DAT Domain 4: Quantitative Reasoning Welcome to your DAT Domain 4: Quantitative Reasoning 1. Domain of study DAT: Quantitative Reasoning If the function \( f(x) = 2x^2 + 3x - 5 \) is graphed, at what x-coordinate does its vertex occur? \(-0.75\) \(-1.5\) \(1.5\) \(0.75\) None 2. Domain of study DAT: Quantitative Reasoning A rectangle has a length that is twice its width. If the area of the rectangle is 288 square units, what is its perimeter? 72 units 68 units 64 units 96 units None 3. Domain of study DAT: Quantitative Reasoning What is the sum of the series \( 3 + 6 + 12 + ... \) up to 8 terms? 1539 765 1536 3075 None 4. Domain of study DAT: Quantitative Reasoning If \( 5^x \times 5^{x+2} = 5^{13} \), what is the value of \( x \)? 4.5 5.5 6 6.5 None 5. Domain of study DAT: Quantitative Reasoning A circular gear with radius 15 cm turns another gear with radius 5 cm. If the larger gear makes 10 revolutions, how many revolutions does the smaller gear make? 10 30 50 60 None 6. Domain of study DAT: Quantitative Reasoning What is the 50th term of the arithmetic sequence 2, 5, 8, ...? 149 150 151 152 None 7. Domain of study DAT: Quantitative Reasoning A train traveling at a constant speed takes 2 seconds to completely pass a pole. If it takes 20 seconds to pass a platform 100 meters long, what is the length of the train? 90 meters 100 meters 110 meters 120 meters None 8. Domain of study DAT: Quantitative Reasoning If the equation \( \frac{1}{x-1} + \frac{1}{x+1} = \frac{2}{3} \) is solved for \( x \), what is one possible value? 2 3 4 5 None 9. Domain of study DAT: Quantitative Reasoning A tank is filled by three pipes with uniform flow. The first pipe alone takes 12 hours to fill the tank, the second alone takes 15 hours, and the third alone takes 20 hours. How long will it take all three pipes working together to fill the tank? 4 hours 4.5 hours 5 hours 5.5 hours None 10. Domain of study DAT: Quantitative Reasoning If \( \log_b(81) = 4 \), what is \( b \)? 2 3 4 5 None 11. Domain of study DAT: Quantitative Reasoning What is the next number in the sequence 2, 6, 12, 20, 30, ...? 40 42 44 46 None 12. Domain of study DAT: Quantitative Reasoning If the function \( g(t) = t^3 - 6t^2 + 11t - 6 \) has roots at \( t = 1, 2, 3 \), what is \( g(4) \)? 0 2 4 6 None 13. Domain of study DAT: Quantitative Reasoning In a group of 60 people, 30 drink coffee, 20 drink tea, and 10 drink neither. How many drink both coffee and tea? 10 20 0 30 None 14. Domain of study DAT: Quantitative Reasoning A jar contains 6 red, 4 blue, and 5 green balls. If three balls are picked at random, what is the probability that they are all of the same color? \(\frac{1}{91}\) \(\frac{1}{154}\) \(\frac{1}{210}\) \(\frac{1}{455}\) None 15. Domain of study DAT: Quantitative Reasoning If \( x \) and \( y \) are integers such that \( x^2 + y^2 = 13 \) and \( x > y \), what is \( y \)? -2 -1 0 1 None 16. Domain of study DAT: Quantitative Reasoning A pizza is sliced into 8 equal pieces. If a person eats 1/4 of the pizza and then 1/2 of what remains, how many pieces of the pizza are left? 3 4 5 6 None 17. Domain of study DAT: Quantitative Reasoning What is the smallest integer \( n \) for which \( 2^n \) is greater than \( 10,000 \)? 12 13 14 15 None 18. Domain of study DAT: Quantitative Reasoning If a square has a diagonal of 10 cm, what is the area of the square? 50 cm^2 75 cm^2 100 cm^2 125 cm^2 None 19. Domain of study DAT: Quantitative Reasoning The function \( f(x) = 4x - 1 \) intersects the function \( g(x) = -2x + 3 \) at what point? (0, -1) (0, 3) (1, 3) (1, -1) None 20. Domain of study DAT: Quantitative Reasoning A cube has a volume of 27 cubic meters. What is the total surface area of the cube? 54 m^2 81 m^2 108 m^2 162 m^2 None 1 out of 20 Time is Up! Time's up
