SSAT <- Upper Level SSAT <- 2014 SSAT Free Practice Test - Quantitative Section Questions with Answers + Explanations 2014 SSAT Free Practice Test - Quantitative Section Questions with Answers + Explanations 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 12345678910111213141516171819202122232425262728293031 2014 SSAT Free Practice Test - Quantitative Section Questions with Answers + Explanations 1 / 31 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. Each question consists of a word problem followed by four answer choices. You may write in your test booklet; however, you may be able to solve many of these problems in your head. Next take a look at the four answer choices and select the best one. Which of the following is. NOT a multiple of 3? 20 30 36 45 96 Multiples of 3 include: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, etc. Comparing these with the answers provided, notice that the number 20 is not a multiple of 3. 2 / 31 For all real numbers m, * m = 10m - 10. What is * 8? 70 60 17 7 0 Substitute 8 for m. * 8 = 10(8) - 10 = 80 - 10 = 70. 3 / 31 If * m = 100, then m = 11 12 13 120 130 If * m = 10m - 10 and * m = 100, then 10m - 10 = 100. Solve for m: 10m = 110, m = 11. 4 / 31 At Nifty Thrifty Buy 'N Sell, an item that usually sells for $12 is on sale for $8. What approximate discount does that represent? 10% 25% 33% 50% 66% The total discounted amount is $4 ($12 - $8). The discount percentage is calculated as (4/12) × 100 = 33%. 5 / 31 In Jackie's golf club, 14 of the 21 members are right-handed. What is the ratio of left-handed members to right-handed members? 1:2 2:1 2:3 3:4 4:3 The number of left-handed members is equal to 21 - 14 = 7. The ratio of left-handed to right-handed members is 7:14, which simplifies to 1:2. 6 / 31 The sum of five consecutive positive integers is 55. What is the square of the greatest of these integers? 5 9 13 81 169 Let the five consecutive integers be x, x+1, x+2, x+3, and x+4. Their sum is 5x + 10 = 55, so x = 9. The greatest integer is 9 + 4 = 13, and 13^2 = 169. 7 / 31 \( 2^2 × 2^3 × 2^4 = \) 2^4 64 2^8 2^9 2^7 When multiplying powers with the same base, add the exponents. 2^2 × 2^3 × 2^4 = 2^(2+3+4) = 2^9. 8 / 31 If the area of a square is 121, what is the length of one side of the square? 121 115 121s 11s 11 The area of a square is equal to (side length)^2. If the area is 121, the side length is √121 = 11. 9 / 31 If 5 books cost d dollars, how many books can be purchased for 7 dollars? 7d/5 35d d/35 35/d 5d/7 Set up a ratio for this problem and solve it. Let x represent the number of books purchased with 7 dollars. \( frac{5}{d} = frac{x}{7} \) Using cross-multiplication, you get: \( x = frac{35}{d} \). 10 / 31 If g is an even integer, h is an odd integer, and j is the product of g and h, which of the following must be true? j is a fraction. j is an odd integer. j is divisible by 2. j is between g and h. j is greater than 0. The product of an even integer (g) and an odd integer (h) is always an even number. So, \( j \) is divisible by 2. Try using numbers: if \( g = -4 \) and \( h = 5 \), then \( j = -4 imes 5 = -20 \). Since -20 is even, the correct choice is (C). 11 / 31 What is the reciprocal of 5/6? 1/6 5/6 6/5 5 6 Finding the reciprocal of a number involves flipping its numerator with its denominator. The reciprocal of \( frac{5}{6} \) is \( frac{6}{5} \). 12 / 31 If \( \frac{1}{4}N = 2 \), then \( \frac{1}{8}N \) = 1/2 1 2 8 16 First solve for \( N \) in the equation \( frac{1}{4}N = 2 \). Multiply both sides by 4: \( N = 8 \). Now substitute \( N = 8 \) into \( frac{1}{8}N \), giving \( frac{1}{8} imes 8 = 1 \). 13 / 31 In Figure 1, the number of shaded triangles is what fractional part of the total number of triangles? (See Figure 1) ssat figure 1 1/3 2/5 2/3 1/8 3/2 There are 10 triangles, and 4 of them are shaded. So, the fraction of shaded triangles is \( frac{4}{10} = frac{2}{5} \). 14 / 31 If the largest of five consecutive whole numbers is 11, then the average of these numbers is 6 7 8 9 10 The average of consecutive integers is equal to the middle term. If the largest number is 11, the numbers are 7, 8, 9, 10, and 11. The middle term, and thus the average, is 9. 15 / 31 \( \frac{2}{3} \times \frac{3}{6} \times \frac{1}{4} = \) 1/12 1/6 3/4 1 2 The easiest way to solve this problem is by canceling terms first and then multiplying. \( frac{2}{3} imes frac{3}{6} imes frac{1}{4} = frac{1}{12} \). 16 / 31 If cats sleep 3/5 of every day, how many full days would a cat sleep in a five-day period? 1/4 3/4 1 3 4 If a cat sleeps \( frac{3}{5} \) of every day, then in 5 days, a cat sleeps \( 5 imes frac{3}{5} = 3 \) full days. 17 / 31 What is the least number that can be added to 2,042 to produce a result divisible by 9? 1 2 3 5 6 To determine if a number is divisible by 9, the sum of the digits must equal a number divisible by 9. The sum of the digits in 2,042 is 2 + 0 + 4 + 2 = 8. By adding 1 to this number, the sum of the digits becomes 9, which is divisible by 9. 18 / 31 An art club of 7 boys and 6 girls makes craft projects. If the girls average 3 projects each and the boys average 4 projects each, what is the total number of projects produced by this group? 5 9 22 23 46 The 6 girls make 3 projects each for a subtotal of 6 × 3 = 18 projects. The 7 boys make 4 projects each for a subtotal of 7 × 4 = 28 projects. The total number of projects made is 18 + 28 = 46. 19 / 31 The area of a rectangle with width 4 and length 10 is equal to the area of a triangle with base 8 and height of what? 1 2 3 4 10 The area of the rectangle is 10 × 4 = 40 square units. The area of a triangle is given by the formula \( A = frac{1}{2} imes ext{base} imes ext{height} \). Setting the areas equal: \( 40 = frac{1}{2} imes 8 imes h 40 = 4h h = 10 \). 20 / 31 If \( r \circ s \) = (r*s) - (r+s) What is the value of \( r \circ s \) if \( r = 8 \) and \( s = 4 \)? 20 16 12 8 4 The operation defined is \( r circ s = (r imes s) - (r + s) \). Substituting the values: \( 8 circ 4 = (8 imes 4) - (8 + 4) = 32 - 12 = 20 \). 21 / 31 If \( r \circ s \) = (r*s) - (r+s) If \( L(5 \circ 4) = 33 \), then what is \( L \)? 3 4 5 6 7 Given that \( L(5) = 3 \), you can solve for \( L \) using the equation \( 5L = 33 L = frac{33}{5} = 6.6 \). 22 / 31 Jessie scores an 89, 87, and 92 on her first 3 exams. What must she score on her fourth exam to receive an average of 91? 92 96 98 99 100 To score an average of 91 on 4 exams, the total of the 4 exams must equal 91 × 4 = 364. On her first 3 exams, Jessie scored a total of 89 + 87 + 92 = 268. Therefore, she needs 364 - 268 = 96 points on her last exam. 23 / 31 Solve for x: \( 3x + 8 = 10x - 13 \) 5/7 -5/7 -35 -3 3 To solve for x, start with \( 3x + 8 = 10x - 13 8 + 13 = 10x - 3x 21 = 7x x = 3 \). 24 / 31 If the price of a handbag is $75.00 before a discount of 25%, what is the final discounted price? $11.25 $60.00 $63.75 $75.00 $56.25 A 25% discount can be calculated as follows: 25% expressed as a decimal is 0.25, so the discount is 0.25 × 75 = $18.75. Subtracting this from the original price gives: 75 - 18.75 = $56.25. 25 / 31 Find the height of a triangle whose base is 15 inches and whose area is 150 square inches. 5 inches 5 square inches 10 inches 10 square inches 20 inches The formula for the area of a triangle is \( A = frac{1}{2} imes ext{base} imes ext{height} 150 = frac{1}{2} imes 15 imes h 150 = 7.5h h = 20 \). 26 / 31 A train travels at a speed of 60 miles per hour. How long will it take to travel 180 miles? 2 hours 3 hours 4 hours 5 hours 6 hours To find the time, use the formula: Time = Distance ÷ Speed. So, Time = 180 miles ÷ 60 miles/hour = 3 hours. 27 / 31 If a rectangle has a length that is twice its width and the perimeter is 48 cm, what are the dimensions of the rectangle? 8 cm and 16 cm 6 cm and 12 cm 10 cm and 20 cm 5 cm and 10 cm 4 cm and 8 cm Let width = w. Then, length = 2w. The perimeter formula is P = 2(length + width) = 48. So, 2(2w + w) = 48 leads to 6w = 48, thus w = 8. The dimensions are 8 cm and 16 cm. 28 / 31 If a car's value depreciates by 15% each year, what will its value be after 2 years if it starts at $20,000? $15,000 $14,450 $16,000 $13,000 $12,000 After 1 year: Value = 20000 × (1 - 0.15) = 20000 × 0.85 = $17,000. After 2 years: Value = 17000 × 0.85 = $14,450. 29 / 31 In a right triangle, if one angle is 30 degrees and the hypotenuse is 10 units, what is the length of the side opposite the 30-degree angle? 5 units 10 units 7.5 units 8.66 units 6 units In a 30-60-90 triangle, the ratio of the sides opposite the 30-degree, 60-degree, and 90-degree angles is 1:√3:2. Therefore, the side opposite the 30-degree angle is 10 × 1/2 = 5 units. 30 / 31 If the sum of three consecutive integers is 45, what are the integers? 13, 14, 15 14, 15, 16 12, 13, 14 15, 16, 17 16, 17, 18 Let the integers be x, x+1, and x+2. Then, x + (x + 1) + (x + 2) = 45. Simplifying gives 3x + 3 = 45, so 3x = 42, hence x = 14. The integers are 14, 15, and 16. 31 / 31 A cylinder has a radius of 3 cm and a height of 10 cm. What is the volume of the cylinder? (Use π ≈ 3.14) 84.78 cm³ 282.6 cm³ 94.2 cm³ 75.36 cm³ 36 cm³ The volume V of a cylinder is given by the formula V = πr²h. Thus, V = 3.14 × (3)² × 10 = 3.14 × 9 × 10 = 282.6 cm³. 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