Gruber's Complete GRE Guide 2015   Gruber, Gary R
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Gruber's Complete GRE Guide 2015 Gruber, Gary R


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refer to the figure below:
 A
D
B
C
ABCD is a rectangle.
 73. What is BC if AD 5 6?
(A) 4
(B) 6
(C) 8
(D) 10
(E) 12
 74. What is DC if AB 5 8?
(A) 4
(B) 6
(C) 8
(D) 10
(E) 12
 75. What is DB if AC 5 10?
(A) 4
(B) 6
(C) 8
(D) 10
(E) 12
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48 \u2022 GRUBER\u2019S COMPLETE GRE GUIDE 2015
Questions 76277 refer to the diagram below:
10
4
 76. The area of the figure is
(A) 14
(B) 40
(C) 80
(D) 28
(E) None of these.
 77. The perimeter of the figure is
(A) 14
(B) 28
(C) 36
(D) 40
(E) None of these.
Questions 78279 refer to the figure below:
A
D
3
B
C
ABCD is a square; AD 5 3.
 78. What is the area of the square?
(A) 9
(B) 12
(C) 16
(D) 20
(E) None of these.
 79. What is the perimeter of the square?
(A) 9
(B) 12
(C) 16
(D) 20
(E) None of these.
 80. The volume of the rectangular solid below is
(A) 48
(B) 64
(C) 128
(D) 72
(E) None of these.
4
2
8
L. Number Lines
Questions 81282 refer to the diagram below:
3 2 1 1 2 3
a
0
b
22 2 111
 81. Which best defines the range in values of b?
(A) 22 , b , 1
(B) 0 , b , 2
(C) 0 , b , 1
(D) 23 , b , 3
(E) 0 , b
 82. Which best defines the range in values of a?
(A) 22 , a
(B) 22 , a , 21
(C) 22 , a , 0
(D) a , 21
(E) 23 , a , 0
M. Coordinates
Questions 83285 refer to the diagram below:
(g, h) (a, b)
(e, f ) (c, d)
b b
a
x
a
y
x
 83. How many of the variables a, b, c, d, e, f, g, h are 
positive?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
 84. How many of the variables a, b, c, d, e, f, g, h are 
negative?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
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THE 101 MOST IMPORTANT MATH QUESTIONS YOU NEED TO KNOW HOW TO SOLVE \u2022 49
 85. If a 5 3, b 5 4, what is x?
(A) 3
(B) 4
(C) 5
(D) 6
(E) None of these.
 86. 
 
(4, 3)
(2, 1)
x
y
What is the slope of the line above?
(A) 21
(B) 0
(C) 11
(D) 12
(E) 13
N. Inequalities
Note: Any variable can be positive or negative or 0.
 87. If x . y, then 4x . 4y
(A) always
(B) sometimes
(C) never
 88. If x 1 y . z, then y . z 2 x
(A) always
(B) sometimes
(C) never
 89. If 24 , 2x, then 14 . 1x
(A) always
(B) sometimes
(C) never
 90. If m . n, where q is any number, then qm . qn
(A) always
(B) sometimes
(C) never
 91. If x . y and p . q, then x 1 p . y 1 q
(A) always
(B) sometimes
(C) never
 92. If x . y and p . q, then xp . qy
(A) always
(B) sometimes
(C) never
O. Averages
 93. What is the average of 30, 40, and 80?
(A) 150
(B) 75
(C) 50
(D) 45
(E) None of these.
 94. What is the average speed in mph of a car traveling 
40 miles in 4 hours?
(A) 160
(B) 10
(C) 120
(D) 30
(E) None of these.
P. Shortcuts
 95. Which is greater? Don\u2019t calculate a common 
denominator!
16
7 or 
7
3
(A) 
16
7
(B) 
7
3
(C) They are equal.
(D) A relationship cannot be determined.
 96. Add 
12
7
5
3
+ 5
(A) 1 60
11
(B) 1 60
13
(C) 1 60
15
(D) 
17
10
(E) None of these.
 97. Subtract: 
12
7
5
3\u2013 5
(A) 
60
12
(B) 2 60
3
(C) 21 60
11
(D) 
7
4
(E) None of these.
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50 \u2022 GRUBER\u2019S COMPLETE GRE GUIDE 2015
 98. 
250
4 5
(A) .016
(B) .04
(C) .004
(D) .025
(E) None of these.
Note: Do not divide 250 into 4 in the above question!
 99. What is c if
 200 2 and 80 3 ?
a b c a b
= + + = +
(A) 160
(B) 140
(C) 120
(D) 100
(E) None of these.
 100. What is the value of 95 3 75 2 95 3 74? (Don\u2019t 
multiply 95 3 75 or 95 3 74!)
(A) 65
(B) 75
(C) 85
(D) 95
(E) None of these.
 101. Find the value of
 
5 7
140 15
#
# (Don\u2019t multiply 140 3 15!)
(A) 20
(B) 40
(C) 60
(D) 90
(E) None of these.
GRE2015_P03.indd 50 4/18/14 11:27 AM
51
101 Math Questions: 
Answers, Diagnoses, Solutions, 
Generalizations, and Rules
GRE2015_P03.indd 51 4/18/14 11:27 AM
52
101 Math Questions: 
Answers
A. Fractions
 1. B
 2. A
 3. A
 4. C
 5. B
B. Even]Odd Relationships
 6. A
 7. B
 8. B
 9. B
 10. A
 11. B
 12. B
C. Factors
 13. A
 14. C
 15. B
 16. D
 17. C
 18. A
 19. D
 20. A
 21. C
D. Exponents
 22. C
 23. B
 24. B
 25. C
 26. A
 27. A
 28. A
 29. C
 30. A
 31. B
 32. D
E. Percentages
 33. B
 34. C
 35. C
F. Equations
 36. C
 37. A
 38. B
 39. A
 40. A
G. Angles
 41. B
 42. A
 43. A
 44. C
H. Parallel Lines
 45. B
 46. A
 47. B
 48. B
 49. A
 50. A
 51. B
I. Triangles
 52. A
 53. A
 54. B
 55. B
 56. B
 57. C
 58. B
 59. C
 60. C
 61. B
 62. B
 63. D
 64. A
 65. B
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THE 101 MOST IMPORTANT MATH QUESTIONS YOU NEED TO KNOW HOW TO SOLVE \u2022 53
J. Circles
 66. B
 67. A
 68. B
 69. A
 70. C
K. Other Figures
 71. C
 72. B
 73. B
 74. C
 75. D
 76. B
 77. B
 78. A
 79. B
 80. B
L. Number Lines
 81. C
 82. B
M. Coordinates
 83. D
 84. D
 85. C
 86. C
N. Inequalities
 87. A
 88. A
 89. A
 90. B
 91. A
 92. B
O. Averages
 93. C
 94. B
P. Shortcuts
 95. A
 96. A
 97. A
 98. A
 99. A
 100. D
 101. C
GRE2015_P03.indd 53 4/18/14 11:27 AM
54
Basic Skills Math Diagnosis
 *If you got any of Complete Math Refresher:
 the answers to Refer to the numbered
 the following sections listed below of the
 questions Math Refresher (Part 6, 
 wrong, study starting on page 187)
 answers to those Page in text for a refresher
Math area Total questions questions. for review on the applicable rules.
A. Fractions 5 125 55 1012112, 1232129
B. Even\u2013Odd Relationships 7 6212 55 6032611
C. Factors 9 13221 55256 409
D. Exponents 11 22232 56 4292430
E. Percentages 3 33235 57 106, 107, 114
F. Equations 5 36240 57 4062409
G. Angles 4 41244 57258 5002503
H. Parallel Lines 7 45251 58 504
I. Triangles 14 52265 58260 306\u2013308, 505\u2013516
J. Circles 5 66270 61 310\u2013311, 524\u2013529
K. Other Figures 10 71280 61262 3032305, 309, 3122316, 517\u2013523
L. Number Lines 2 81282 62 410a
M. Coordinates 4 83286 62 410b2418
N. Inequalities 6 87292 63 4192428
O. Averages 2 93294 63 601
P. Shortcuts 7 952101 63264 128, 609
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55
Solutions, Generalizations, and Rules
A. Fractions
 1. (B)
Alternate way:
c
b
a
c
b
a
c
c
c
b c
ac
b
ac#
#
= = =
 2. (A)
1
1
1
1
y
y
y
INVER
T T
O
MULT
IPL
Y
 3. (A)
c
b
a
c
b
a
b
b
cb
a#
#
= = =
bc
a
 4. (C)
 5. (B)
Alternate way:
a
b
b
a
a
b a
b
a a
a
b a
b
a
b
b
a
b b
b
a b
b
a
2 2 2
2
2
#
#
#
#
= = = = =
B. Even]Odd Relationships
 6. (A) ODD 3 ODD 5 ODD
3 3 3 5 9; 5 3 5 5 25
 7. (B) ODD 1 or 2 ODD 5 EVEN 
5 1 3 5 8
5 2 3 5 2
 8. (B) EVEN 3 EVEN 5 EVEN
2 3 2 5 4; 4 3 2 5 8
 9. (B) EVEN 1 or 2 EVEN 5 EVEN
6 1 2 5 8; 10 2 4 5 6
 10. (A) (ODD)ODD 5 ODD
33 5 3 3 3 3 3 5 27 (odd)
127 5 1 (odd)
 11. (B) (EVEN)EVEN 5 EVEN
22 5 4 (even); 42 516 (even)
 12. (B) (EVEN)ODD 5 EVEN
23 5 2 3 2 3 2 5 8 (even)
41 5 4 (even)
C. Factors
 13. (A) (x 1 3)(x 1 2) 5 x2 \u2026
 
 
(x 1 3)(x 1 2) 5 x2 1 2x 1 3x \u2026
 
(x 1 3)(x 1 2) 5 x2 1 2x 1 3x 1 6
 
(x 1 3)(x 1 2) 5 x2 1 5x 1 6
 14. (C) (x 1 3)(x 2 2) 5 x2 \u2026
 
 
(x 1 3)(x 2 2) 5 x2 2 2x 1 3x \u2026
 
(x 1 3)(x 2 2) 5 x2 2 2x 1 3x 2 6
 
(x 1 3)(x 2 2) 5 x2 1 x 2 6
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56 \u2022 GRUBER\u2019S COMPLETE GRE GUIDE 2015
 15. (B) (x 2 3)( y 2 2) 5 xy \u2026
 
 
(x 2 3)( y 2 2) 5 xy 2 2x 2 3y \u2026
 
 
(x 2 3)( y 2 2) 5 xy 2 2x 2 3y 1 6
 16. (D) (a 1 b)(b 1 c) 5 ab \u2026
 
 
(a 1 b)(b 1 c) 5 ab 1 ac 1 b2 \u2026
 
(a 1 b)( b 1 c)