 ## Full Length SSAT Upper Level Math Practice Test

If you want to prepare for the SSAT Upper Level Math Practice Test? It’s time to taking a Full-length SSAT Upper Level Math Practice Test. It is the best way to simulate test day. To challenge your skills and simulate the full length SSAT Upper Level Math Practice Test day experience, score your tests using the answer keys.

### The Most Comprehensive SSAT Upper Level Math Preparation Bundle

$76.99$36.99
52% Off*

Includes SSAT Upper Level Math Prep Books, Workbooks, and Practice Tests

## SSAT Upper Level Math Practice Test 3

Section 1

25 questions
Total time for this section: 30 Minutes
You may NOT use a calculator for this test.

1- If $$\frac{30}{A} \ + \ 3=9$$, then $$30 \ + \ A=$$ ?
(A) $$25$$
(B) $$30$$
(C) $$15$$
(D) $$35$$
(E) $$20$$
2- A shaft rotates $$450$$ times in $$12$$ seconds. How many times does it rotate in $$16$$ seconds?
(A) $$600$$
(B) $$100$$
(C) $$250$$
(D) $$550$$
(E) $$300$$
3- How many tiles of $$5$$ cm$$^2$$ is needed to cover a floor of dimension $$4$$ cm by $$20$$ cm?
(A) $$20$$
(B) $$16$$
(C) $$26$$
(D) $$35$$
(E) $$8$$
4- What is the value of the sum of the tens and thousandths in number $$3,428.698712$$?
(A) $$8$$
(B) $$12$$
(C) $$9$$
(D) $$14$$
(E) $$10$$
5- Which of the following statements is correct, according to the graph below? (A) Number of books sold in April is was $$\frac{1}{2}$$the number of books in sold in July.
(B) Number of books sold in July was less than half the number of books sold in May.
(C) Number of books sold in June was twice the number of books sold in April.
(D) Number of books sold in July was equal to the number of books sold in April plus the number of books sold in June.
(E) More books were sold in April than in July.
6- A school wants to give each of its $$24$$ top students a football ball. If the balls are in boxes of four, how many boxes of balls they need to purchase?
(A) $$7$$
(B) $$10$$
(C) $$15$$
(D) $$3$$
(E) $$6$$
7- $$15.246 \ ÷ \ 0.006$$?
(A) $$2,541$$
(B) $$2.541$$
(C) $$25.410$$
(D) $$25410$$
(E) $$250.410$$
8- Alex earns $$\ 460$$ for his first $$20$$ hours of work in a week and is then paid $$2.5$$ times his regular hourly rate for any additional hours. This week, Alex needs $$\ 630$$ to pay his rent, bills and other expenses. How many hours must he work to make enough money in this week?
(A) $$30$$
(B) $$25$$
(C) $$23$$
(D) $$40$$
(E) $$54$$
9- If $$120\$$% of a number is $$60$$, then what is the $$70\$$% of that number?
(A) $$35$$
(B) $$50$$
(C) $$65$$
(D) $$25$$
(E) $$70$$
10- $$\frac {1 \frac{{5}}{{2}} \ + \frac {3}{5}}{{4 \frac {3}{2}} \ - \frac {15}{4}}$$is approximately equal to.
(A) $$4.68$$
(B) $$2.54$$
(C) $$6.35$$
(D) $$3.34$$
(E) $$5.25$$
11-

The average weight of $$12$$ girls in a class is $$62$$ kg and the average weight of $$24$$ boys in the same class is $$74$$ kg. What is the average weight of all the $$36$$ students in that class?

(A) $$75$$
(B) $$70.5$$
(C) $$70$$
(D) $$60.75$$
(E) $$65$$
12- If $$2 \ ≤ \ x \ < \ 6$$, what is the minimum value of the following expression?
$$2 \ x \ + \ 3$$
(A) $$8$$
(B) $$2$$
(C) $$4$$
(D) $$7$$
(E) $$5$$
13- What is the answer of $$8.5 \ ÷ \ 0.20$$?
(A) $$40$$
(B) $$42.5$$
(C) $$400$$
(D) $$\frac{1}{42}$$
(E) $$\frac{1}{40}$$
14- If $$x \ ∎ \ y=\sqrt{x^2 \ + \ y}$$, what is the value of $$4 \ ∎ \ 9$$?
(A) $$4$$
(B) $$7$$
(C) $$6$$
(D) $$5$$
(E) $$\sqrt{5}$$
15- There are four equal tanks of water. If $$\frac{1}{2}$$ of a tank contains $$250$$ liters of water, what is the capacity of the four tanks of water together?
(A) $$2000$$
(B) $$202$$
(C) $$500$$
(D) $$50$$
(E) $$1000$$
16- Two-kilograms apple and three-kilograms orange cost $$\ 36.4$$. If one-kilogram apple costs $$\ 3.2$$ how much does one-kilogram orange cost?
(A) $$\ 10$$
(B) $$\ 8$$
(C) $$\ 6.5$$
(D) $$\ 10.5$$
(E) $$\ 5$$
17- Jenny  and Mary can finish a job together in $$120$$ minutes. If Jenny can do the job by herself in $$6$$ hours, how many minutes does it take Mary to finish the job?
(A) $$138$$ minutes
(B) $$210$$ minutes
(C) $$150$$ minutes
(D) $$180$$ minutes
(E) $$100$$ minutes
18- What is the value of $$x$$ in the following figure? (A) $$130$$
(B) $$135$$
(C) $$145$$
(D) $$110$$
(E) $$165$$
19- The sum of six different negative integers is $$- \ 65$$. If the smallest of these integers is $$- \ 12$$, what is the largest possible value of one of the other five integers?
(A) $$- \ 5$$
(B) $$- \ 10$$
(C) $$- \ 4$$
(D) $$- \ 15$$
(E) $$- \ 7$$
20- John’s current age is $$42$$ years, and Ann’s current age is $$6$$ years old. In how many years John’s age will be $$4$$ times Ann’s age?
(A) $$4$$
(B) $$6$$
(C) $$8$$
(D) $$10$$
(E) $$14$$
21- A football team won exactly $$60\%$$ of the games it played during last session. Which of the following could be the total number of games the team played last season?
(A) $$26$$
(B) $$32$$
(C) $$40$$
(D) $$41$$
(E) $$16$$
22- What is the slope of a line that is perpendicular to the line $$6 \ x \ - \ 2 \ y=16$$ ?
(A) $$4$$
(B) $$8$$
(C) $$- \ \frac{1}{3}$$
(D) $$- \ \frac{1}{2}$$
(E) $$12$$
23- The Jack Library is ordering some bookshelves. If is the number of bookshelf the library wants to order, which each costs $$\ 90$$ and there is a one-time delivery charge of $$\ 750$$, which of the following represents the total cost, in dollar, per bookshelf?
(A) $$90 \ x \ + \ 750$$
(B) $$90 \ + \ 750 \ x$$
(C) $$\frac{90 \ x \ + \ 750}{x}$$
(D) $$\frac{90 \ x \ + \ 750}{90}$$
(E) $$\frac{90 \ x \ - \ 750}{x}$$
24- The width of a box is one fourth of its length. The height of the box is one third of its width. If the length of the box is $$24$$ cm, what is the volume of the box?
(A) $$288$$ cm$$^3$$
(B) $$54$$ cm$$^3$$
(C) $$650$$ cm$$^3$$
(D) $$420$$ cm$$^3$$
(E) $$520$$ cm$$^3$$
25- A cruise line ship left Port A and traveled $$60$$ miles due west and then $$120$$ miles due north. At this point, what is the shortest distance from the cruise to port A?
(A) $$50$$ miles
(B) $$250$$ miles
(C) $$42$$ miles
(D) $$150$$ miles
(E) $$230$$ miles

SSAT Upper Level Math

Test 3   Section 2

25 questions
Total time for this section: 30 Minutes
You may NOT use a calculator for this test.

26- There are $$11$$ marbles in the bag A and $$13$$ marbles in the bag B. If the sum of the marbles in both bags will be shared equally between two children, how many marbles bag A has less than the marbles that each child will receive?
(A) $$1$$
(B) $$5$$
(C) $$6$$
(D) $$2$$
(E) $$4$$
27- When number $$84,752$$ is divided by $$220$$, the result is closest to?
(A) $$300$$
(B) $$350$$
(C) $$385$$
(D) $$420$$
(E) $$120$$
28- To paint a wall with the area of $$36$$m$$^2$$, how many liters of paint do we need if each liter of paint is enough to paint a wall with dimension of $$45$$ cm$$× \ 100$$ cm?
(A) $$450$$
(B) $$100$$
(C) $$80$$
(D) $$240$$
(E) $$180$$
29- If the perimeter of the following figure be $$24$$, what is the value of $$x$$? (A) $$2$$
(B) $$3$$
(C) $$6$$
(D) $$9$$
(E) $$12$$
30- If John’s mark is k more than Will, and Johns mark is $$14$$, which of the following can be Will’s mark?
(A) $$14 \ - \ k$$
(B) $$14 \ + \ k$$
(C) $$14 \ k$$
(D) $$k \ + 4$$
(E) $$k \ - \ 4$$

### SSAT Upper Level Math for Beginners

$24.99$14.99
40% Off*

The Ultimate Step by Step Guide to Preparing for the SSAT Upper Level Math Test

31- A driver rests one hour and $$8$$ minutes for every $$6$$ hours driving. How many minutes will he rest if he drives $$24$$ hours?
(A) $$4$$ hours and $$32$$ minutes
(B) $$5$$ hours and $$25$$ minutes
(C) $$2$$ hours and $$40$$ minutes
(D) $$6$$ hours and $$40$$ minutes
(E) $$4$$ hours
32- The price of a sofa is decreased by $$25\%$$ to $$\ 450$$. What was its original price?
(A) $$\ 600$$
(B) $$\ 250$$
(C) $$\ 475$$
(D) $$\ 360$$
(E) $$\ 700$$
33- Which of the following expression is not equal to $$6$$?
(A) $$12 \ × \ \frac{1}{2}$$
(B) $$24 \ × \ \frac{1}{4}$$
(C) $$4 \ × \ \frac{3}{2}$$
(D) $$6 \ × \ \frac{5}{5}$$
(E) $$6 \ × \ \frac{1}{6}$$
34- A library has $$900$$ books that include Mathematics, Physics, Chemistry, English and History.
What is the product of the number of Mathematics and number of English books? (A) $$56400$$
(B) $$40500$$
(C) $$45000$$
(D) $$35200$$
(E) $$36000$$
35- A library has $$900$$ books that include Mathematics, Physics, Chemistry, English and History.
What are the values of angle $$α$$ and $$β$$ respectively? (A) $$108^\circ, 54^\circ$$
(B) $$45^\circ, 160^\circ$$
(C) $$45^\circ, 130^\circ$$
(D) $$120^\circ, 130^\circ$$
(E) $$65^\circ, 80^\circ$$
36- If $$6 \ y \ + \ 6 \ < \ 24$$, then $$y$$ could be equal to?
(A) $$4$$
(B) $$1.5$$
(C) $$9$$
(D) $$5.5$$
(E) $$7$$
37- Find the perimeter of following shape. (A) $$30$$
(B) $$10$$
(C) $$24$$
(D) $$6$$
(E) $$14$$
38- If the area of the following rectangular ABCD is $$90$$, and E is the midpoint of AB, what is the area of the shaded part? (A) $$45$$
(B) $$30$$
(C) $$15$$
(D) $$12$$
(E) $$50$$
39- If $$2 \ x \ + \ 3 \ y=36$$ and $$x \ - \ z=12$$, what is the value of $$x$$?
(A) It cannot be determined from the information given
(B) $$2$$
(C) $$10$$
(D) $$14$$
(E) $$6$$
40- The capacity of a red box is $$20\%$$ bigger than the capacity of a blue box. If the red box can hold $$30$$ equal sized books, how many of the same books can the blue box hold?
(A) $$32$$
(B) $$12$$
(C) $$25$$
(D) $$45$$
(E) $$8$$
41- There are $$70.5$$ liters of gas in a car fuel tank. In the first week and second week of April, the car uses $$4.65$$ and $$35.7$$ liters of gas respectively. If the car was park in the third week of April and $$10.31$$ liters of gas will be added to the fuel tank, how many liters of gas are in the fuel tank of the car?
(A) $$40.46$$ liters
(B) $$50.25$$ liters
(C) $$25$$ liters
(D) $$58$$ liters
(E) $$32$$ liters
42- What is the average of circumference of figure A and area of figure B?$$(π=3)$$ (A) $$32$$
(B) $$24$$
(C) $$34$$
(D) $$60$$
(E) $$53$$
43- Which of the following could be the value of x if $$\frac{4}{7} \ + \ x \ > \ 3$$?
(A) $$\frac{1}{2}$$
(B) $$3$$
(C) $$\frac{4}{3}$$
(D) $$\frac{4}{6}$$
(E) $$\frac{2}{5}$$
44- If $$a \ × \ b$$ is divisible by $$3$$, which of the following expression must also be divisible by $$3$$?
(A) $$0$$
(B) $$3 \ a \ - \ b$$
(C) $$a \ - \ 3 \ b$$
(D) $$\frac{a}{ b}$$
(E) $$4 \times \ a \times \ b$$
45- In the following figure, point Q lies on line n, what is the value of y if $$x = 25$$? (A) $$10$$
(B) $$25$$
(C) $$30$$
(D) $$35$$
(E) $$40$$
46- A number is chosen at random from $$1$$ to $$20$$. Find the probability of not selecting a composite number. (A composite number is a number that is divisible by itself, $$1$$ and at least one other whole number)
(A) $$1$$
(B) $$0$$
(C) $$\frac{8}{20}$$
(D) $$\frac{5}{20}$$
(E) $$\frac{5}{4}$$
47- If a gas tank can hold $$20$$ gallons, how many gallons does it contain when it is $$\frac{3}{4}$$full?
(A) $$10$$
(B) $$8$$
(C) $$15.5$$
(D) $$150$$
(E) $$15$$
48- $$855 \ ÷ \ 6=$$?
(A) $$\frac{800}{6} \ + \ \frac{50}{6} \ + \ \frac{5}{6}$$
(B) $$\frac{800}{6} \times \ \frac{50}{6} \times \ \frac{5}{6}$$
(C) $$\frac{800}{6} \ - \frac{50}{6} \ - \ \frac{5}{6}$$
(D) $$800 \div \frac{50}{6} \div \ \frac{5}{6}$$
(E) $$800 \times \frac{50}{6} \times \ \frac{5}{6}$$
49- What is the missing term in the given sequence?
$$1 \ , \ 2 \ , \ 4 \ , \ 7 \ , \ 11 \ , \ 16 \ , \ 22 \ , \ ..... \ , \ 37$$
(A) $$32$$
(B) $$30$$
(C) $$29$$
(D) $$27$$
(E) $$31$$
50- $$450 \ - \ 5 \frac{4}{14}=$$?
(A) $$444 \frac{5}{7}$$
(B) $$444 \frac{8}{7}$$
(C) $$446\frac{8}{14}$$
(D) $$446\frac{1}{5}$$
(E) $$446 \frac{1}{14}$$
 1- Choice D is correct The correct answer is $$35$$$$\frac{30}{A} \ + \ 3=9 → \frac{30}{A}=9 \ - \ 3=6$$→$$30=6 \ A → A=\frac{30}{6}=5$$$$30 \ + \ A=30 \ + \ 5=35$$ 2- Choice A is correct The correct answer is $$600$$Number of rotates in $$16$$ second equals to: $$\frac{450 \ × \ 16}{12}=600$$ 3- Choice B is correct The correct answer is $$16$$The area of the floor is:$$4$$ cm $$× \ 20$$ cm $$= 80$$ cm$$^2$$The number of tiles needed $$= 80 \ ÷ \ 5 = 16$$ 4- Choice C is correct The correct answer is $$9$$The digit in tens place is $$2$$.The digit in the thousandths place is $$7$$.Therefore;$$2 \ + \ 7=9$$ 5- Choice A is correct 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:$$380 \ < \ 760$$ 6- Choice E is correct The correct answer is $$6$$Number of packs equal to: $$\frac{24}{4}=6$$Therefore, the school must purchase $$6$$ packs. 7- Choice A is correct The correct answer is $$2,541$$$$15.246 \ ÷ \ 0.006=\frac{\frac{15,246}{1,000}}{{\frac{6}{1,000}}}=\frac{15,246}{6}=2,541$$ 8- Choice C is correct 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: $$20 \ + \ 3=23$$ 9- Choice A is correct 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:$$0.7 \ × \ 50=35$$ 10- Choice A is correct The correct answer is $$4.68$$$$\frac{1 \ \frac{5}{2} \ + \ \frac{3}{5}}{4 \ \frac{3}{2} \ - \ \frac{15}{4}} = \frac{\frac{7}{2} \ + \ \frac{3}{5}}{\frac{11}{2} \ - \ \frac{15}{4}} = \frac{\frac{35 \ + \ 6}{10}}{\frac{22 \ - \ 15}{4}}$$$$\frac{\frac{41}{10}}{\frac{7}{4}} = \frac{41 \times 2}{7 \times 5} = \frac{164}{35} \cong 4.68$$ 11- Choice C is correct The correct answer is $$70$$Average $$=\frac{sum \ of \ terms }{number \ of \ terms}$$The sum of the weight of all girls is: $$12 \ × \ 62 = 744$$ kgThe sum of the weight of all boys is: $$24 \ × \ 74 = 1776$$ kgThe sum of the weight of all students is: $$744 \ + \ 1776 =2520$$ kgThe average weight of the $$36$$ students: $$\frac{2520}{36}=70$$ 12- Choice D is correct 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 $$7$$ 13- Choice B is correct The correct answer is $$42.5$$$$8.5 \ ÷ \ 0.20=\frac{8.5}{0.20}=\frac{\frac{{85}}{10}}{\frac{20}{100}}=\frac{85 \ × \ 100}{20 \ × \ 10}=\frac{85}{20} \ × \frac{100}{10}=4.25 \ × \ 10=42.5$$ 14- Choice D is correct The correct answer is $$5$$$$4∎9=\sqrt{4^2 \ + \ 9}=\sqrt{16 \ + \ 9}=\sqrt{25}=5$$ 15- Choice A is correct The correct answer is $$2000$$Let $$x$$ be the capacity of one tank. Then, $$\frac{1}{2} x=250→ x=250 \ × \ 2=500$$ LitersThe amount of water in four tanks is equal to: $$4 \ × \ 500=2000$$ Liters 16- Choice A is correct The correct answer is $$\ 10$$Let $$x$$ be the cost of one-kilogram orange, then:$$3 \ x \ + \ (2 \ × \ 3.2)=36.4→$$$$3 \ x \ + \ 6.4=36.4→$$$$3 \ x=36.4 \ - \ 6.4→$$$$3 \ x=30→$$$$x=\frac{30}{3}=\ 10$$ 17- Choice A is correct The correct answer is $$138$$ minutesLet $$b$$ 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 18- Choice C is correct The correct answer is $$145$$ degreesAll angles in a triangle sum up to $$180$$ degrees. Then:$$x=35 \ + \ 110=145$$ 19- Choice D is correct 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: $$- \ 65=(- \ 12) \ + \ (- \ 11) \ + \ (- \ 10) \ + \ (- \ 9) \ + \ (- \ 8) \ + \ x→$$$$- \ 65=- \ 50 \ + \ x→$$$$x=- \ 65 \ + \ 50=- \ 15$$ 20- Choice B is correct 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 $$20$$. 21- Choice C is correct 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 $$16=0.60 \ × \ 16=9.6$$ 22- Choice C is correct 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:$$m_{1} \ × \ m_{2} = - \ 1 ⇒ 3 \ × \ m_{2} = - \ 1 ⇒$$$$m_{2} = - \ \frac{1}{3}$$ 23- Choice C is correct 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: $$\frac{Total \ cost}{number \ of \ items}=\frac{90 \ x \ + \ 750}{x}$$ 24- Choice A is correct 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$$^3$$ 25- Choice C is correct The correct answer is $$42$$ milesUse the information provided in the question to draw the shape.Use Pythagorean Theorem:$$a^2 \ + \ b^2 = c^2$$$$60^2 \ + \ 120^2 = c^2 ⇒$$$$3600 \ + \ 14400 = c^2 ⇒$$$$18000 = c^2 ⇒$$$$c =42$$ 25- Choice C is correct The correct answer is $$42$$ milesUse the information provided in the question to draw the shape.Use Pythagorean Theorem:$$a^2 \ + \ b^2 = c^2$$$$60^2 \ + \ 120^2 = c^2 ⇒$$$$3600 \ + \ 14400 = c^2 ⇒$$$$18000 = c^2 ⇒$$$$c =42$$ 26- Choice A is correct The correct answer is $$1$$$$\frac{13 \ + \ 11}{2}=\frac{24}{2}=12$$ Then:$$12 \ - \ 11=1$$ 27- Choice C is correct The correct answer is $$385$$$$\frac{84752}{202} \cong 385.2363 \cong 385$$ 28- Choice C is correct The correct answer is $$80$$ litersThe 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 29- Choice C is correct 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: $$2 \ +\ 4 \ + \ 2 \ + \ 12 \ + \ 12=32≠20$$ 30- Choice A is correct 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 $$14 \ - \ k$$ 31- Choice A is correct The correct answer is $$4$$ hours and $$32$$ minutesNumber of times that the driver rests $$=\frac{24}{6}=4$$Driver’s rest time $$= 1$$ hour and $$8$$ minutes $$= 68$$ minutesThen, $$4 \ × \ 68$$ minutes $$=272$$ minutes$$1$$ hour $$= 60$$ minutes $$→ 272$$ minutes $$= 4$$ hours and $$32$$ minutes 32- Choice A is correct 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 $$x=450 ⇒$$$$0.75 \ x=450 ⇒$$$$x=450 \ ÷ \ 0.75=\ 600$$ 33- Choice E is correct 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. $$6 \ × \ \frac{1}{6}=\frac{6}{6}=1≠6$$ 34- Choice B is correct 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:$$225 \ × \ 180=40,500$$ 35- Choice A is correct The correct answer is $$108^°, 54^°$$The angle $$\alpha$$ is:$$0.3 \ × \ 360=108^°$$The angle $$β$$ is:$$0.15 \ × \ 360=54^°$$ 36- Choice B is correct 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. 37- Choice C is correct 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: $$1 \ + \ 5 \ + \ 1 \ + \ 4 \ + \ 1 \ + \ 2 \ + \ 1 \ + \ 6 \ + \ 2 \ + \ 1=24$$ 38- Choice A is correct 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 $$=2 \ x=2 \ (22.5)=45$$ 39- Choice A is correct The correct answer is: it cannot be determined from the information givenWe have two equations and three unknown variables, therefore $$x$$ cannot be obtained. 40- Choice C is correct 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:$$x=\frac{30}{1.20}=25$$ 41- Choice A is correct The correct answer is $$40.46$$ litersAmount of available petrol in tank:$$70.5 \ - \ 4.65 \ - \ 35.7 \ + \ 10.31=40.46$$ liters 42- Choice C is correct 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 $$=\frac{36 \ + \ 32}{2}=\frac{68}{2}=34$$ 43- Choice B is correct 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. $$x=\frac{2}{5}→ \frac{4}{7} \ + \ \frac{2}{5}=\frac{20 \ + \ 14}{35}=\frac{34}{35} \cong 0.9 \ <\ 3$$ 44- Choice E is correct 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. 45- Choice C is correct 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. $$y=40→ x \ + \ 45 \ + \ y \ + \ 2 \ x \ + \ y=25 \ + \ 45 \ +\ 40 \ + \ 2 \ (25) \ + \ 40=200≠180$$ 46- Choice C is correct 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 $$=\frac{number \ of \ desired \ outcomes}{number \ of \ total \ outcomes} = \frac{8}{20}$$ 47- Choice E is correct The correct answer is $$15$$$$\frac{3}{4} \ × \ 20=\frac{60}{4}=15$$ 48- Choice A is correct The correct answer is $$\frac{800}{6} \ + \ \frac{50}{6} \ + \ \frac{5}{6}$$$$855 \ ÷ \ 6=\frac{855}{6}=\frac{800 \ + \ 50 \ + \ 5}{6}=\frac{800}{6} \ + \ \frac{50}{6} \ + \ \frac{5}{6}$$ 49- Choice C is correct 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 $$22 \ + \ 7 = 29$$ 50- Choice A is correct The correct answer is $$444 \frac{5}{7}$$$$450 \ - \ 5 \ \frac{4}{14}=(449 \ - \ 5) \ + \ (\frac{14}{14} \ - \ \frac{4}{14})= 444 \frac{10}{14}=444 \frac {5}{7}$$

### The Most Comprehensive SSAT Upper Level Math Preparation Bundle

$76.99$36.99
52% Off*

Includes SSAT Upper Level Math Prep Books, Workbooks, and Practice Tests

### Practice Test 1

Simulate test day with an official practice test. Then, score your test. The answers come with explanations so you can learn from your mistakes.

### Practice Test 2

Simulate test day with an official practice test. Then, score your test. The answers come with explanations so you can learn from your mistakes.

## More Articles

### ISEE Upper Level Mathematics Formulas

$6.99$6.99

### CLEP College Algebra Exercise Book 2020-2021

$23.99$18.99

### ATI Teas Math in 7 Days

$18.99$14.99

### The Most Comprehensive SSAT Upper Level Math Preparation Bundle

$76.99$36.99