SSAT <- Upper Level SSAT <- 2012 SSAT Practice Test - Mathematics Achievement (Quantitative Reasoning 2) 2012 SSAT Practice Test - Mathematics Achievement (Quantitative Reasoning 2) Share Quiz Get Embed Code Copy the code below to embed this quiz on your website: <iframe src="https://tutorone.ca/practice-test/?embed=true" width="100%" height="800" style="border: none; max-width: 100%;" data-source="tutorone" allowfullscreen></iframe> Copy Code 12345678910111213141516171819202122232425 2012 SSAT Practice Test - Mathematics Achievement (Quantitative Reasoning 2) 1 / 25 A gas tank is 1/4 empty. When full, the tank holds 20 gallons. How many gallons are in the tank now? 3 6 8 12 15 If the tank is ¼ empty, it must be ¾ full: 3/4 the total capacity of 20 gallons is 15 2 / 25 Which of the following is the least? \( \frac{1}{4} + \frac{2}{3} \) \( \frac{3}{4} - \frac{1}{3} \) \( \frac{1}{12} \div \frac{1}{4} \) \( \frac{3}{4} \times \frac{1}{3} \) \( \frac{1}{12} \times 4 \) The value of choice (A) is \( frac{11}{12} \), the value of choice (B) is \( frac{5}{12} \), the value of choice (C) is \( frac{1}{3} \) or \( frac{4}{12} \), the value of choice (D) is \( frac{1}{4} \) or \( frac{3}{12} \), and the value of choice (E) is \( frac{1}{3} \) or \( frac{4}{12} \). Therefore, choice (D) has the least value. 3 / 25 If the sum of \( x \) and \( x + 3 \) is greater than 35, which is a possible value for \( x \)? - 18 - 12 - 2 12 18 If \( x + (x + 3) > 35 \), then \( 2x > 32 \). So \( x > 16 \). The only answer that is appropriate is 4 / 25 If a square has a perimeter of 100, what is the length of each side? 4 1 2 25 110 The perimeter of a square is found by summing the lengths of each side. Because the lengths are equal on a square, you can multiply one side by 4 to get the perimeter. Therefore, \( 4s = 100 \), so \( s = 25 \). 5 / 25 If a Set R contains four positive integers whose average is 7, what is the greatest number Set R could contain? 4 9 25 33 36 To find the greatest value of the four, assume the remaining three values are the least possible positive integers, 1. The average then is \( frac{1 + 1 + 1 + x}{4} = 7 \). Solve for \( x \). \( 3 + x = 28 \), so \( x = 25 \). 6 / 25 Which of the following is most nearly 40% of $9.95? $8.00 $4.00 $14.50 $12.00 $6.75 Round $9.95 to $10.00 and find 40% of 10. \( 40% = frac{40}{100} = 0.40 \). \( 0.40 times 10 = 4 \). 7 / 25 One fifth of a class chose electricity for the topic of a science project. If 4 students chose this topic, how many students are in the class? 20 10 8 5 2 Four students make up one fifth of a class. Translating this into a mathematical equation, you get \( frac{1}{5} times c = 4 \). Solving for \( c \), \( c = 4 times 5 = 20 \). 8 / 25 Don is 8 years older than Peter. In 7 years, Don will be twice as old as Peter is now. How old is Peter now? 5 10 15 25 35 Let \( d \) represent Don's age now and \( d + 7 \) represent Don's age in 7 years. Let \( p \) represent Peter's age now. Set up mathematical equations for the problem. \( d = p + 8 \), and \( d + 7 = 2p \). Substituting \( d = p + 8 \) into the second equation: \( (p + 8) + 7 = 2p \), solving gives \( p + 15 = 2p \), so \( p = 15 \). 9 / 25 If \( p \) pieces of candy cost \( c \) cents, how much will 20 pieces of candy cost? pc/20 cents. 20c/p cents. 20pc cents. 20p/c cents. 20 + p + c cents. Set up a ratio for this problem and solve: \( p \) represents the number of pieces of candy purchased for \( c \) cents (\( frac{p}{c} \)). 20 pieces of candy can be purchased for \( x \) cents (\( frac{20}{x} \)). Using cross-multiplication, \( px = 20c \), so \( x = frac{20c}{p} \). 10 / 25 Durant's Trading Company earned profits of $75,000 in 1990. In 1998, their profit was $4,500,000. The profit from 1998 was how many times as great as it was in 1990? 2 4 6 10 60 $4,500,000 is \( t \) times greater than $75,000. \( 4,500,000 = 75,000t \), so \( t = frac{4,500,000}{75,000} = 60 \). 11 / 25 ABC is a right triangle. If \( angle b = 45 ° \), and the side opposite \( b \) is equal to 5, then \( v^2 \) (where \( v \) is the hypotenuse) is equal to: 64 50 25 10 It cannot be determined This is a 45-45-90 triangle. Since this is true, the base is also 5 units long. By the Pythagorean Theorem, \( v^2 = 5^2 + 5^2 = 25 + 25 = 50 \). 12 / 25 A pet goat eats 3 pounds of oats and 2 pounds of grass each day. When the goat has eaten a total of 30 pounds, how many pounds of grass has been eaten? 6 8 10 12 60 Let \( o \) represent the amount of oats eaten and \( g \) the amount of grass eaten. Since 1.5 times as many pounds of oats are eaten as grass, we have \( o = frac{3}{2} g \). The total amount eaten is \( o + g = 30 \). Substituting the value of \( o \) into the equation gives \( frac{3}{2} g + g = 30 \), so \( frac{5}{2} g = 30 \), and \( g = 12 \). 13 / 25 If \( 2x - 4 = 50 \), what is \( \frac{x}{9} \)? 6 3 0 9 1 First, solve for \( x \): \( 2x - 4 = 50 \), so \( 2x = 54 \), and \( x = 27 \). Now, \( frac{x}{9} = frac{27}{9} = 3 \). 14 / 25 One half the difference between the number of degrees in a rectangle and the number of degrees in a triangle is: 360 240 180 90 45 There are 180° in a triangle and 360° in a rectangle (made up of four 90° angles). The difference is \( 360^{circ} - 180^{circ} = 180^{circ} \). One half of \( 180^{circ} \) is \( 90^{circ} \). 15 / 25 A zoo has 3 times as many gorillas as tigers. There are 3 more tigers than zebras at the zoo. If \( z \) represents the number of zebras, how many gorillas are there in terms of \( z \)? 3z z + 3 z + 6 3z + 3 3z + 9 Let \( g \) represent the number of gorillas, and let \( t \) represent the number of tigers. Since there are 3 times as many gorillas as tigers, \( g = 3t \). There are 3 more tigers than zebras, so \( t = z + 3 \). Substituting this into the equation for \( g \), we get \( g = 3(z + 3) = 3z + 9 \). 16 / 25 In the fraction \( \frac{xy}{z} \), if the value of \( z \) is doubled and the value of \( x \) is halved, the value of the fraction is: multiplied by four decreased by \( \frac{1}{2} \) increased by \( \frac{1}{2} \) doubled divided by four Doubling the denominator of a fraction divides the value by 2. Halving one of the factors in the numerator also halves the value of the fraction. Doing both divides the original value by 4. 17 / 25 40 is 10 percent of: 1.60 160 200 250 400 Since 10% is \( frac{1}{10} \), multiply 40 by 10 to find the full amount: \( 40 times 10 = 400 \). 18 / 25 How much larger than 80 is 100? 18% 20% 25% 35% 40% 100 is 20 larger than 80. 20 is one fourth, or 25%, of 80. Therefore, 125% of 80 is equivalent to 100. 19 / 25 3/8 inches on a scale drawing is equivalent to one foot at full scale. What distance on the drawing will represent 40 inches? \( \frac{1}{8} \text{ inches} \) \(\frac{7}{8} \text{ inches}\) \(1 \frac{1}{4} \text{ inches}\) \(2 \frac{1}{3} \text{ inches}\) \(8 \frac{8}{9} \text{ inches}\) 40 inches equals \( 3frac{1}{3} \) feet. Since \( frac{1}{8} \) inch represents 1 foot, multiply \( frac{1}{8} \) by 3.33 to get approximately \( 1frac{1}{4} \) inches. 20 / 25 What is \( 6 \times 2 / 3 + 1/3 \times 9 \)? \( \frac{2}{3} \) 12 7 54 168 Bracket the multiplication and division first, and solve the problem: \( (6 times 2) / 3 + (1/3 times 9) = 12 / 3 + 3 = 4 + 3 = 7 \). 21 / 25 If x + 3 < 12, what can x be? less than 15 greater than 16 equal to 15 less than 9 equal to 9 Since \( x + 3 < 12 \), we can subtract 3 from both sides, giving us \( x < 9 \). Thus, \( x \) can be any number less than 9. 22 / 25 If \( a = 16 \), \( b = 2 \), and \( c = 3 \), what is the value of \( \sqrt{a + 36 + c} \)? 16 7 7.42 4 ? Substituting the values into the expression: \( sqrt{16 + 36 + 3} = sqrt{55} \), which is approximately \( 7.42 \). 23 / 25 What is the average of \( -3, 17, 0, -1, \) and \( 12 \)? 5 3(0) 2 - 3 - 6 To find the average, sum the numbers and divide by the number of addends: \( frac{-3 + 17 + 0 - 1 + 12}{5} = frac{25}{5} = 5 \). 24 / 25 In the fraction \( \frac{A}{3} \), A can be replaced by all of the following EXCEPT: - 3 2 - 1 -2 If we substitute \( A = -3 \), the denominator of the fraction becomes zero. A denominator of zero is undefined in mathematics. 25 / 25 What is \( 1011 \div 10 \) equivalent to? 0. 0010101 101.1 0. 010101 0. 1001 1.0101 Simply move the decimal point one place to the left: \( 1011 div 10 = 101.1 \). Your score is Follow us on socials! 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