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GMAT Math Prep

GMAT Math Prep. February 9, 2009. GMAT Prep Day 4. Finish data sufficiency problems from session 3 Short QUIZ with timed problems Break Word Problems CD for next week. Data Sufficiency Flow Diagram. Read the question. Is statement (1) sufficient to answer the question?. YES. NO.

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GMAT Math Prep

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  1. GMAT Math Prep February 9, 2009

  2. GMAT Prep Day 4 • Finish data sufficiency problems from session 3 • Short QUIZ with timed problems • Break • Word Problems • CD for next week

  3. Data Sufficiency Flow Diagram Read the question Is statement (1) sufficient to answer the question? YES NO Is statement (2) sufficient to answer the question? Is statement (2) sufficient to answer the question? YES NO YES NO Are statements (1) and (2) TOGETHER sufficient to answer the question? YES NO D A B C E

  4. SUMMARY Outcome Answer A B C D E YES NO NO YES NO NO YESYES NO NO YES NO

  5. 33. What distance did Jane travel? (1) Bill traveled 40 miles in 40 mins. (2) Jane traveled at the same average rate as Bill • Answer: E • Answer: E

  6. 34. What number is 15% of x ? (1) 18 is 6 percent of x (2) of x is 200? • Answer: D

  7. 3 . 2 6 35. If “box” and “triangle” represents single digits in the decimal above, what digit does box represent? (1) When the decimal is rounded to the nearest tenth, 3.2 is the result (2) When the decimal is rounded to the nearest hundredth, 3.24 is the result. • Answer: E

  8. 36. The profit from the sale of a certain appliance increases, though not proportionally, with the number of units sold. Did the profit exceed $4 million on sales of 380,000 units? (1) The profit exceeded $2 million on sales of 200,000 units. (2) The profit exceeded $5 million on sales of 350,000 units. • Answer: B

  9. 37. What is the value of xy – yz ? (1) y = 2 (2) x – z = 5 • Answer: C

  10. x 38. Will the first 10 volumes of a 20-volume encyclopedia fit upright in the book rack shown above? (1) x = 50 cm (2) Twelve of the volumes have an average (arithmetic mean) thickness of 5 cms. • Answer: E

  11. x meters 39. The circular tub has a band painted around its circumference, as shown above. What is the surface area of this painted band? (1) x = 0.5 (2) the height of the tub is 1 meter • Answer: E

  12. 40. What is the value of the integer “n”? (1) n (n + 1) = 6 (2) • Answer: B

  13. 41. The inside of a rectangular carton is 48 cm long, 32 cm wide, and 15 cm high. The cartoon filled to capacity with “k” identical cylindrical cans of fruit that stand upright in rows and columns, as indicated above. If the cans are 15 cm. high, what is the value of “k”? (1) each can has a radius of 4 cm (2) six of the cans fit exactly along the length of the carton. • Answer: D

  14. x – 4 = z y – x = 8 8 – z = t 42. For the system of equations given, what is the value of z ? (1) x = 7 (2) t = 5 • Answer: D

  15. 43. Is x equal to 5? (1) x > 5 (2) x < 5 • Answer: C

  16. Answer: B 44. The table above shows the distance, in kilometers, by the most direct route, between any two of the four cities, R, S, T, and U. For example, the distance between city R and City U is 62 km. What is the value of “x”? (1) by the most direct route, ST is twice SR (2) by the most direct route, TU is 1.5 times RT

  17. 45. What is the value of the two-digit integer x ? (1) The sum of the two digits is 3 (2) x is divisible by 3 • Answer: E

  18. 46. What is the tenths digit in the decimal representation of a certain number? (1) the number is less than (2) the number is greater than • Answer: E

  19. 47. If the two floors in a certain building are 9 feet apart, how many steps are there in a set of stairs that extends from the first floor to the second floor of the building? (1) each step is foot high (2) each step is 1 foot wide • Answer: A

  20. 48. If xy is not equal to 0, is < 0? (1) x = -y (2) - x = - (-y) • Answer: D

  21. 49. How many people are directors of both company K and company R? (1) There were 17 directors present at a joint meeting of the directors of company K and company R, and no directors were absent (2) Company K has 12 directors and company R has 8 directors • Answer: C

  22. 50. If x and y are positive, is greater than 1? (1) x y > 1 (2) x – y > 0 • Answer: B

  23. Practice Quiz #2 8 questions 1:45 per question

  24. 1. • –1/20 • -1/100 • 1/100 • 1/20 • 1/5

  25. 2. Three business partners, Q,R, and S, agree to divide their total profit for a certain year in ratios of 2:5:8, respectively. If Q’s share was $4000, what was the total profit of the business partners for the year? • $26,000 • $30,000 • $52,000 • $60,000 • $300,000

  26. 3. If x books cost $5 each and y books cost $8 each, then the average (arithmetic mean) cost, in dollars per book is equal to: • (5x + 8y)/(x + y) b) (5x + 8y)/(xy) c) (5x + 8y)/13 d) (40xy)/(x + y) e) (40xy)/13

  27. 4. When 10 is divided by the positive integer n, the remainder is n - 4. Which of the following could be the value of n? • 3 • 4 • 7 • 8 • 12

  28. 5. Increasing the original price of an article by 15 percent and then increasing the new price by 15 percent is equivalent to increasing the original price by • 32.25% • 31.00% • 30.25% • 30.00% • 22.50%

  29. -10 • -4 • 0 • 4 • 10 6. If x = -1, then –(x4 + x3 + x2 + x)

  30. 7. If 1/2 of the money in a certain trust fund was invested in stocks, 1/4 in bonds, 1/5 in a mutual fund, and the remaining $10,000 in a government certificate, what was the actual amount of the trust fund? • $100,000 • $150,000 • $200,000 • $500,000 • $2,000,000

  31. Data Sufficiency 8. What is the value of the integer p? • Each of the integers 2, 3, and 5 is a factor of p. • Each of the integers 2, 5, and 7 is a factor of p.

  32. End of Quiz Check Answers

  33. 1. • –1/20 • -1/100 • 1/100 • 1/20 • 1/5

  34. 2. Three business partners, Q,R, and S, agree to divide their total profit for a certain year in ratios of 2:5:8, respectively. If Q’s share was $4000, what was the total profit of the business partners for the year? • $26,000 • $30,000 • $52,000 • $60,000 • $300,000

  35. 3. If x books cost $5 each and y books cost $8 each, then the average (arithmetic mean) cost, in dollars per book is equal to: • (5x + 8y)/(x + y) b) (5x + 8y)/(xy) c) (5x + 8y)/13 d) (40xy)/(x + y) e) (40xy)/13

  36. 4. When 10 is divided by the positive integer n, the remainder is n - 4. Which of the following could be the value of n? • 3 • 4 • 7 • 8 • 12

  37. 5. Increasing the original price of an article by 15 percent and then increasing the new price by 15 percent is equivalent to increasing the original price by • 32.25% • 31.00% • 30.25% • 30.00% • 22.50% Too obvious

  38. -10 • -4 • 0 • 4 • 10 6. If x = -1, then –(x4 + x3 + x2 + x)

  39. 7. If 1/2 of the money in a certain trust fund was invested in stocks, 1/4 in bonds, 1/5 in a mutual fund, and the remaining $10,000 in a government certificate, what was the actual amount of the trust fund? • $100,000 • $150,000 • $200,000 • $500,000 • $2,000,000

  40. Data Sufficiency 8. What is the value of the integer p? • Each of the integers 2, 3, and 5 is a factor of p. • Each of the integers 2, 5, and 7 is a factor of p. E

  41. Word Problems Common Types

  42. Word Problems • Read the entire problem & answers for overview • Focus: • Given • Find • Known • Picture or diagram? • Solution—have you answered the correct question?

  43. “Rate” type problems • Rate = quantity persome unit of measure • Miles per hour • Gallons per mile • Packages per minute • Cells of bacteria per petri dish • “Parent” formula for rate problems • Quantity = rate * (per unit measure) • e.g: distance = speed * time

  44. Rate Example 1 • The postal service handles 3,000 letters per minute. • If they process 60,000 letters, how long will the processing take? Quantity = rate * (per unit measure) 60,000 letters = 3000 lpm * x x = 20 minutes

  45. Rate Example 2 • The postal service handles 3,000 letters per minute. • If they operate at this rate for one 8-hour shift, how many letters will be processed? Quantity = rate * (per unit measure) x = 3000 lpm * 480 min x = 1,440,000 letters

  46. “Shared” work or “shared” rates • Key concept w/ shared work or rates is • Add the rates • Example: two machines make 1000 bolts, machine A does it in 4 hours, machine B does it in 5 hours. How long does it take them to make 1000 bolts when working together?

  47. “Shared” work or “shared” rates • Example: two machines make 1000 bolts, machine A does it in 4 hours, machine B does it in 5 hours. How long does it take them to make 1000 bolts when working together? • Rate A: 1000 bolts per 4 hours = 250 bolts per hour • Rate B: 1000 bolts per 5 hours = 200 bolts per hour • A and B together: 250 bph + 200 bph = 450 bph

  48. “Shared” work or “shared” rates • Rate A: 1000 bolts per 4 hours = 250 bolts per hour • Rate B: 1000 bolts per 5 hours = 200 bolts per hour • A and B together: 250 bph + 200 bph = 450 bph Quantity = rate * (per unit measure) 1000 bolts = 450 bph * x x = 2.22 hr

  49. Mixture Problems • Key concept: • “follow the solute” • Solute = the stuff in the solution • Alcohol, acid, salt, flour, fat, etc. • Example: How many liters of 15 % salt solution should be added to 5 liters of 8 % salt solution to make a 10 % solution?

  50. Mixture Problems • Example: How many liters of 15 % salt solution should be added to 5 liters of 8 % salt solution to make a 10 % solution? Salt + Salt = More Salt • Let x = liters of 15% salt solution .15 x + .08 ∗ 5 = .10 ∗ (x + 5)

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