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Motion Problems 1

Motion Problems 1. One hour after Yolanda started walking from X to Y, a distance of 45 miles, Bob started walking along the same road from Y to X. If Yolanda’s walking rate was 3 miles per hour and Bob’s was 4 miles per hour, how many miles had Bob walked when they met? (A) 24 (B) 23

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Motion Problems 1

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  1. Motion Problems 1 One hour after Yolanda started walking from X to Y, a distance of 45 miles, Bob started walking along the same road from Y to X. If Yolanda’s walking rate was 3 miles per hour and Bob’s was 4 miles per hour, how many miles had Bob walked when they met? (A) 24 (B) 23 (C) 22 (D) 21 (E) 19.5

  2. Motion Problems 2 How many miles long is the route from Houghton to Callahan? (1) It will take 1 hour less time to travel the entire route at an average rate of 55 miles per hour than at an average rate of 50 miles per hour. (2) If will take 11 hours to travel the first half of the route at an average rate of 25 miles per hour.

  3. Variation 1 • On a certain airline, the price of a ticket is directly proportional to the number of miles to be traveled. If the ticket for a 900-mile trip on this airline costs $120, which of the following gives the number of dollars changed for a k-mile trip on this airline? • (2k)/15 • 2/(15k) • 15/(2k) • (15k)/2 • (40k)/3

  4. Variation 2 • In a certain formula, p is directly proportional to s and inversely proportional to r. If p = 1 when r = 0.5 and s = 2, what is the value of p in terms of r and s ? • s/r • r/(4s) • s/(4r) • r/s • (4r)/s

  5. Set/Overlapping 1 • In company X, 30 percent of the employees live over ten miles from work and 60 percent of the employees who live over 10 miles from work are in car pools. If 40 percent of the employees of company X are in car pools, what percent of the employees of company X live ten miles or less from work and are in car pools? • 12% (D) 28% • 20% (E) 32% • 22%

  6. Set/Overlapping 2 In each production lot for a certain toy, 25 percent of the toys are red and 75 percent of the toys are blue. Half the toys are size A and half are size B. If 10 out of a lot of 100 toys are red and size A, how many of the toys are blue and size B? (A) 15 (B) 25 (C) 30 (D) 35 (E) 40

  7. Set/Overlapping 3 Out of a total of 1,000 employees at a certain corporation, 52 percent are female and 40 percent of these females work in research. If 60 percent of the total number of employees work in research, how many male employees do NOT work in research? (A) 520 (B) 480 (C) 392 (D) 208 (E) 88

  8. Venn Diagrams Out of 40 students, 14 are taking English and 29 are taking Chemistry. If 5 students are in both classes, how many students are in neither classes? (A) 1 (B) 2 (C) 4 (D) 8 (E) 10

  9. Counting Techniques • Worst case. • Ordered places or “for each”. • 3. Permutation (Can be done by number 2). • 4. Combination.

  10. Worst Case Of the science books in a certain supply room, 50 are on botany, 65 are on zoology, 90 are on physics. 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science?   (A) 81  (B) 159  (C) 166  (D) 285  (E) 324

  11. Ordered Places 1 Katie must place five stuffed animals--a duck, a goose, a panda, a turtle and a swan in a row in the display window of a toy store. How many different displays can she make if the duck and the goose must be either first or last? (A) 120 (B) 60 (C) 24 (D) 12 (E)  6

  12. Ordered Places 2 The president of a country and 4 other dignitaries are scheduled to sit in a row on the 5 chairs represented above. If the president must sit in the center chair, how many different seating arrangements are possible for the 5 people?  (A) 4  (B) 5  (C) 20  (D) 24  (E) 120

  13. Ordered Places 3 In how many arrangements can a teacher seat 3 girls and 3 boys in a row of 6 if the boys are to have the first, third, and fifth seats? (A)      6 (B)     9 (C)     12 (D)     36 (E)    720

  14. “FOR EACH” If a customer makes exactly 1 selection from each of the 5 categories listed below, what is the greatest number of different ice cream sundaes that a customer can create?  12 ice cream flavours 10 kinds of candy   8 liquid toppings   5 kinds of nuts   With or without whip cream. (A) 9600 (B) 4800 (C) 2400 (D) 800 (E) 400

  15. Ordered Places or Permutation Given a selected committee of 8, in how many ways, can the members of the committee divide the responsibilities of a president, vice president, and secretary? (A) 120 (B) 336 (C) 56 (D) 1500 (E) 100

  16. Ordered Places or Permutation How many four-digit numbers can you form using ten numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) if the numbers can be used only once? (A) 72 (B) 5000 (C) 4536 (D) 10 000 (E) 210

  17. Combination 1 From a group of 8 secretaries, select 3 persons for a promotion. How many distinct selections are there? (A) 56 (B) 336 (C) 512 (D) 9 (E) 200

  18. Combination 2 A person has the following bills: $1, $5, $10, $20, $50. How many unique sums can one form using any number of these bills only once? (A) 10 (B) 15 (C) 31 (D) 35 (E) 40

  19. Permutation/Combination 1 In a certain contest, Fred must select any 3 of 5 different gifts offered by the sponsor. From how many different combinations of 3 gifts can Fred make his selection? (A) 10 (B) 15 (C) 20 (E) 30 (F) 60

  20. Permutation/Combination 2 Ben and Ann are among 7 contestants from which 4 semifinalist are to be selected. Of the different possible selections, how many contain neither Ben nor Ann? (A) 5 (B) 6 (C) 7 (D) 14 (E) 21

  21. Probability (Simple) P(A) = ( # favorable outcomes of A)/( total possible outcomes of A) For example, consider a deck of 52 cards; P (A = ace) = = 4/52 = 1/13 P(A = spade) = = 13/52 = 1/4

  22. Example 1 Two fair six-sided dice are rolled; what is the probability of having 5 as the sum of the number?

  23. Example 2 Two six-sided dice are rolled; what is the probability of having 12 as the sum of the numbers?

  24. Probability (Compound) • P(A and B) = P(A) • P(B) • P(A or B) = P(A) + P(B) – P(A and B) • P( not A) = 1 – P(A) • NOTE: if A and B have nothing in common • then P(A and B) = 0

  25. Example 1 If a fair coin is tossed twice, what is the probability that on the first toss the coin lands heads and on the second toss the coin lands tails? (A)    1/6 (B)      1/3 (C)     1/4 (D)    1/2 (E)     1

  26. Example 2 If a fair coin is tossed twice what is the probability that it will land either heads both times or tails both times? (A)      1/8 (B)1/6 (C)     1/4 (D)       1/2 (E)     1

  27. Example 3 A bowman hits his target in 1/2 of his shots. What is the probability of him missing the target at least once in three shots?

  28. Example 4 What is the probability that a card selected from a deck will be either an ace or a spade? (A)      2/52 (B)      2/13 (C)       7/26 (D)      4/13 (E)      17/52

  29. Example 5 If someone draws a card at random from a deck and then, without replacing the first card, draws a second card, what is the probability that both cards will be aces?

  30. Example 6 If there are 30 red and blue marbles in a jar, and the ratio of red to blue marbles is 2:3, what is the probability that, drawing twice, you will select two red marbles if you return the marbles after each draw?

  31. Example 7 Now consider the same question as example 6 with the condition that you do not return the marbles after each draw.

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