PRAXIS Math Practice 5003

18. The ratio of the number of adults to the number of children on a certain bus tour was 4 to 22. If the total number of passengers on the bus tour was 91, how many adults were on the tour? 14 48 65 69 77

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10. If triangle ABC in the xy-plane shown above is shifted 7 units to the right and 4 units up, what would be the coordinates of point A after the shift? (1, -2) (4, -2) (4, 2) (5, -2) (5, 2) A Start (-2)(-2)

(5, 2)

6. If 5(2x+1)=3(x+4)−5, what is the value of x ?

2/7 Solve the equation by first using the distributive property: 5(2x+1)=3(x+4)−5 becomes 10x+5=3x+12−5. Combining similar terms yields the equation 10x+5=3x+7. After subtracting 3x from both sides of the equation to get 7x + 5 = 7, subtracting 5 from both sides yields the equivalent equation 7x =2. The answer is found by dividing each side of this equation by 7.

39. The price of a coat was reduced from $90 to $72 at the end of the season. By what percent was the price of the coat reduced? A. 8% B. 10% C. 18% D. 20% E. 25%

20% Option (D) is correct. The original price of the coat was $90, and the sale price was $72, so the amount of the discount would be 90−72=18 dollars. Amount of Discount = Original Price 90 × .08, .10, .18, .20, .25. 90 x .20 = 18. 20% off original..

17. Of the 25 fish in a tropical fish tank, 10 are guppies, 4 are swordtails, and the rest are tetras. One fish is to be randomly selected from the fish tank. What is the probability that the fish selected will not be a guppy? 25 1125 1425 3/5 2125

3/5

44. In the last step of a computation, Evelyn added 290 instead of subtracting 290. What one number can Evelyn subtract from her final result of 3,710 so that the correct result of the computation is displayed on the calculator and she does not have to clear her calculator and start over? A. 290 B. 435 C. 580 D. 855 E. 870

580 Option (C) is correct. Since Evelyn added 290 to a number instead of subtracting 290 from the number, the number would be off by 290 + 290 = 580. The final result of 3,710 would need to have 580 subtracted from it in order for the calculation to be corrected on her calculator.

2. Answer the question below by clicking on the correct response. Question: Sarah rolls a fair, six-sided number cube, numbered 1 through 6, five times and rolls a 3, 4, 1, 4, and 4 in that order. What is the probability that she will roll a 4 on her sixth roll? • A. 1/6 • B. 1/3 • C. 1/2 • D. 3/5 • E. 5/6

A Option (A) is correct. Because the number cube is fair, each roll is independent of the others and equally likely. Since there is one number 4 on the six-sided cube, the probability of rolling a 4 on any roll is 1/6 .

7. Answer the question below by clicking on the correct response. Question: In which of the following are the numbers ordered from least to greatest? A. −1, −1/2,1/9,1/5−1,−1/2,1/9,1/5 B. −1/2, /−1,1/5,1/9−1/2, −1,1/5,1/9 C. 15,1/9, /−1,−1/2 1/5,1/9,−1,−12 D. −1/2,1/5,1/9, −1/2,1/5,1/9, −1 E. 1/9, 1/5, −1/2,−1,1/9,1/5,−1/2,−1

A Option (A) is correct. The numbers should be ordered from left to right on the number line from the most negative number to the largest positive number: −1<−1/2<1/9<1/5.

27. The arch above is constructed of 5 nearly congruent stones, each of which is in the shape of a right prism with trapezoid bases. Based on the approximate measurements provided, which of the following best approximates the volume of the entire arch? (The area of a trapezoid with bases b1 and b2 and height h is 12(b1+b2)h.) A. 900 cubic feet B. 1,050 cubic feet C. 1,140 cubic feet D. 2,160 cubic feet E. 4,320 cubic feet

Option (D) is correct. The volume of a right trapezoidal prism is equal to the height of the prism times the base area of the trapezoid, and is given by the formula V=12(b1+b2)⋅h⋅l, where b1 and b2 are the trapezoid bases, h = the height of the trapezoid, and l = the height of the prism. By substituting the values given: V=12(b1+b2)⋅h⋅l V=12(14+ 10)⋅12⋅3 V= 432 One trapezoidal stone is 432 cubic feet. Since there are 5 nearly congruent stones, 432⋅5=2,160. Therefore, the entire arch is approximately 2,160 cubic feet.

22. 12.1, 12.3, 11.9, 11.6, 11.2, 11.4, 11.1, 11.3, 11.2 Question: Marcy ran the 100-meter dash 9 times in competitions during the spring. Her times, in seconds, are listed above. What is the range of Marcy's times, in seconds? 0.8 0.9 1.0 1.1 1.2

1.2

11. 1.4, 1.8, 2.2, 2.0, 1.0, 1.9, 1.2, 2.1, 1.7 What is the median of the numbers in the list above? 1.2 1.4 1.7 1.8 1.9

1.8 Option (D) is correct. The median of an ordered set of data is the number positioned where there are an equal number less than the number and greater than the number (that is, the number in the "middle"). Rearranging the nine numbers from least to greatest, the list becomes 1.0, 1.2, 1.4, 1.7, 1.8, 1.9, 2.0, 2.1, 2.2, where 1.8 is the fifth (middle) number in the list.

46. The figure above shows a right circular cone with base radius 6 and height 20. The shaded portion of the figure is a right circular cone with height 10. The volume of the smaller cone is what fraction of the volume of the larger cone? (The volume of a right circular cone with base radius r and height h is 13πr2h.)

18 Correct Answer: 18 On the larger cone, the radius r1 is 6 when the height h1 is 20. The smaller shaded cone is similar to the larger cone, so rules for similarity can be used to determine the radius of the smaller cone. Since the height of the smaller cone h 2 given is 10, which is half of the larger cone's height of 20, the radius of the smaller cone r2 should be half the radius of the larger cone, which is half of 6, or 3. The question asks what fraction of the volume the smaller cone is compared to the larger cone, which leads to the following ratio, set up using the volume formula for each cone that was given in the problem. Volume of small cone /Volume large cone 1/3πr22h 213πr21h 1=1/3π(3)21013π(6)220=(9)10(36)20=90720=18

8. If x6 is between 3 and 4, which of the following could be the value of x ? 14 17 20 25 26

25 Option (C) is correct. When the numbers 3 and 4 are written as fractions with a denominator of 6, we need to find a value of x which satisfies the inequality 186<x6<246. This requires a number that lies between 18 and 24. The only number among the given choices that does this is 20.

19. On a certain day, the temperature was 37°F at 10 A.M. and 52°F at 3 P.M. If the temperature rose at a constant rate from 10 A.M. to 3 P.M. on that day, what was the temperature at noon? 42°F 43°F 44°F 45°F 46°F

43 Option (B) is correct. On a certain day, the temperature at 10 A.M was 37° F and at 3 P.M. was 52° F. Since the temperature throughout the 5-hour time period increased at a constant rate, each hour, the temperature increased the same amount. 52−375=155=3 gives the amount in which the temperature increased each hour. The table below shows the time and corresponding temperature each hour. Time Temperature (degrees F) 10 A.M. 37° 11 A.M. 40° 12 noon 43° 1 P.M. 46° 2 P.M. 49° 3 P.M. 52° At noon, the temperature was 43° F.

45. On a map that is drawn to scale, 6 inches represents a distance of d miles. Which of the following represents the distance, in inches, of d+1 miles on the map? d(d+1)/6 6(d+1)/d d+16/d 6d/d+1 6/d(d+1)

6(d+1)/d Option (B) is correct. The given ratio of 6 inches represents d miles can be written as 6d. Another ratio must be written for the distance d + 1 , but since the distance for d + 1 is not known, it can be called x, since that is what is being solved for in the problem. This leads to the equation 6d=xd+1. Cross-multiplication can be used to solve and gives 6(d+1)=dx. Dividing both sides by d to isolate x, gives x=6(d+1)d.

3. Which of the following expressions is equivalent to the expression 21−6x for all values of x ? 5−2(8−3x) 6+3(5−2x) 25−(4−6x) 3(4−2x)−9 7(3−2x)−8x

6+3(5−2x) Option (B) is correct. Using the distributive property, 6+3(5−2x)=6+15−6x=21−6x. None of the other selections is equivalent to this.

29. Allison works for a computer software company. She earns $225 per week plus $25 for each software package that she sells that week. If she wants to earn at least $400 this week, what is the minimum number of software packages that she must sell this week?

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32. Robert sets up a conversion as follows: 4miles×5,280feet 1mile×12inches1foot Question: Which of the following conversions is he performing? Miles to feet Miles to inches Feet to miles Inches to miles Inches to feet

A

38. A bag contains a number of solid-colored marbles, of which 6 are red, 7 are blue, and the rest are yellow. If a person were to draw a marble at random from the bag, the probability that the marble drawn would be red is 14. How many yellow marbles are in the bag? A. 11 B. 12 C. 13 D. 14 E. 15

A Add the blue and red marbles, they equal 13. i need to get a 4 as the denominator once reduced. 13 plus 11 gives me 24. The 6 red marbles as the numerator over the 11 yellow marbles as the denominator gives you 6/24 which reduced is 1/4. the answer is 11 yellow marbles are in the bag.

13. 1/4, 9/8, 2/3, 1/2, k, π Question: The five numbers shown above are listed in order from least to greatest. Which of the following could be the value of k Indicate all such values. A. 2 B. .516 C. 238 D. 7‾‾√ E. 17‾‾‾√

A. 2 C. 238 D. 17‾‾‾√ The correct answers are (A), (C), and (D). This problem can be answered using estimation. The value of k lies between 2312 (a number slightly less than 2 ) and π (a number slightly more than 3). Since 516<1 and 17‾‾‾√>4, they can be eliminated easily. The other three choices are greater than or equal to 2 and less than 3, which are in the necessary interval.

15. Which of the following sequence of steps, when completed, will solve the equation −6+3y=1 for y ? Subtract 1 from both sides of the equation, then divide both sides of the new equation by −6. Subtract 1 from both sides of the equation, then divide both sides by 6. Add 6 to both sides of the equation, then divide both sides by 3. Add 6 to both sides, then subtract 3 from both sides. Divide both sides of the equation by 3, then subtract 6 from both sides.

Add 6 to both sides, then subtract 3 from both sides.

55. If the speed of light is 1,080,000,000 kilometers per hour, how far does light travel in 100 hours? 1.08×10^9 kilometers 1.08×10^11 kilometers 1.08×10^13 kilometers 10.8×10^14 kilometers 108×10^15 kilometers

B 1.08×10^11 kilometers Option (B) is correct. The number 1,080,000,000 should be written in scientific notation as 1.08×10^9. Multiplying any number by 100 would have the same effect as adding two zeros to the number, thus increasing the exponent by 2, so light travels 1.08×10^11 km in 100 hours.

36. The total cost, t, in dollars, for c children to attend a camp is estimated by the equation t=650c+5,600. If $20,000 is available to pay for children to attend the camp what is the greatest number of children that can attend the camp? A.21 B. 22 C. 23 D. 24 E. 25

B Option (B) is correct. Using the equation, the total cost t for c children to attend a camp is given by t = 650c + 5,600, where the total cost is a maximum of $20,000 available to pay for a certain number of children to attend camp. t = 650c + 5,600 20,000 = 650c + 5,600 14,400 = 650c 14,400650=c c ≈ 22.15 Although there is a remainder, c represents the number of children. Since you cannot have a part of a person, 22 is the greatest number of children that can attend the camp using $20,000.

53. A triangle has sides of length 4, 7, and x. Which of the following could be the value of x ? Indicate all such values. A. 2.9 B. 4.5 C. 6.25 D. 7 E. 12

B,C,D The correct answers are (B), (C), and (D). The triangle inequality states that the length of the longest side of a triangle must be less than the sum of the lengths of the other two sides. Examination of each case is required. If x = 2.9, then the sum of 2.9 + 4 = 6.9, which is less than the longer side of 7, so (A) cannot be a value of x. If x = 4.5, then the sum of 4.5 + 4 = 8.5, which is longer than the longest side of 7, so (B) could be a value of x. If x = 6.25, then the sum of 6.25 + 4 = 10.25, which is longer than the longest side of 7, so (C) could be a value of x. If x = 7, then it would be an isosceles triangle with lengths of 7 for two of the sides, and a length of 4 for the other side, so (D) could be a value of x. If x = 12, then the longest side of the triangle would now be 12 and the other two sides would have to sum to be larger than 12. Since 4 + 7 = 11, which is less than 12, (E) cannot be a value of x.

49. Which of the following questions are statistical questions? Indicate all such questions. A. How long is Mike's foot? B. When do university students eat lunch? C. What is the weight of John's math textbook? D. How many coffee drinks do customers at a coffee shop order?

B,D The correct answers are (B) and (D). A statistical question is a question that one would expect to get a variety of answers for and not just a single answer. (A) would give only a single answer for the length of Mike's foot and (C) would give only a single answer for the weight of John's math textbook, so they are not statistical questions. For (B) and (D), one would expect to get a variety of answers, so they are statistical questions.

4. Answer the question below by clicking on the correct response. Question: Justine observed that the more time she spent studying for a test the higher her test score was. Which of the following graphs could be the graph of the relationship Justine observed between the time she studied for a test and her test score?

C Option (C) is correct. For a graph to indicate that more time studying results in a higher test score, an increase in time will also show an increase in the test score. Of the five options, only (C) shows a graph that has this property.

1. The graph above shows the relationship between the cost of a luncheon and the number of people attending the luncheon. According to the graph, what is the cost per person? • A. $7.50 • B. $12.00 • C. $15.00 • D. $17.50 • E. $30.00

C Option (C) is correct. To find the cost per person, divide Total Cost by Number of People for any point on the graph where exact numbers can be determined. Two such values are (4, 60) and (8, 120) , so the cost per person is 604=1208=$15.00 .

48. James walked 212 miles in 23 of an hour. What was his average speed, in miles per hour? A. 3 1/4 B. 3 1/2 C. 3 3/4 D. 3 7/8 E. 4 1/4

C 3 3/4 21223=5223=52(32)23(32)=1541=154=334 miles per hour.

42. The ages, in years, of 6 cars in a parking lot are 6, 14, 5, 1, 8, and x. If the average (arithmetic mean) of the 6 ages is 7 years, what is the value of x ?

Correct Answer: 8 The meAn or average is the total divided by the total of cars. Add the numbers and divide by 6, the number of cars in the parking lot. When you add the 6 numbers together you get 42. 42 divided by the total amount of cars you want 6, then you get 7. Subtract the total number of given car ages 34, from the new total number which is 42, this gives you 8. The unknown car age is 8.

5. A right circular cylinder with base B is shown. If a plane that is neither parallel nor perpendicular to base B passes through the cylinder, which of the following could be the shape of the intersection of the plane and the cylinder? An ellipse with circumference less than the circumference of B An ellipse with circumference greater than the circumference of B An ellipse with circumference equal to the circumference of B A circle with circumference less than the circumference of B A circle with circumference greater than the circumference of B

Correct Answer: B Option (B) is correct. A plane that is parallel to the base intersects the cylinder in a circle, but because the intersecting plane is not parallel, the intersection is an ellipse. One of the axes of the ellipse is equal to the diameter of the base, but the other axis (in the direction of the tilt) is larger than the diameter. That means that the circumference of the ellipse is greater than the circumference of the base.

12. If 1/7x−2=1, then x= -7 3 9 15 21

Correct Answer: E Option (E) is correct. Solve this equation by first adding 2 to both sides, resulting in an equivalent equation 1/7x=3. Multiplying both sides of this equation by 7 yields 7(1/7x)=7(3) or x=21.

33. A landscaping service needs to apply fertilizer to 5 lawns, each having an area of 7,800 square feet. One bag of fertilizer covers 2,500 square feet. What is the least number of bags of fertilizer that must be used? 13 14 15 16 17

D 15.6 or 16 Option (D) is correct. Each lawn the landscaper must fertilize has an area of 7,800 square feet. Since there are 5 lawns, the landscaper must have enough fertilizer to cover 7,800⋅5=39,000 square feet of lawn. Each bag of fertilizer covers 2,500 square feet of lawn. To find the number of bags needed, divide the total area of lawns by 2,500 square feet. 39,0002,500=15.6 Since 15.6 is not enough to cover all the lawns, the number of bags must be rounded up. Therefore, the total number of bags needed to cover the 5 lawns is 16 bags.

37. Of the following, which is most likely to be the height of a high school athlete? A. 3 yards B. 10 feet C. 124 inches D. 200 centimeters E. 400 millimeters

D D, 200 centimeters is approximately 6.5 feet, which is reasonable. (A) 3 yards, 3x3=9 feet, (B) 10 feet, and (C) 124 inches, divide by 12 = 12 feet, all are 9 feet or greater, and (E) 400 millimeters is too small.

24. A carpenter wants to build a diagonal brace for a rectangular gate that is 5 feet wide and 7 feet high, as shown in the figure. Approximately what is the length, in feet, of the diagonal brace? A.5.5 B.6.5 C.7.5 D.8.5 E.9.5

D Option (D) is correct. Since the gate shown is rectangular, the unknown length of the diagonal brace can be found using the Pythagorean theorem. a2+b2=c2, where a = 7 feet, b = 5 feet, and c is the length of the diagonal brace. 72+52=c2 49+25=c2 74=c2 74−−√=c c≈8.6 feet

41. A large wheel has a diameter of 30 inches, and a small wheel has a diameter of 20 inches. How many revolutions does the small wheel need to make to travel the same distance that the large wheel travels in 240 revolutions? A. 160 B. 240 C. 320 D. 360 E. 420

D 360 Option (D) is correct. For each revolution of either wheel, the distance that the wheel would travel is equal to the wheel's circumference, which can be found using either C=2πr or C=πd, where C is the circumference, r is the radius, and d is the diameter. Since we are given the diameter, the latter will be used. The larger wheel travels a total distance of 240 times the circumference of the larger wheel which is 240(30π)=7,200π. The smaller wheel has a circumference of 20π. To figure how many revolutions the smaller wheel would need to go so that it would travel the same distance of 7,200π that the larger wheel traveled, 7,200π20π=360. Or, the smaller wheel would need to make 360 revolutions to travel the same distance that the larger wheel could travel in 240 revolutions.

35. P is 6 times Q, and Q is 2 less than 9 times R. Which of the following statements describes the relationship between P and R ? P is 2 less than 15 times R. P is 2 less than 54 times R. P is 12 less than 15 times R. P is 12 less than 54 times R. P is 18 less than 15 times R.

D P is 12 less than 54 times R. Option (D) is correct. By translating each word expression, P is 6 times Q, or P=6Q and Q is 2 less than 9 times R, which means Q=9R−2. To describe the relationship between P and R, substitute the value of Q into P's equation. P=6QP=6(9R−2)P=54R−12 Therefore, P is 12 less than 54 times R.

54. Jermaine promised to donate a total of z dollars to a charity by donating x dollars immediately and then donating a fixed constant amount of dollars each month for m months. Which of the following expressions represents the fixed constant amount of dollars Jermaine promised to donate each month? z−xm z−mx zx−m z−xm zm−x

D z−x/m Option (D) is correct. The total amount that Jermaine promised to donate is z dollars. He will donate x dollars immediately and a fixed amount monthly over m months. The amount he will have left to pay after donating x dollars can be expressed as z−x. This amount is to be spread out over m months, so each month Jermaine would owe z−xm dollars to the charity.

26. A principal of a certain high school wants to ask a sample of students how they feel about a new school policy that will drop football as a varsity sport. Which of the following methods of selecting the sample will yield the most valid information about the feelings of all the students at the school? A. Interviewing twelfth-grade students on campus at random as they change classes B. Selecting a random sample of current football players C. Choosing two students at random from each science class on a given day D.. Sending a questionnaire to all students currently enrolled and using the returned questionnaires as the sample E.. Selecting a random sample from a list of all students currently enrolled at the school

E Option (E) is correct. A list of students currently enrolled gives a population where the group of students fit a particular description or set of conditions. Since the principal wants to ask a sample of students, a random sample where each member of this population has an equal chance of being included will give the principal an idea of what the entire population might look like.

31. If x+z=15 and w+y=10, what is the value of (3w+3y)(2x+2z) ? 150 300 450 600 900

E Option (E) is correct. 900. In the expression (3w+3y)(2x+2z), a factor of 3 can be factored from the first parenthetical and a factor of 2 can be factored from the second parenthetical. 3(w+y)⋅2(x+z) The values of x+z and w+y can be substituted so that: 3(w+y)⋅2(x+z)=3(10)⋅2(15)=30⋅30=900.

47. The median and range of 15 measurements are 18 and 5, respectively. If 3 is subtracted from each of the 15 measurements, which of the following statements regarding the median and range of the modified 15 measurements must be true? A. The median and range will both decrease. B. The median and range will both stay the same. C. The median will stay the same, but the range will decrease. D. The median will stay the same, but the range will increase. E. The median will decrease, but the range will stay the same.

E. The median will decrease, but the range will stay the same. Option (E) is correct. The range would change because it is the middle number and you subtract 3 from it it decreases. The range is the difference between the largest number and the smallest number, in this set of numbers the range stays the same. The largest number and the smallest number have nothing to do with middle number in this set. The range is still 5.

50. Which of the following is equivalent to x/2+y/3 ? A. x+y/5 B. x+y/6 C. 3x+2y D. 3x+2y/5 E. 3x+2y/6

E. Option (E) is correct. To add fractions they must have a common denominator. The least common denominator for 2 and 3 is 6. x/2 y/3 CD=6 set up problem. 3x/6 and 2y/6 together make 3x + 2y all over 6