\), Plug in the values of \(a\) and \(b\) in the equation: \(a = 2\) and \(b = 4\)
\(y = 3 \ (2) \ (4) \ +\ 2 \ (4)^2= 24 \ + \ 2 \ (16) = 24 \ + \ 32 = 56\)

The correct answer is \(\frac{1}{3}, \frac{2}{5}, \frac{3}{7}, \frac{5}{6}\)
\(\frac{1}{3}\cong 0.33\)
\(\frac{2}{5} \cong 0.4\)
\(\frac{3}{7} \cong 0.42\)
\(\frac{5}{6}=0.83\)

The correct answer is \(11\)
\(\frac{(2 \ + \ 5)^2}{7} \ + \ 4=\frac{(7)^2}{7} \ +\ 4=\frac{49}{7} \ + \ 4=7 \ + \ 4=11\)

The correct answer is \(0.02 \ x \ + \ 6000\)
\(x\) is the number of all sales profit and \(2\%\) of it is:
\(2\%\ × \ x=0.02 \ x\)
Employee’s revenue: \(0.02 \ x \ + \ 6000\)

The correct answer is \(12 \ π\)
Use the formula of the area of circles.
Area \(= π \ r^2 ⇒\)
\(36 \ π = π \ r^2 ⇒\)
\(36 = r^2 ⇒ r = 6\)
Radius of the circle is \(6\).
Now, use the circumference formula:
Circumference \(= 2 \ π \ r = 2 \ π \ (6) = 12 \ π\)

The correct answer is \(18\)
Prime factorizing of \(36=2 \ × \ 2 \ × \ 3 \ × \ 3\)
Prime factorizing of \(54=2 \ × \ 3 \ × \ 3 \ × \ 3\)
GCF \(=2 \ × \ 3 \ × \ 3=18\)

The correct answer is \(25\)
\(\frac{2}{3}\) Of \(150=\frac{2}{3} \ × \ 150=100\)
\(\frac{1}{4}\) Of \(100 =\frac{1}{4} \ × \ 100=25\)

The correct answer is \(144\)
\(0.5 \ x=(0.2) \ × \ 20→\)
\(x=8→(x \ + \ 4)^2=\)
\((8 \ + \ 4)^2=\)
\((12)^2=144\)

The correct answer is \(36^\circ\)
The sum of all angles in a quadrilateral is \(360\) degrees.
Let \(x\) be the smallest angle in the quadrilateral. Then the angles are:
\(x, 2 \ x, 3 \ x, 4 \ x\)
\(x \ + \ 2 \ x \ + \ 3 \ x \ + \ 4 \ x=360→\)
\(10 \ x=360→x=36\)
The angles in the quadrilateral are: \(36^°, 72^°, 72^°\), and \(180^°\)
The smallest angle is \(36\) degrees.

The correct answer is \(40\)
Length of the rectangle is: \(\frac{2}{3} \ × \ 12=8\)
Perimeter of rectangle is: \(2 \ × \ (8 \ + \ 12)=40\)