GMAT Math Prep

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

• 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

• 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 lt k lt 7, for how
  many different values of k is there a triangle
  with sides 2, 7, and k?
• One
• Two
• Three
• Four
• Five

8

• 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

• 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

• 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 lt k lt 7, for how
  many different values of k is there a triangle
  with sides 2, 7, and k?
• One
• Two
• Three
• Four
• Five

16

• 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 lt k lt 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 lt k lt 6
26
Try the first givenby itself.
27
14. Is the integer k a prime number? (1)
2k 6 (2) 1 lt k lt 6
YES
28
2. Try the second givenby itself.
29
14. Is the integer k a prime number? (1)
2k 6 (2) 1 lt k lt 6
NO
30
3. Look at your two answers together.
31
14. Is the integer k a prime number? (1)
2k 6 (2) 1 lt k lt 6
YES
NO
32
4. If either answer is YESthen you are
finished.
33
3 Possibilities

• YES
• NO
• NO
• YES
• YES
• YES

• A
• B
• D

34
14. Is the integer k a prime number? (1)
2k 6 (2) 1 lt k lt 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

• YES NO
• NO YES
• NO NO
• YES YES
• NO NO

• A
• B
• C
• D
• E

YES
NO
43
(No Transcript)
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
51

• A thoroughly blended biscuit mix includes only
  flour and baking powder. What is the ratio of the
  number of grams of baking powder to the number of
  grams of flour in the mix?
• (1) Exactly 9.9 grams of flour is contained in
  10 grams of the mix.
• (2) Exactly 0.3 gram of baking powder is
  contained in 30 grams of the mix.

Answer D
52
3. What is the value of ? (1) (2)
x2 4
Answer B
53

• 4. Is r greater than 0.27?
• (1) r is greater than .
• (2) r is equal to .

Answer B
54
5. What is the value of the sum of a list of n
odd integers? (1) n 8 (2) The square of
the number of integers on the list is 64.
Answer E
55
k
m

• 6. In the figure above, if lines k and m are
  parallel, what is the value of x ?
• (1) y 120
• (2) z 60

Answer D
56

• What percent of a group of people are women with
  red hair?
• (1) Of the women in the group, 5 percent have
  red hair.
• (2) Of the men in the group, 10 percent have
  red hair.

Answer E
57

• If r and s are positive integers, r is what
  percent of s ?
• (1)
• (2)

Answer D
58

• Is it true that a gt b ?
• (1) 2a gt 2b
• (2) a c gt b c

Answer D
59
10. In a certain class, one student is to be
selected at random to read. What is the
probability that a boy will read? (1)
Two-thirds of the students in the class are
boys. (2) Ten of the students in the class are
girls.
Answer A
60
(No Transcript)
61
SUMMARY

• Outcome

• Answer

• YES NO
• NO YES
• NO NO
• YES YES
• NO NO

• A
• B
• C
• D
• E

YES
NO
62
11. If 5x 3y 17, what is the value of x
? (1) x is a positive integer. (2) y
4x
Answer B
63
12. Does the product jkmn equal 1 ? (1)
(2)
Answer B
64
13. A certain expressway has exits J, K, L, and
M, in that order. What is the road distance from
exit K to exit L? (1) The road distance from
exit J to exit L is 21 kilometers. (2) Th
e road distance from exit K to exit M is
26 kilometers.
Answer E
65
14. Is the integer k a prime number? (1) 2k
6 (2) 1 lt k lt 6

• Answer A

66

• Answer D

15. If ab ? 0, in what quadrant of the
coordinate system does point (a, b) lie? (1)
(b, a) lies in quadrant IV. (2) (a, -b) lies in
quadrant III.
67
16. Is x greater than 1.8 ? (1) x gt
1.7 (2) x gt 1.9

• Answer B

68
17. If n is an integer, is n 1 odd
? (1) n 2 is an even integer. (2) n 1
is an odd integer.

• Answer D

69
18. Is 1 lt x lt 2 ? (1) 0 lt x (2) x lt 3

• Answer E

70
(No Transcript)
71
SUMMARY

• Outcome

• Answer

• YES NO
• NO YES
• NO NO
• YES YES
• NO NO

• A
• B
• C
• D
• E

YES
NO
72
19. Water is pumped into a partially filled tank
at a constant rate through an inlet pipe. At the
same time, water is pumped out of the tank at a
constant rate through an outlet pipe. At what
rate, in gallons per minute, is the amount of
water in the tank increasing? (1) The amount
of water initially in the tank is 200
gallons. (2) Water is pumped into the tank at
a rate of 10 gallons per minute and out of the
tank at a rate of 20 gallons every 2 ½ minutes.

• Answer B

73
20. Is x a negative number ? (1) 9x gt
10x (2) x 3 is positive

• Answer A

74
21. Does 2m 3n 0 ? (1) m ? 0. (2) 6m
9n

• Answer B

75
22. What is the value of the integer x
? (1) x is a prime number. (2) 31 x
37

• Answer E

76
23. If P, Q, and R are three distinct points, do
line segments PQ and PR have the same length
? (1) P is the midpoint of line segment
QR. (2) Q and R lie on the same circle with
center P.

• Answer D

77
24. Is the number x between 0.2 and 0.7
? (1) 560x lt 280 (2) 700x gt 280

• Answer C

78
25. If i and j are integers, is i j an
even integer ? (1) i lt 10 (2) i j

• Answer B

79
26. If n k m, what is the value of
k? (1) n 10 (2) m 10 n

• Answer B

80
27. Is the triangle above equilateral ? (1) x
y (2) z 60

• Answer C

81
28. Is x an integer ? (1) is an
integer. (2) 2x is an integer.

• Answer A

82
29. What is the value of x ? (1) 2x 1
0 (2) (x 1)2 x2

• Answer D

83

• 30. What is the value of ?
• (1) k r 20
• (2) kr 64

• Answer C

84

• 31. If x is equal to one of the nos.
• what is the value of x ?
• (1)
• (2)

• Answer E

85

• 32. In triangle PQR, if PQ x, QR x 2, PR
  y, which of the three angles of triangle PQR is
  the greatest degree?
• (1) y x 3
• (2) x 2

• Answer A

86

• 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

87

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

• Answer D

88

• 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

89

• 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

90

• 37. What is the value of xy yz ?
• (1) y 2
• (2) x z 5

• Answer C

91

• 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

92

• 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

93

• 40. What is the value of the integer n?
• (1) n (n 1) 6
• (2)

• Answer B

94

• 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

95
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

96

• 43. Is x equal to 5?
• (1) x gt 5
• (2) x lt 5

• Answer C

97

• 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

98

• 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

99

• 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

100

• 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

101

• 48. If xy is not equal to 0, is lt 0?
• (1) x -y
• (2) - x - (-y)

Answer D
102

• 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

103

• 50. If x and y are positive, is greater
  than 1?
• (1) x y gt 1
• (2) x y gt 0

• Answer B