SSAT <- Upper Level SSAT <- 2013 SSAT Quantitative Math Practice Questions 2013 SSAT Quantitative Math Practice Questions 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 2013 SSAT Quantitative Math Practice Questions 1 / 25 Directions: Any figures that accompany questions in this section may be assumed to be drawn as accurately as possible EXCEPT when it is stated that a particular figure is not drawn to scale. Letters such as x, y and n stand for real numbers. If 1/4 of a number is less than 16, then the number is always less than 64 equal to 4 greater than 4 equal to 64 greater than 64 Call the number N. Write an inequality using the information given. Remember, "of" means multiply. 1/4XN<16. We need to isolate N, our unknown value. Multiplying both sides by the reciprocal of 1/4 which is 4 produces a result of N<16 x 4, and thus N < 64 . (A) is correct. 2 / 25 The perimeter of a square with a side length of 5 is how much less than the perimeter of a rectangle with sides of length 8 and width 6? 8 6 4 2 0 The perimeter of a square is given by \(P = 4s\), and the perimeter of a rectangle is given by \(P = 2(l + w)\). For the square: \( P = 4 times 5 = 20 \). For the rectangle: \( P = 2(8 + 6) = 28 \). The difference is \(28 - 20 = 8\). 3 / 25 \( \frac{1}{5} + \frac{2}{7} + \frac{3}{4} - \frac{1}{5} - \frac{1}{7} + \frac{1}{4} - \frac{1}{7} \) \( \frac{1}{2}\) \( \frac{2}{3}\) 1 2 \( \frac{3}{4}\) Simplify the expression step by step. Group terms with the same denominators: \( (frac{1}{5} - frac{1}{5}) + (frac{2}{7} - frac{1}{7} - frac{1}{7}) + (frac{3}{4} + frac{1}{4}) \) simplifies to: \( 0 + 0 + 1 = 1 \). 4 / 25 On a test with 50 questions, Mark scored 72%. How many questions did Mark answer correctly? 36 21 16 5 4 To find the number of correct answers, multiply 72% by 50: \( 72% = frac{72}{100} = 0.72 times 50 = 36 \). Mark answered 36 questions correctly. 5 / 25 Five less than a number is one third of that number. What is the number? 12 \( \frac{15}{2}\) \( \frac{5}{3}\) 6 Let the number be \(x\). The problem states that \(x - 5 = frac{1}{3}x\). Solving this: \( x - frac{1}{3}x = 5 rightarrow frac{2}{3}x = 5 rightarrow x = frac{5 times 3}{2} = frac{15}{2} = 7.5 \). 6 / 25 Which of the following is a multiple of both 4 and 5? 10 45 50 60 90 To find the least common multiple (LCM) of 4 and 5, note that the LCM must be divisible by both numbers. The LCM of 4 and 5 is 20, so multiples of 20 will satisfy the condition. Among the given choices, 90 is divisible by both 4 and 5. 7 / 25 The ratio of 7 to 4 is equal to the ratio of 35 to what number? 7 8 12 14 20 Set up a proportion: \( frac{7}{4} = frac{35}{x} \). Solving for \(x\), we get: \( 7x = 35 times 4 = 140 rightarrow x = 20 \). 8 / 25 A class of 35 girls and 24 boys built a haunted house for the Halloween carnival. If \( \frac{1}{5} \) of the girls and \( \frac{2}{3} \) of the boys participated, what fraction of the total class participated? \( \frac{1}{5}\) \( \frac{2}{3}\) \( \frac{2}{15}\) \( \frac{1}{7}\) \( \frac{23}{59}\) There are 35 girls and 24 boys in the class, a total of 59 students. One-fifth of the girls, or \( frac{35}{5} = 7 \), and two-thirds of the boys, or \( frac{2}{3} times 24 = 16 \), participated. Thus, \(7 + 16 = 23\) students participated, and the fraction of the total class is \( frac{23}{59} \). 9 / 25 If \(y = \frac{1}{8}\), for what value of \(z\) will \(y @ z = 0\)? -4 4 6 8 16 We are given that \(y @ z = y times z - 2 = 0\). Plugging in \(y = frac{1}{8}\), we have: \( frac{1}{8} times z - 2 = 0 rightarrow frac{1}{8}z = 2 rightarrow z = 16 \). 10 / 25 If \(y @ 3 = 10\), then what is the value of \(y\)? 1 2 4 6 12 Use the definition of \(y @ z = y times z - 2\) and substitute \(z = 3\) into the equation: \( y times 3 - 2 = 10 \). Solving this gives: \( y times 3 = 12 rightarrow y = 4 \). 11 / 25 For all real numbers \(y\) and \(z\), let \(y @ z = y \times z - 2\). What is \(3 @ 9\)? 15 19 25 27 21 To solve this, apply the given operation: \( 3 @ 9 = 3 times 9 - 2 = 27 - 2 = 25 \). Therefore, \(3 @ 9 = 25\). 12 / 25 According to the graph in Figure 5, what is the average number of 911 calls made from Monday through Thursday, inclusive? Monday: 500, Tuesday: 1,000, Wednesday: 500, Thursday: 1,500. 500 750 875 1,000 1,125 The average formula is: \( text{Average} = frac{text{Sum of the terms}}{text{Number of terms}} \). Adding the number of calls made on each day, we have: \( 500 + 1,000 + 500 + 1,500 = 3,500 \). There are four days, so the average is: \( frac{3,500}{4} = 875 \). 13 / 25 When 17 is divided by 4, the remainder is the same as when 82 is divided by what number? 10 9 8 7 6 The remainder when 17 is divided by 4 is 1, since \( 17 - (4 times 4) = 1 \). Now, we need to find which number, when divided into 82, gives a remainder of 1. Since \( 9 times 9 = 81 \), dividing 82 by 9 also leaves a remainder of 1. Therefore, the answer is 9. 14 / 25 According to the graph in Figure 4, how many chocolate ice cream cones were sold? 25 30 50 75 100 The pie chart shows that chocolate makes up 1/4 of the total cones sold. With 300 total cones sold, the number of chocolate cones is: \( 1/4 times 300 = 75 \). Therefore, 75 chocolate cones were sold. 15 / 25 At sunset, the temperature was 10 degrees. By midnight, it had dropped another 16 degrees. What was the temperature at midnight? 12 degrees below zero. 6 degrees below zero. 0 degrees. 12 degrees above zero. 20 degrees above zero. The temperature was initially 10 degrees. It then dropped 16 degrees. So, we subtract 16 from 10: \( 10 - 16 = -6 \). Therefore, the temperature at midnight was -6 degrees, or 6 degrees below zero. 16 / 25 \( \frac{7}{8} - \frac{6}{8} \) 0.58 0.5 0.375 0.25 0.125 To solve \( frac{7}{8} - frac{6}{8} \), subtract the fractions to get: \( frac{7 - 6}{8} = frac{1}{8} \). In decimal form, this is equal to 0.125. 17 / 25 According to a census report for Country A, 10.75 out of every 100 families live in rural areas. Based on this report, how many of the 20 million families in Country A live in rural areas? 430,000 2,150,000 43,000 4,300 430 The problem tells us that 10.75 out of 100 families live in rural areas, which can be interpreted as 10.75%. To find how many families that is in a population of 20 million, we calculate: \( 10.75% times 20,000,000 = 2,150,000 \). Therefore, 2.15 million families live in rural areas. 18 / 25 If \(a - 7 = 3b - 3\), what does \(a + 5\) equal? b - 1 4b - 1 3b + 9 3b + 16 It cannot be determined from the information given. Using the information given, isolate \(a\): \( a = 3b - 3 + 7 = 3b + 4 \). Thus, \(a = 3b + 4\). Next, add 5 to both sides of this equation: \( a + 5 = 3b + 4 + 5 = 3b + 9 \). 19 / 25 Which of the following can be expressed as \( (J + 5) \times 3 \), where \( J \) is a whole number? 40 52 64 73 81 The question asks which choice can be written as \( (J + 5) times 3 \). Since 3 is a factor of the expression, the answer must be a multiple of 3. The sum of the digits of 81 is 9, which is a multiple of 3. Therefore, (E) is correct. 20 / 25 A book is placed on a flat table surface. Which of the following best shows all of the points where the book touches the table? white square dark eclipse white trapezoid white circle dark rectangle The question asks for all the points where the book touches the table. Answer choice (A) is incorrect because it only includes the boundary of the points. Answer choice (E) shows all the points that touch the table, including those inside the rectangle. Therefore, (E) is correct. 21 / 25 In a line segment \(AD = 110\), and the distances \(AB = CD\), where \(AB\) is twice the distance of \(BC\), how far apart are points B and D? 11 30 33 44 66 Let \(BC = x\), then \(AB = 2x\), and since \(AB = CD\), we also have \(CD = 2x\). The total length of \(AD\) is: \( AD = AB + BC + CD = 2x + x + 2x = 5x = 110 \). Solving for \(x\), we get \(x = 22\). Therefore, the distance between points B and D is: \( BD = BC + CD = x + 2x = 3x = 66 \). 22 / 25 If \( (x - y) + 2 = 6 \) and \(\) y < 3 [/latex], which of the following CANNOT be the value of [latex] x [/latex]? - 3 0 1.5 4 8 The equation is \( (x - y) + 2 = 6 \). First, subtract 2 from both sides: \( x - y = 4 \). Adding \( y \) to both sides, we get \( x = y + 4 \). Since \(\) y < 3 [/latex], [latex] x < 7 [/latex]. Therefore, the only choice that is not less than 7 is 8, so [latex] x [/latex] cannot be 8. 23 / 25 A man bought a piece of land for 60 thousand dollars. Then he spent 3 million dollars to build a house on it. The cost of the house is how many times the cost of the land? 5 20 50 200 500 To find how many times the cost of the house is compared to the land, we divide the cost of the house by the cost of the land: \( frac{3,000,000}{60,000} = frac{300}{6} = 50 \). Therefore, the house costs 50 times more than the land. 24 / 25 In the right triangle ABC, what is the value of side \(a\) if angle A is 45 degrees? Side \(a\) is the side opposite to angle A. 4 6 8 9 It cannot be determined from the information given. The sum of the three interior angles of any triangle is 180 degrees. In this case, angle A is 45 degrees, and angle B is 90 degrees (as it is a right triangle). So, the remaining angle C must also be 45 degrees. This means triangle ABC is a 45-45-90 triangle. In such triangles, the two legs are equal. Hence, side \(a\) is equal to the given side, which is 6. 25 / 25 In a basketball game, Team A scored 39 points and Team B scored more points than Team A. If Team B has 8 players, the average score of the players on Team B must have been at least how many points? 1 5 6 8 12 The minimum number of points Team B could have scored is one more than Team A, or 40. Using the average formula, we have: \( text{Average} = frac{text{Sum of terms}}{text{Number of terms}} \). We are given that the sum is 40 points and the number of players is 8. Thus, \( text{Average} = frac{40}{8} = 5 \). The average score of the players on Team B must have been at least 5 points per player. Your score is Follow us on socials! 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