Hiring - Step 2: Maths Superior Test

Maths Superior Test
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1. When Mr. Mayer went to the grocery store he spent $5 on grapes and $4.50 on peaches. If grapes cost $2 per pound and peaches cost $1.50 per pound, how many total pounds of grapes and peaches did Mr. Mayer purchase?

2.5 pounds3 pounds5.5 pounds8 pounds8.5 pounds

2. 2x + 4 = 8, 6x + 12 =

2481624

3. The scatterplot above shows the ages of a group of 15 married couples along with the graph of the equation y = x, where y represents the husband’s age and x represents the wife’s age. The age of the wife is 36 in the married couple represented by point A. How old is the husband?

3736353433

4. Which of the following points on the number line below has the same value as ⎟ x − y⎟ ?

ABCDE

5. The square of a number equals the sum of 21 and 4 times the number. Which of the following could be the number?

−7−4−334

6. The diagram above represents the cost to set up a computer network, in thousands of dollars. What is the least amount of money it will cost to guarantee that there will be a connection between each point on the network?

$180,000$150,000$120,000$90,000$70,000

7. 648 same-size cubes fill a rectangular box. The dimensions of the rectangular box are 18 inches by 27 inches by 36 inches. What is the length of the side of each cube?

3 inches6 inches9 inches18 inches27 inches

8. What is the average of the lengths of the five segments seen above?

4.84.63.83.63.4

9. A person’s weight on the moon is one-sixth of her or his weight on Earth. If a person weighs 30 pounds on the moon, how much would the person weigh on Earth?

5 pounds30 pounds60 pounds150 pounds180 pounds

10. In the figure above, the two semicircles have centers that are midpoints of the side of the rectangle. What is the area of the shaded region?

16−4π24−4π32−4π16−2π32−2π

11. Triangle ABC is an equilateral triangle. Rectangle DEFG is inscribed in triangle ABC. What is the value of x?

3045607590

12. 2x − y = 4 and −x + y = 2, x =

23468

13. Which of the following statements is true about the lengths of the sides of triangle ABC below?

AB < BC < ACAB < AC < BCBC < AB < ACAC < BC < ABBC < AC < AB

14. The average of six consecutive positive integers is 4.5. What is the median of these six integers?

33.544.55

15. There are six soccer teams in a league. Every team must play every other team twice. How many games must be played?

612153060

16. n + 5 = 8, 3(n + 5) =

815162430

17. A certain hat style comes in five different colors and three different sizes. How many different hats of this style are there?

235815

18. Five groups of men, 10 men in each group, have the following average ages: 36,42,32,34, and 40. What is the sum of the ages of all 50 men?

1843685521,8403,680

19. The product xy equals every value in the interval [−2,4] and no values outside the interval. Which of the following describes possible values for x and y?

−4 ≤ x ≤ 8 and 0 ≤ y ≤ 2.−1 ≤ x ≤ 2 and −2 ≤ y ≤ 0−2 ≤ x ≤ 1 and 0 ≤ y ≤ 2-1 ≤ x ≤ 2 and −2 ≤ y ≤ 0−2 ≤ x ≤ 1 and −2 ≤ y ≤ 0

20. In the figure above, what is the value of x in terms of a and b?

a−180b−180180−a180−ba+b−180

21. A network with n points and a segment joining each point to every other point is called a complete network of size n. If k is the number of segments in a complete network of size n, which of the following is the number of segments in a complete network of size n + 1?

k+nk+n+1k+n+2k+2n+1k+2n+2

22. If 4a − 7 > 9, then which of the following cannot be equal to a?

357911

23. (y+7)+k=y−2,k=

−2.5−4.5−5−9−18

24. A complete network of size n is n points connected by line segments, as shown above. What is the minimum number of segments that must be removed from a complete network of size 5 so that one point has no segments connected to it?

12345

25. A translation in the xy-coordinate plane is as follows: for every positive horizontal move of 4 there is a positive vertical move of 2. Starting at the point (5,7) the translation goes to (x,31). What is the value of x?

1217244853

26. The sum of the heights of six people is 336 inches. No two people are the same height. What is the mean height of the third and fourth tallest people if the mean and the median height of all six people are equal?

8467.25656.557

27. The figure above is formed by inscribing a square in a circle. If the circumference of the circle is 16π, what is the area of the shaded regions?

64π−12864π12832π−6496π

28. Let c be the number of distinct prime factors of 34. Let k be the number of distinct prime factors of 37. What is the value of ck?

12468

29. A copy center charges $0.07 per copy up to and in- cluding 100 copies, $0.05 for every copy over 100 up to and including 300 copies, and $0.03 for every copy over 300 copies. How much does it cost to make 500 copies?

$6$7$10$15$23

30. The area of the circle shown above is 81π. What is the length of arc PQR?

18π15π12π6π3π

31. The table above displays the results of a survey given to an equal number of males and females. How many of the females surveyed graduated from college?

29,00023,00016,00013,00010,000

32. What is the intersection point for the graphs of the lines y = 2x + 7 and y = 3x + 2?

(9,25)(5,17)(−17,−5)(−7,17)(17,−7)

33. The ratio of married employees to the total number of employees at a company is 3 to 5. If there are a total of 1,000 employees at the company, how many are not married?

300400600700800

34. In the figure above, what is the value of z in terms of x and y?

2x+2y−1802x+2y−3603x+3y−360360−2x+2y540−3x−3y

35. When a number is increased by 8, the original value is 75% of the new value. What is the original value of the number?

2361824

36. There are 4 blue, 6 red, and 8 green marbles in a jar. What is the least number of marbles that can be removed, without replacing, to guarantee that a chosen marble is red?

1112131415

37. In the graph of h(x) above, h(a) = 1, which of the following is not a possible value of a?

-7-2347
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