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DAT Quantitative Reasoning Practice
Questions
If tan θ = 5/12 and sin θ > 0, then cos θ =? a. -5/ b. 12/ c. 13/ d. -12/ e. 0 - b. 12/ tanθ = opp/adj = 5/ c = sqrt(5^2 + 12^2) = sqrt(25 + 144) = sqrt(169) = 13 cosθ = adj/hyp = 12/ If 60% of x equal to 30% of 20, then what is the value of (x + 5)^2? a. 25. b. 26 c. 26. d. 2025 e. 225 - e. 225 0.6x = (0.3) x 20 → x = 10 (x + 5)^2 → (10 + 5)^2 = (15)^2 = 225 In the xy-plane, the point (4,3) and (3,2) are on line A. Which of the following equations of lines is parallel to line A?
a. y = 3x b. y = 10 c. y = x d. y = 2x e. y = x - e. y = x Slope of line A is: m = (y2 - y1)/(x2 - x1) = (3 - 2)/(4 - 3) = 1 Parallel lines have the same slope and only choice (e.) has slope of 1. When point A (10,3) is reflected over the y-axis to get the point B, what are the coordinates of point B? a. (10,3) b. (-10,-3) c. (-10,3) d. (10,-3) e. (0,3) - c. (-10,3) When points reflected over y-axis, the value of y in the coordinates doesn't change and the sign of the x changes. Therefore, the coordinate point B is (-10, 3). If f(x) = 2x^3 + 5x^2 + 2x and g(x) = -2, what is the value of f(g(x))? a. 36 b. 32 c. 24 d. 4 e. 0 -
→ 2500 = c^2 → c = 50 x is y% of what number? a. 100x/y b. 100y/x c. x/100y d. y/100x e. xy/100 - a. 100x/y Let the number be A. Then: x = y% * A Solve for A. x = y/100 * A Multiply both sides by 100/y: x * 100/y = y/100 * 100/y * A A = 100x/y If cotangent of an angle β is 1, then tangent of angle β is a. - b. 0 c. 1 d. 2 e. 3 - c. 1 Tangent = 1/cotangent = 1 What is the value of y in the following system of equations?
3x - 4y = - -x + 2y = 10 a. - b. - c. 1 d. 4 e. 5 - e. 5 How long does a 420-mile trip take moving at 50 miles per hour (mph)? a. 4 hours b. 6 hours and 24 minutes c. 8 hours and 24 minutes d. 8 hours and 30 minutes e. 10 hours and 30 minutes - c. 8 hours and 24 minutes When 40% of 60 is added to 12% of 600, the resulting number is: a. 24 b. 72 c. 96 d. 140 e. 180 - c. 96 A ladder leans against a wall forming a 60o angle between the ground and the ladder. If the bottom of the ladder is 30 feet away from the wall, how long is the ladder?
d. 160% e. 180% - c. 140% If 3x/16 = (x-1)/4, then x =? a. 1/ b. 3/ c. 3 d. 4 e. 9/4 - d. 4 Find the distance between the point of intersection of the lines x - y = 2 and y = 4 and the point (6,3). a. 1 b. 2 c. √ d. 2√ e. 3√2 - a. 1 x - y = 2 and y = 4 x - 4 = 2 → point of intersection is (6,4) distance = (x2-x1)2+(y2-y1) = (6-6)2+(3-4)2 = 0+1 = 1 = 1 Evaluate (2.004)^ a. 4. b. 4.
c. 4. d. 4. e. 4.001760 - b. 4. (2.004)2 = 4. A wagon was loaded with 20 boxes each weighing 500 kg. If the maximum weight limit for the wagon is 20 tons, how much more weight can be loaded? (use 1 ton = 907 kg) a. 81.40 kg b. 814.0 kg c. 8,140 kg d. 81,400 kg e. 8.140 kg - c. 8,140 kg 20 x 907 = 18,140 kg 500 x 20 = 10,000 kg 18,140 kg - 10,000 kg = 8,140 kg A square is inscribed in a circle. The side of the square is 2 meters. What is the area of the circle not occupied by the square? a. 2π - 4 b. 4π - 6 c. 4π - 8 d. 4π - 3 e. None of the above - a. 2π - 4
A pair of playing dice is thrown. What is the probability of getting a sum of 5? a. 1/ b. 1/ c. 1/ d. 1/ e. 1/27 - d. 1/ A and B can do a job alone in 10 days and 12 days, respectively. A starts working along and 5 days later B joins to finish the work together. For how many days has B worked on the job? a. 32/ b. 24/ c. 30/ d. 24/ e. 2 - c. 30/ A train of 300 meters long passes a lamp post in 12 seconds. How long will it take to cross a 450 meter bridge? a. 15 seconds b. 30 seconds c. 45 seconds d. 60 seconds e. 75 seconds - b. 30 seconds At present, the age ratio of A and B is 1:2. Ten years later the ratio is 2:3. What is the present age of B?
a. 5 years old b. 10 years old c. 20 years old d. 30 years old e. 40 years old - c. 20 years old (1/6) + (3/8) - (5/12) = a. 1/ b. 5/ c. 1/ d. 23/ e. -1/8 - c. 1/ A farmer has a rectangular garden with a perimeter of 72 feet. If one side is 4 feet longer than the other, then what is the area of the garden? a. 320 feet^ b. 1476 feet^ c. 1280 feet^ d. 324 feet^ e. 672 feet^2 - a. 320 feet^ Which is the smallest? a. 11/ b. 5/ c. 1/
b. 53. What is 8% of 4% of 2? a. 64 b. 0. c. 0. d. 6. e. 0.0064 - e. 0. If Chad has a 2-sided coin, what is the probability he will flip the coin on heads three times in a row? a. 1/ b. 1/ c. 1/ d. 1/ e. 1/16 - d. 1/ Brandon shoots free throws at a ratio of 3:2 for made to misses, respectively. If he misses 150 shots then how many free throws did he make? a. 450 b. 150 c. 300 d. 320 e. 225 - e. 225 If the average of a and b is 5 and c = 10. What is the average of a, b, and c?
a. 10 b. 20/ c. 5 d. 7. e. 6 - b. 20/ A few years back Kevin bought a new car for $30,000 but since then it has depreciated by half. Now Kevin is again buying a new car with his trade in worth 25% of the new car. What is the value of the new car? a. $30, b. $15, c. $18, d. $45, e. $60,000 - e. $60, If a + b > a - b, then which of the following must be true? a. b ≤ 0 b. a - b > b - a c. a > 0 d. a = 0 e. None of the above. - e. None of the above. What is the square root of (.25 x 2.25)? a. 2 b. 0.
(x^2 -3) / (x-1) = 1 / (x-1) What is the value for x that makes this statement true? a. 3, - b. -4, 4 c. -6, 6 d. 0, 1 e. 2, -2 - e. 2, - If 1 inch equals 2.5 centimeters them how many centimeters is 25 feet? a. 10 cm b. 100 cm c. 1000 cm d. 750 cm e. 500 cm - d. 750 cm Which value is the largest? a. 2sin(0) b. 2sin(π/6) c. sin(π/4) d. 2sin(π/2) e. sin(π/3) - d. 2sin(π/2) Brant is x feet tall. At what angle must the sun be at for his shadow to equal his height?
a. sin 1 b. cos 1 c. arcsin 1 d. arccos 1 e. arctan 1 - e. arctan 1 0.4 is 30% of x. What is x =? a. 12/ b. 4/ c. 40/ d. 10/ e. 8/5 - b. 4/ Jen is building a playground with a perimeter of 280 feet. If the length is 10 feet less than twice the width, then what is the area? a. 7295 feet b. 17475 feet c. 11545 feet d. 654 feet e. 4500 feet2 - e. 4500 feet (8 x 105) x (5 x 10-2) =? a. 4.0 x 10^ b. 4.0 x 10^- c. 4.0 x 10^
c. 5 lbs. 6 oz. If a and b are prime numbers and a = x/b then which of the following could x =? a. 20 b. 24 c. 33 d. 36 e. 40 - c. 33 Jacob is one fourth the age of his dad. In three and a half years he will be one third the age of his dad. How old is Jacob now? a. 4 b. 5 c. 6 d. 7 e. 8 - d. 7 At Adam's graduation there were 224 seniors graduating. If the ratio of girls to boys was 7 to 9 then how many girls were graduating with Adam? a. 98 b. 177 c. 128 d. 130 e. 110 - a. 98
If two x's and four o's are placed in a bag, then what is the probability that two draws from the bag at random, without replacement, will yield two x's? a. 3/ b. 2/ c. 1/ d. 1/ e. 1/9 - c. 1/ Brian receives 6 magazines at the begining of each month. If he wants to read 2 magazines, then how many combinations of 2 could he select? a. 12 b. 6 c. 15 d. 11 e. 36 - c. 15 What is the distance between the two points (2, 6) and (-1, 3) on a graph? a.. 3√ b. 6 c. 9√ d. 18 e. 4 - a.. 3√ 3x + 2y is what percent of 6x2 + y, if x = 2 and y = 6? a. 30%
