algebra and arithmetic page 186 - 199

8/12/2019 Algebra and Arithmetic Page 186 - 199

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Chapter No. 19 Arithmetic and Algebra

186

1. (19 18 17 16) (20 19 18 17) =A) 36 B) 6 C) 4 D) 1 E) 2

2. If 3x2 = 7, then 4x=

A) 3 B) 5 C)

3

20 D) 9 E) 12

3. Of the following, which is closest to 3 30 ?

A) 6 B) 5 C) 4 D) 3 E) 2

4. Which of the following is a solution toxx2= 1?

A) 1 B) 0 C) D) 1 E) None of these

5. Ifxy0,

xy

x 1

A)xyx

11 B)

xyy

x 1 C) x

y

1 D)

xyy

11 E)

yxy

11

6. 2[2x+ (3x+ 5x)]

(3x+ 5x) =A) 4x B) 8x C) 10x D) 12x E) 22x

7. If ,03

2

y

xwhich of the following must be true?

A)x= 2 and y= 3 B)x= 2 and y3 C)x= 0 and y= 0 D)x= -2 and y= 3

E)x= -2 and y3

8.3

69 22

=

A) 1 B)

9

15 C) 5 D) 8 E) 15

9. If 3(x+ 2) =x4, thenx=A) 5 B) 3 C) 1 D) 3 E) 5

10. Ifx2+ 2xy+ y

2= 9, then (x+ y)

4=

A) 3 B 18 C) 27 D) 36 E) 81

CHAPTER

19

ARITHMETIC AND ALGEBRA

PRACTICE TEST


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187

11.

22

3

11

2

11

=

A)36

25 B)

3

1 C)

6

1 D)

9

1 E)

18

1

12. 6x2

15x

21 =A) 3(2x+ 7)(x1) B) 3(2x7)(x+ 1) C) 3(2x1)(x+ 7) D) 9x

221 E) 9x21

13. If 2x+ y= 8 and 3x= 6, then y=A) 2 B) 4 C) 6 D) 8 E) 12

14. Ifx= 3 and y= 3, what is the value of (3 + x)(3 y)?A) 36 B) 12 C) 0 D) 12 E) 36

15. 2

22

2

46

A) 1 B) 2 C) 3 D) 4 E) 5

16. If y= 2x

1, what is the value ofxin terms of y?

A) 12

y B)

2

1

2

y C)

2

1

2

y D) 1

2

y E)

2

1y

17.

2222

22222

A) 1 B) 2 C) 4 D) 8 E) 16

18. If 4xis 6 less than 4y, then yx=

A) 24 B)2

3 C)

3

2 D)

2

3 E) 24

19. (1

x)(x

1) =A) (x1)

2 B) (x1)

2 C) 0 D)x

21 E) 1 x

2

20. If 8x3y= 24 and y = 0, thenx=A) 3 B) 4 C) 5 D) 6 E) 8

21. If n= 3, what is the value of 22n

+ 1?A) 9 B) 13 C) 17 D) 33 E) 65

22. 3 2

2

A) B) 1 C) 3 D) 6 E) 6

23. If 7x

4y= -1 and 5x+ 3y= 52, thenx

y=A) 4 B) 3 C) 3 D) 4 E) 5

24. If 2x+ 3y= 15 and y= 1, then 2x=A) 18 B) 12 C) 10 D) 9 E) 3

25. If 2632

x

, thenx=

A) 8 B) 4 C) 4 D) 6 E) 8


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26. (3 100)+(4 1)+(5 1,000)+(6 10)=A) 3,456 B) 3,564 C) 4,635 D) 5,346 E) 5,364

27. Of the following, which is most nearly equal to3

2?

A) 4

3

B) 6

5

C) 9

7

D) 15

11

E) 21

15

28. If ,3

1

3

43

xxthenx=

A) 7 B) 9 C) 11 D) 13 E) 15

29.

6

9

4

9

4

9

4

9

4

9

4

9

4

A)27

2 B)

9

4 C)

3

2 D)

3

8 E) 6

30. If y =ba

a

and ,

b

ax what is yin terms ofx?

A)x

1 B) 1 +x C)

x

11 D)

x1

1 E)

x

x

1

31.

4

1

3

1

4

1

3

1

A) 0 B)7

1 C)

2

1 D) 1 E) 7

32. Of the following, which is the closest approximation to

?

51.0

261.0942.972

A) 1 B) 5 C) 10 D) 20 E) 100

33. If y0 and 2x+ y= 12, then which of the following is NOT a possible value of x?A) 12 B) 10 C) 8 D) 6 E) 4

34. If 4x+ 3y= 8 and ,4

1

2

xwhat is the value of y?

A)3

4 B) 2 C)

3

7 D) 3 E)

3

10

35. Forx2 andx3,

32

2

x

x

x

A) 1 B)3

1

x C)

52

2

x

x D)

322

xx

x E)

3264

2

xx

xx


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189

36. If 9x3 = 15, then 3x1 =

A)3

5 B) 3 C) 5 D) 6 E) 45

37. If the sum of 12, 15, andxis 45, then the product of 5 and (x+ 2) isA) 100 B) 92 C) 80 D) 41 E) 25

38.

4

3

3

3

2

2

2

1

1

A)9

1 B)

12

13 C)

12

29 D) 8 E) 9

39. 0.50% =

A)500

1 B)

200

1 C)

50

1 D)

20

1 E)

2

1

40. If 1512 x

, thenx=

A) 5 B) 7 C) 13 D) 28 E) 29

41. If 2(x+ y) = 5, then, in terms ofx, y=

A) x2

5 B) x

2

5 C) x25 D)

25

x E)

22

5 x

42. 223 A) 1 62 B) 61 C) 625 D) 325 E) 1

43. Ifx

3

8

5 and ,

5

1y what is the value ofx+ 6y?

A)30

41 B) 2 C)

5

16 D) 6 E)

15

203

44. The expression21

21

is equivalent to which of the following?

A) 1 + 23

2 B) 2

3

21 C) 1 D) 3 + 22 E) 223

45. 2

1

4

1

8

1

16

1

32

1

32

1

A)4

3 B)16

15 C)32

31 D) 1 E)2

3

46. Ifx= 2w, z= 3x, and wz 0, what is the value of ?2

wz

x

A)3

2 B) 1 C)

3

4 D) 4 E) 6


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47. The expression ,1

1

1

n

n

where nis not equal to 0 or 1, is equivalent to which of the following?

A)1

1

n B)

n1

1 C) n1 D)

1n

n E)

n

n

1

48. 320

+ 320

+ 320

=A) 9

60 B) 9

20 C) 3

60 D) 3

23 E) 3

21

49. Which of the following is NOT a divisor of 264?A) 4 B) 8 C) 9 D) 11 E) 12

50. If 3(x+ 1) = 4x1, thenx=

A)7

4 B)

4

3 C) 2 D) 3 E) 4

51.

22

4

1

24

3

2

A)8

37 B)

2

9 C) 3 D) 1 E)

2

1

52. If n+ n= k+ k + kand n + k=5, then n=A) 2 B) 3 C) 5 D) 6 E) 9

53. If 2x= 7 and 3y= 2, then 9xy=A) 14 B) 18 C) 21 D) 28 E) 63

54. If ,16x thenx=

A) 4 B) 8 C) 16 D) 32 E) 256

55. If 2rs= 3s2r, what is sin terms of r?

A)3

r B)

2

r C) r D) 2r E) 3r

56. If 0.768 =100

x, thenxis closest to which of the following?

A) 0.77 B) 0.80 C) 8 D) 76 E) 77

57. Ifx= 2 and y = -2, then 2x2y=A) 8 B) 0 C) 4 D) 6 E) 8

58. What value ofxsatisfies the equationx

1 = 1

x?A) 2 B) 1 C) 0 D) 2 E) No value

59. If n1 = ,3

2then n+ 1 =

A)3

4 B)

3

5 C)

3

7 D)

3

8 E)

3

11


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191

60. Multiplying which of the following by the nonzero number7

25 xwill give a product of 1?

A)x25

7

B)

52

7

x C)

52

7

x D)

7

52 x E) 7(2x5)

61. If 2x+ 7 = 12, then 4x7 =A) 2 B) 2.5 C) 3 D) 10 E) 13

62. Ifx + y= n, thenx2+ 2xy+ y

2=

A) 2n B) n2 C) n(x y) D) n

2+ 2y(n y) E) n

2+xnx

2

63. Ifxis an integer and y= 9x+ 13, what is the greatest value of xfor which yis less than 100?A) 12 B) 11 C) 10 D) 9 E) 8

64. If7

1of a certain number is 4, then

4

1of the number is

A)16

7 B) 2 C)

7

16 D) 7 E) 28

65. If a+ b= 10, then

22

ab

ba

A) 5 B) 10 C) 15 D) 20 E) 25

66. If the sum of the first npositive integers is equal to 2

1nn, then the sum of the first 25 positive

integers isA) 51 B) 52 C) 313 D) 325 E) 326

67. If ,9

12

3

12

xthenx=

A)2

3 B)

2

5 C) 4 D)

2

13 E) 7

68.

512

5272712

A) 0 B) 1 C)7

60 D) 27 E) 189

69. Ifx y = 0, thenxymust equal which of the following?A) 0 B) 1 C)x D)x

2 E)x

2y

70. If ,7

7

4

13

n then nis

A) greater than 3 B) between 2 and 3 C) between 1 and 2 D) between 0 and 1E) less than 0

71. If y= 2, then y+ (y2)3=

A) 32 B) 34 C) 64 D) 66 E) 128

72. If 6 + 5x= 30 x, thenx=A) 4 B) 5 C) 6 D) 7 E) 8


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73. Which of the following is equal to 456(72) + 28(456)A) (72)(456 + 28) B) (456) (72 + 28) C) (456 + 28) (72 + 456) D) (456 + 72) (28 + 456)E) (456 + 456) (72 + 28)

74. If k=7

6xand k0, then

k

x

7

2

A)6

1 B)49

12 C)7

2 D)3

1 E)7

6

75. If 2x+ y= 10 and 2x= 4, then y=A) 2 B) 6 C) 7 D) 8 E) 14

76.

3

3

4

A) B) 3 C) 4 D) 12 E) 36

77.

3

33 23

A) 0 B) 1 C) 3 D) 6 E) 9

78. If of a certain number is 2, then of the number is

A)8

1 B) C) 1 D) 4 E) 8

79. 2.34 2 5

1

A) 0.09 B) 0.14 C) 0.19 D) 0.29 E) 0.32

80. If n ,11

5

11

6 then n=

A) 11 B) 1 C)11

1 D)

11

1 E) 11

81. Which of the following expressions has (have) the same value for n= 5 as for n= ?5

1

I. n +n

1

II. n n

1

III.

n

n

1

A) I only B) II only C) III only D) I and II E) II and III

82. Ifp=3

2and r= 4, then

9

13 pp

r

A) 1 B)9

5 C)

9

5 D) 1 E)

9

11


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83. If 3x+ 5 = 2x+ 10, thenx=A) 1 B) 2 C) 3 D) 5 E) 15

84.3

1

3

1 equals how many twelfths?

A) 2 B) 4 C) 6 D) 8 E) 9

85. Of the following fractions which has the least value?

A)7

8 B)

9

8 C)

6

5 D)

8

7 E)

9

7

86. If a = 3b+ c, what is the value of bwhen a= 17 and c= 2?

A) 5 B)3

16 C) 12 D) 15 E) 45

87. 6

3

1

A) 2 B)2

1 C)

3

1 D)

9

1 E)

18

1

88. If 4x2y= 8, what is the value of 2xy?A) 3 B) 4 C) 5 D) 6 E) It cannot be determined

89. What is the least numberxfor which (2x+ 1) (x2) = 0?

A) 2 B) 1 C)2

1 D)

2

1 E) 2

90. 52.68 100

1

A) 0.05268 B) 0.5268 C) 5.268 D) 526.8 E) 52.680

91. If bc= 3, and a+ c= 32, then a + b=A) 30 B) 35 C) 40 E) 42 E) 50

92. If x 0, then

2

32

x

xx

A)x2 B)x

3 C)x

4 D)x

5 E)x

93. Seven is equal to how many thirds of seven?

A)3

1 B) 1 C) 3 D) 7 E) 21

94. Which of the following equals the reciprocal ofxy

1 , wherex

y

10?

A) yx

1 B)

x

y C)

1x

y D)

1xy

x E)

1xy

y

95. 1125642 A) 6 B) 18 C) 36 D) 120 E) 1,296


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96. What is the remainder when 63is divided by 8?

A) 5 B) 3 C) 2 D) 1 E) 0

97. If y= 3xand z= 2y, then in terms ofx,x + y + z =A) 10x B) 9x C) 8x D) 6x E) 5x

98. Which of the following equations can be used to find the value ofxif 8 more than 9xis 3 times thesum of 6 andx?A) 9x+ 8 = 3x+ 6 B) 8 + 9x= 3(x6) C) 9x+ 8 = 3(x+ 6) D) 3(8 + 9x) = 6xE) 9x+ 8 = 3 + 6 +x

99. Which of the following is equivalent to

32

1

2?

A) 24 B) 2

2 C)

2

1 D)

22

1 E)

42

1

100. If 6x4 = 5x+ 3, thenx=A) 7 B) 1 C) 1 D) 7 E) 12

101. Ifpis a positive integer, which of the following could be a prime number?A) 8p B) 8p+ 1 C) 8p+ 2 D) 8p+ 4 E) 8p+ 6

102. The sum of 2 numbers,xand y, equals twice their product. Ifx= 3, what is the value of y?

A)8

1 B)

5

3 C)

2

3 D)

3

5 E)

3

7

103. If n6

1=5

1, then n=

A)30

1 B)

6

5 C)

5

6 D) 6 E) 30

104. The value of

4

31

7

51 is

A)28

1 B)

14

3 C)

28

9 D)

28

13 E)

2

1

105.

305

118

3

1

155

29

3

2

A) 2 B) 1 C)2

1 D)

3

1 E)

4

1

106. If 2x= -10, then 4x26x5 =

A) 65 B) 75 C) 125 D) 130 E) 135

107. Ifx0, then

xx

x 1

7

7

A)x

x

6

6 B)

x

x

7

6 C)

x

x

7

76 D)

7

1 E)

7

1


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195

108. 1+2

1+3

1+

4

1+5

1=

A)25

32 B)

60

117 C)

25

52 D)

50

109 E)

60

137

109. If y= 21

2 x

andx= 3, then y=A) 8 B) 16 C) 32 D) 64 E) 128

110. If 6x4y= 2 andx= 3, thenx+ y=A) 4 B) 5 C) 7 D) 12 E) 19

111. Ifx+ 2y= 2xy, thenx=

A) y B)3

y C) y D) 2y E) 3y

112. In the equation kx+ y= 16, kis a constant. If y= 6 whenx= 2, what is the value of ywhenx= 4?

A) 8 B) 4 C)4

11 D) 5 E) 12

113. If aand bare integers and ab= 6, then a + b CANNOT beA) 0 B) less than 6 C) greater than 6 D) an even integerE) an odd integer

114. If ax+ by= 10, then 2ax+ 2by=A) 5 B) 12 C) 14 D) 20 E) 40

115.

01.0

001.01.0

A) 0.01 B) 0.001 C) 0.0001 D) 0.00001 E) 0.000001

116. If ,3

2

1 yx what is yin terms ofx?

A) x5

2 B)

5

2

5

2x C) 1

5

2x D)

5

2

2

5x E) 1

2

3x

117. If 9 is4

3n, what number is

6

5n?

A) 10 B) 12 C) 14.4 D) 15 E) 27

118. Ifx= 3, y= -1, and z= 1, which of the following is (are) true?I. x + y + z = 3II. y + 2z = 2

III. x

2z= 1A) I only B) III only C) I and II only D) I and III only E) I, II, and III

119. Of the following, which is closest to ?9.9

39726.0

A) 1 B) 10 C) 70 D) 100 E) 700


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196

120. Ifxyz0 and if n=y

xzand ,

z

xyq then

nq

1

A)z

x B)

y

x C)xyz D)x

2 E)

2

1

x

121. If 2x

5 = 25, thenx=

A) 30 B) 20 C) 15 D) 122

1 E) 5

122. If 2x+ 1 = 9 and y=x2, then y=

A) 25 B) 16 C) 8 E) 4 E) 2

123. What is the least prime number greater than 83?A) 85 B) 87 C) 88 D) 89 E) 91

124. If 2 16 =p 4 8, thenp=A) 8 B) 4 C) 2 D) 1 E)

125. If a+ 3 = 4, what is the value of37

aa ?

A)2

1 B) 2 C)

3

7 D) 3 E) 4

126.

6

11

9

24

A)27

133 B)

21

76 C)

16

44 D)

11

28 E)

4

5

127. If ,4

3

y

xthen

y

yx

A)7

3 B)

7

4 C) 1 D)

7

11 E)

4

7

128. Which of the following numbers is both a factor of 48 and a multiple of 6?A) 2 B) 8 C) 12 D) 16 E) 18

129. If 2n= 32, then n

2=

A) 25 B) 32 C) 64 D) 256 E) 1,024

130. |-2| + |7| + |-2 + 7| =

A) 18 B) 14 C) 10 D) 5 E) 0

131. If 1 x= 1 + 3x, thenx=

A) 0 B) C) D)3

2 E) 1


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197

132. 3

2

2

3

A) 1 B)6

7 C)

3

4 D) 2 E)

6

13

133. Which of the following is greater than 1?

A)005.0

0004.0 B)

0001.0

000006.0 C)

003.0

01.0 D)

006.0

003.0 E)

01.0

001.0

134. If a= 2, b= 4, and c= 5, then

ba

c

c

ba C)

A) 1 B)30

11 C) 0 D)

30

11 E) 1

135. If ,1x

ythen y + x=

A) 2 B) 1 C) 0 D) 1 E) 2

136.

4

882

10

101010

A) 2(104) B) 2(10

6) C) 10

8 D) 2(10

8) E) 10

10

137. If q 0 and k= ,2

sqr

then what is rin terms of k, q, and s?

A)q

sk2 B)

q

sk2 C)

q

sk2 D)

q

sqk2 E)

q

sk2

138. If y = 8x+ 12 andx = z + 2, what is yin terms of z?A) z+ 14 B) 8z4 C) 8z+ 10 D) 8z+ 14 E) 8z+ 28

139.

1

1

11

x

x

x

x

A) 0 B) 1 C)1

1

x D)

1x

x E)

1

2

x

x

140. 122+ 13

2

13

1213122

A) 313 B) 289 C) 169 D) 25 E) 1

141. Ifx= 2y= 3z= 36, then the average (arithmetic mean) ofx, y, and z is

A) 33 B) 22 C) 18 D) 12 E) 6

142. The sum of ndifferent positive integers is less than 100. What is the greatest possible value of n?A) 10 B) 11 C) 12 D) 13 E) 14

143. If aand bare positive integers, then the ratio ofb

ato its reciprocal is

A) 1 B)b

a C)

a

b D)

2

2

b

a E)

2

2

a

b


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144. If 2n= 128, then (2

n1)(5

n2) =

A) 107 B) 5(10

6) C) 2(10

6) D) 5(10

5) E) 2(10

5)

145.185.0

81.3is closest to

A) 2,000 B) 200 C) 20 D) 2 E) 0.2

146. Ifxis an odd integer, for which of the following equations must ybe an even integer?A)xy= 5 B)x+ y= 8 C)x+ 2y= 7 D) 2(x+ y) = 7 E) 2x+ y= 6

147. Ifx2y

2= 1 and the average (arithmetic mean) ofxand yis 4, what is the value of xy?

A)8

1 B) C) D) 2 E) 4

148.

4

5

5

A)5

1 B)

4

1 C) 4 D) 5 E)

4

25

149. If (2x1)2= 0, thenx=

A)4

1 B)

2

1 C) 0 D)

2

1 E)

4

1

150. Which of the following is equal to 25,000,000?

A) 25 107 B) 2.5 10

-7C) 2 10

6) + (5 10

5)

D) (20 107

) + (5 106

) E) (2 107) + (5 10

6)


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199

1. E

2. E

3. D

4. E

5. D

6. D

7. E

8. E

9. A

10. E

11. D

12. B

13. B

14. E

15. E

16. C

17. C

18. D

19. A

20. A

21. E

22. C

23. A

24. B

25. C

26. E

27. E

28. D

29. B

30. E

31. E

32. C

33. D

34. B

35. E

36. C

37. A

38. E

39. B

40. D

41. A

42. C

43. D

44. E

45. D

46. A

47. A

48. E

49. C

50. E

51. B

52. B

53. C

54. E

55. C

56. E

57. E

58. B

59. D

60. C

61. C

62. B

63. D

64. D

65. C

66. D

67. B

68. D

69. D

70. B

71. D

72. A

73. B

74. D

75. B

76. C

77. D

78. D

79. B

80. B

81. A

82. D

83. D

84. D

85. E

86. A

87. E

88. B

89. C

90. B

91. B

92. D

93. C

94. E

95. C

96. E

97. A

98. C

99. A

100. D

101. B

102. B

103. C

104. E

105. B

106. C

107. D

108. E

109. B

110. C

111. E

112. B

113. E

114. D

115. A

116. E

117. A

118. D

119. B

120. E

121. C

122. B

123. D

124. D

125. B

126. B

127. E

128. C

129. A

130. B

131. A

132. E

133. C

134. B

135. C

136. B

137. E

138. E

139. D

140. D

141. B

142. D

143. D

144. E

145. C

146. E

147. A

148. C

149. D

150. E

ANSWERS

algebra and arithmetic page 186 - 199

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