1. GMAT Math Prep September 16, 2008

2. GMAT Prep Day 3 • Short QUIZ with timed problems • Data Sufficiency Problems

3. Review QUIZ 2 minutes per problem

4. 1. Rectangular floors X and Y have equal area. If floor X is 12 feet by 18 feet and floor Y is 9 feet wide, what is the length of floor Y, in feet? • 13 ½ • 18 • 18 ¾ • 21 • 24

5. 200 m 200 m 2. In the figure above, all angles shown are right angles. What is the perimeter of the figure? • 400 m b) 200 m c) 800 m d) 40000 m e) 100 m

6. Q (3,2) P 3. In the diagram above, the point on segment PQ that is twice as far from P as from Q is: • (3,1) • (2,1) • (2,-1) • (1.5,0.5) • (1,0)

7. 4. If k is an integer and 2 < k < 7, for how many different values of k is there a triangle with sides 2, 7, and k? • One • Two • Three • Four • Five

8. R (7,4) Q (0,3) P (4,0) 5. In the rectangular coordinate system above, the area of triangle PQR is: • 12.5 • 14 • 16 • 25

9. 6. The perimeter of an isosceles right triangle is . What is the length of the hypotenuse?

10. 7. A right circular cone is inscribed in a hemisphere so that the base of the cone coincides with the base of the hemisphere. What is the ratio of the height of the cone to the radius of the hemisphere?

11. END of QUIZ Check Answers

12. 1. Rectangular floors X and Y have equal area. If floor X is 12 feet by 18 feet and floor Y is 9 feet wide, what is the length of floor Y, in feet? • 13 ½ • 18 • 18 ¾ • 21 • 24

13. 200 m 200 m 200 m 200 m 2. In the figure above, all angles shown are right angles. What is the perimeter of the figure? • 400 m b) 200 m c) 800 m d) 40000 m e) 100 m

14. Q (3,2) P 3. In the diagram above, the point on segment PQ that is twice as far from P as from Q is: • (3,1) • (2,1) • (2,-1) • (1.5,0.5) • (1,0)

15. 4. If k is an integer and 2 < k < 7, for how many different values of k is there a triangle with sides 2, 7, and k? • One • Two • Three • Four • Five

16. R (7,4) Q (0,3) P (4,0) 5. In the rectangular coordinate system above, the area of triangle PQR is: • 12.5 • 14 • 16 • 25

17. 6. The perimeter of an isosceles right triangle is . What is the length of the hypotenuse?

18. 7. A right circular cone is inscribed in a hemisphere so that the base of the cone coincides with the base of the hemisphere. What is the ratio of the height of the cone to the radius of the hemisphere?

19. DATA SUFFICIENCY

20. DATA SUFFICIENCY

21. Data SufficiencyExample

22. 14. Is the integer k a prime number? (1) 2k = 6 (2) 1 < k < 6

23. Data Sufficiency Problems • Read question and one given item at a time • Decide if the problem can be solved with each piece of given info separately • Evaluate if math needs to be performed • Stick with a systematic approach • Vast majority of time • No math is actually required to be done

24. Systematic Approachto Data Sufficiency Problems

25. 14. Is the integer k a prime number? (1) 2k = 6 (2) 1 < k < 6

26. Try the first givenby itself.

27. 14. Is the integer k a prime number? (1) 2k = 6 (2) 1 < k < 6 YES

28. 2. Try the second givenby itself.

29. 14. Is the integer k a prime number? (1) 2k = 6 (2) 1 < k < 6 NO

30. 3. Look at your two answers together.

31. 14. Is the integer k a prime number? (1) 2k = 6 (2) 1 < k < 6 YES NO

32. 4. If either answer is “YES”then you are finished.

33. YES NO NO YES YES YES A B D 3 Possibilities

34. 14. Is the integer k a prime number? (1) 2k = 6 (2) 1 < k < 6 YES NO Answer: A

35. 5. Look at the other remaining possibility: NO NO

36. Two more choices: C and E

37. 6. Can you solve this if you use both pieces of given info? C

38. Three whole numbers have a sum of 20. What are the three numbers? (1) One whole number is 5. (2) One whole number is 8. Answer: C

39. 7. If you cannot solve this even if you use both pieces of given info. E

40. Three whole numbers have a sum of 20. What are the three numbers? (1) One whole number is even. (2) One whole number is odd. Answer: E

41. Data Sufficiency Answer Choices • Answers: • A: 1 only • B: 2 only • C: 1 and 2 needed • D: either 1 or 2 is sufficient • E: neither is sufficient

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

43. 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 D A B Are statements (1) and (2) TOGETHER sufficient to answer the question? YES NO C E

44. Answer: A • The sum of three integers is 24. What are the three integers? • (1) Two of the integers are 4 and 16. • (2) The three integers are even.

45. Answer: B • The sum of three integers is 24. What are the three integers? • (1) The three integers are even • (2) Two of the integers are 5 and 15.

46. Answer: C • The sum of three integers is 24. What are the three integers? • (1) One integer is 8. • (2) One integer is 12.

47. Answer: D • The sum of three integers is 24. What are the three integers? • (1) Two of the integers are 4 and 8. • (2) Two of the integers are 5 and 11.

48. Answer: E • The sum of three integers is 24. What are the three integers? • (1) Two of the integers are odd. • (2) One of the integers is 6.

49. Data Sufficiency Sample Problems

50. How much is 20 percent of a certain number? • (1) 10 percent of the number is 5. • (2) 40 percent of twice the number is 40. Answer: D