Exponents  125a 3 b 6 c 9 

2/3

13. Simplify  3  6 9

1. Solve for the value of x in 3 2 x  3 =  216 x y z 
2, 187. 25b 4 c 6 y 4 z 6
a. b.
a. 0 b. 1 c. 2 d. 3 36a 2 x 2
2. If 3x=6, what is the value of 34x-1?
a. 72 b. 432 c. 216 d. 108
25b 4 c 4 y 6 z 6 25b 6 c 6 y 4 z 4
c. d.
3. Solve for x in 81x/4=1/27. 36a 2 x 2 36a 2 x 2
a. -2 b. 3 c. 2 d. -3 25b 6 c 4 y 6 z 4
4. Find the value of x in the equation
36a 2 x 2
(73) (712) = 73x.
14. Under certain conditions, the
a. 5 b. 3 c. 12 d. 6
production of people informed through
5. Which of the following is equivalent
advertising after t weeks is
to 128x32y?
a. 25x+7y b. 26x+7y
c. 2 7x+5y
d. 27x+6y 25
P (t ) 
6. Which of the following is equivalent 40  12(6  25t )
to 5x+2 + 3(5x+1) – 40(5x)? What value does P(t) approach as t
a. 3(5x) b. -2(5x) becomes larger and larger?
c. 0 d. 5x a. 0.375 b. 0.785
7. Solve for x in the equation 2-100x= c. 0.625 d. 0.500
(0.50)x-4. 15. The number of bacteria after t
a. 4/99 b. -4/99 hours is 5.6(106)3t/5. How long will it
c. 4/101 d. -4/101 take for this number to triple?
8. If 16x = 25, what is the value of 22x? a. 4 hours b. 5 hours
a. 2 b. 3 c. 4 d. 5 c. 6 hours d. 7 hours
9. If 5x = 7y, what is the value of 16. The half-life of a radioactive
5x2/7y2? material is the time in which half of it
a. 25/49 b. 7/5 will disintegrated. If its amount after t
c. 5/7 d. 49/25 years is 5(2-t/90), what is half-life?
9x7 y 5 z 2 a. 45 hours b. 60 hours
10. Simplify . c. 75 hours d. 90 hours
3 xy 3 z 6
17. The population in thousands of a
3x 7 y 2 3x 6 y 2 country is P = 108(2.5)t/20 where t is
a. b.
z4 z5 measured years. How long will it take
3x 5 y 2 3x 5 y 2 for the population to increases by 150
c. d. percent?
z4 z5 a. 20 years b. 23years
( xy 2 ) 4 ( x 3 y 5 z 4 ) 3 c. 15 years d. 18 years
11. Simplify
( x 1 y 2 )( y 3 z  2 ) 1 18. A drug is eliminated from the body
through urination. Suppose that for an
y8 y8 initial dose of 15 milligrams, the
a. b.
x 14 z 12 x 12 z 14 amount x in the body t hours later is
y6 y6 given by x = 10(0.8)t. What
c. 14 12 d. 12 14 percentage of the drug still in the body
x z x z is eliminated each hour?
2 n 1
2( 7 )  5(7 2 n 5 ) a. 32% b. 24%
12. Simplify
3(7 2 n 3 ) c. 16% d. 20%
19. Find the last digit when 13 raised
a. 88.61 b. 86.18
to 655.
c. 61.88 d. 81.68
a. 1 b. 3 c. 7 d. 9
20. Find the last digit of 30. Solve for x in the given equation.
3128+7535+14860 a. 1.224 b. 1.442
a. 0 b. 1 c. 2 d. 3 c. 1.244 d. 1.242
31. Rationalize the denominator of
Radicals 8
.
8x 3 y 2
21. Perform the indicated operations
98  8  50 . 2 x 2 2x
a. b.
a. 4 2 b. 14 2 x2 y x2 y
c. 10 2 d. 6 2 x 2x
c. d. 2
22. Find the principal root of x y x2 y
2,500 x 16 y 10 z 2 . 32. Rationalize the denominator of
a. 25x8y5z2 b. 25x8y5z 10
8 5 2
c. 50x y y d. 50x8y5z 3
.
16a 4
23. Find the principal root of
4
0.00000016a 4 b 20 c 8 . 10  3 4a 2 5  3 4a 2
a. b.
a. 0.02ab5c2 b. 0.02a4b5c2 a2 2a 2
c. 0.20ab5c2 d. 0.20a4b5c2 5  3 2a 2 10  3 2a 2
24. Find the principal root of c. d.
2a 2 a2
6
729 x 12 y 6
33. Rationalize the denominator of
a. 3xy2 b. 3x2y2
128 x
c. 3xy d. 3x2y 5

25. Find the principal root of 375 y 7

243 p 10 5
8,100 x 2 y 3
5  . a. b.
32q 25 15 y 2
3p2 3q 2 5
8,100 x 2 y 3
a.  b.  2
2q 5 2 p5 15 y 2
3p2 3q 2 5
8,100 x 2 y 3
c. d. c. 2 
2q 5 2 p5 15 y 3
26. Simplify the radical 5p
x 13 p
y 7p
5
8,100 x 2 y 3
d.
a. x 2 y  5 p x 2 p y 3 p 15 y 3
b. x 2 y  5 p x 3 p y 2 p 34. Rationalize the numerator f
c. xy 2  5 p x 2 p y 3 p 5
64 x 6 y
d. x 2 y  5 p x 3 p y 2 p 3
16 xy 5
27. Find the principal roof of y y
a. b.
3
15,625r 12
s 15
. x  15 4 x y 7 2
x  15 4 x 2 y 7
a. 25r3s2 b. 25r2s3 x x
3 2 2 3
c. 5r s d. 5r s c. d. s
y  15 4 x 7 y 2 y  15 4 x 2 y 7
28. Solve for x in the given equation
3
2  4 16 8 x  2 .
4
32a 7 b 5
35. Rationalize
a. 32 b. 16 c. 64 d. 8 x  15 16a 8 b
29. Simplify the expression
a. b  20 512ab 3 b. b  20 512a 3 b
  16 p s
4 4 2
 4

c. a  20 512ab 3 d. a  20 512a 3 b
a. 16p4s2 b. -2ps1/2
4 2
c. -16p s d. none of the above
Logarithms
 a. mp = n b. mn = p
36. The base of a common or c. pm = n d. pn = m
Briggsian logarithm is 50. Find the number whose logarithm
a. 2 b. 1 c. 10 d. e is 2.3928
37. The base of a natural, hyperbolic, a. -247.0586 b. 0.3789
or Napierian logarithm is c. -0.3789 d. 247.0586
a. 2 b. 1 c. 10 d. e 51. Find the antilogarithm of 8.20189
38. The value of the Napierian base e – 10
is a. 0.9139 b. -0.9139
a. 1.414213562 b.3.1415926 c. 0.0159 d. -0.0159
c. 2.718281828 d. 10 52. Which of the following is the
39. Find the equivalent of cologarithm of 132 to the base 10?
1 1 1 1 1 a. 7.8794 b. 2.1206
     ... c. -7.7794 d. -2.1206
0! 1! 2! 3! 4!
a. I b. e c.  d. undefined 53. Solve the equation 5x = 64
a. 2.1584 b. 2.8541
40. The whole number part of the
c. 2.5841 d. 2.4581
logarithm is called
54. Solve for x in the equation log3
a. mantissa b. antilogarithm
c. cologarithmd. characteristics 5
x
41. The decimal part of the logarithm 4
is called a. 0.5233 b. 0.2533
a. mantissa b. antilogarithm c. 0.3253 d. 0.3352
c. cologarithmd. characteristics 55. If loga 10 = 0.25, what is the value
42. The characteristics of the of log10 a?
logarithm of 329.65 to the base 10 is a. 2 b. 4 c. 6 d. 5
a. 2 b. -3 c. 3 d. -2 56. Find the value of y in the equation
43. The characteristics of the  ex 
logarithm of 0.00078807 to the base y  In x 2 
10 is e 
a. 3 b. -3 c. 4 d. -4 a. 2 b. 4 c. 6 d. 5
44. The characteristics of the 57. Solve the equation (3x)(52x + 1) =
logarithm of 5.0932 to the base 10 is 63x – 2.
a. 1 b. -2 c. 0 d. -1 a. 4.9902 b. 4.9092
45. The mantissa of the logarithm of c. 4.9920 d. 4.2099
329.65 to the base 10 is 58. If log 2 = x and log 3 = y, find the
a. -0.5181 b. -0.4819 log 1.20.
c. -0.4819 d. -0.5181 a. 2x + y b. 2y
46. The mantissa of the logarithm of c. 2x + y – 1 d. xy – 1
0.00078807 to the base 10 is 59. The number of bacteria after t
a. -0.8966 b. -0.1034 hours is 4.8(104)2t/3. How long will it
c. 0.1034 d. 0.8966 take for the number to triple?
47. The mantissa of the logarithm of a. 4.75 hrs b. 3hrs
5.0932 to the base 10 is c. 3.75hrs d. 4hrs
a. 0.2930 b. 0.7070 60. The population, in thousands, of a
c. -0.2930 d. -0.7070 country is P = 108(1.5)t/20 where t is
48. The equation ax = y in logarithmic measured in years. How long will it
form is take for the population to increase by
a. logx a = y b. logx y = a 125 percent?
c. loga y = x d. loga x = y a. 25years b. 30years
49. The equation logpn = m in c. 35years d. 40years
exponential form is 61. The half – life of radioactive
material is the time in which half of life
it will disintegrate. If the amount after
t years is 5(7-t/90), what is its half – c. A = C d. None of the above
life? 68. Find the negative of the matrix
a. 60.23 yrs b. 63.02yrs 2 0 4
c. 23.06yrs d. 32.06yrs 5  3 8 
 
62. The rate at which a substance is
  2 0  4
converted to another substance is a. 
given by x = x0e -0.07t, where x0 is the  5 3 8 
initial amount of the substance and x  2 0  4
is the amount at any time t in b.  
  5  3  8
seconds. How many seconds must
 2 0 4 
elapse so that 90% of the substance is c. 
converted?  5 3  8
a. 32.89 sec b. 20 19 sec  2 0  4
d. 
c. 35.06sec d. 38.55 sec
 5  3  8 
63. Which of the following is the
2 0 4
logarithm of the imaginary number i? 69. Given the matrix  A  
5 3 8 
  e
i  log e i  log  , find 3 A 
a.  2  b.  2 
 6 0 12 
  e a.  
i  log e i  log  15 9 24 
c.  4  d.  2  6 0 15 
64. Which of the following is the b.  
logarithm of -6? 15  9 24
a. 1.3644 – 0.7782i 6 0 12 
c.  
b. 1.3644 – 0.7782i 15  9 24
c. 0.782 + 1.3644i  6 0 15 
d. 1.3644 + 0.7782i d.  
65. Determine the logarithm of zero to 15 9 24
the base a, where a may be any real 70. Given the matrices
 A  
number greater than 1. 2 0 4

a. imaginary b. zero 5  3 8 
c. positive infinity  3 5 9 
And  B   , find
d. negative infinity
 4 1  2
Matrix
Properties and Operations of Matrices  A   B .
66. Find the size of the matrix  1 5 13
a. 
2 0 4 9 2 6 
5  3 8 
   1 5 13
b. 
a. 3 x 3 b. 2 x 3 9  2 10
c. 3 x 2 d. 2 x 2  1 5 13
67. Given the matrices below c. 
9 2 6
  1 5 13
 A  
0 4
 C   
2 2 0 4 d. 
9 2 10
 3 8   
5 5 3  8
71. Given the matrices
 10 
 A  
2 0 4
 04 22  
 D 
2 0 
 B   5   5  3 8 
5(1)
6
64  5  3  3 5 9 
And  B   , find
 2   4 1  2
Which of the following is true?  A   B .
a. A = D b. A = B
 5 5  5  52  33 
a.  c.  d. 
1 4 6   33 
 
 52
5 5  5 75. Any square matrix  A multiplied
b. 
1 2 10  by an identity of the same order
5 5  5 equals:
c.  a.  0 b. –[A] c. [A] d. [l]
1 4 10 
5 5  5 Types of Matrices
d. 
1 2 6 
 4 3 76. When the number of rows m and
72. Given the matrices  A  
 2 5 the number of columns n are equal,
the matrix is said to be
 6  4
And  B    , find  A B  a. symmetric b. square
 3 1  c. identity d. zero
 33 19   2  1 77. When the elements of a square
a.   b.  1
  3  5  6 

matrix obey the rule aij = aji, the
matrix is said to be
 32  2 18 6 a. symmetric b. square
c.  d.
 14  4 10 9 
  c. identity d. zero
73. Given the matrices 78. When all the elements of a square
 3 2 8 matrix are zero, the matrix is said to
 A   1 5 0 and be
a. symmetric b. square
 9  2 4
c. identity d. zero
 4 10 0  79. When all the elements on the
 B    1 6 2  , find  A B  diagonal of a square matrix are equal
 2 4  3 to unity and all the other elements are
zero, the matrix is said to be
 19 96 0 a. symmetric b. square
  10 45 12 
a.   c. identity d. zero

 21  8 73 80. Find the minor of 4 in the matrix
1 12 8  2 4 1
  1  2 5 
b.  2  1 2  
 5 2 6
7 2 1

1 6 1 2
  26  10  20 a. b.
 5 5 5 2
c.  9  20 10 
1 6 1 2
 26 118  16  c.  d. 
5 5 5 2
2 58 32  81. Find the minor of A31 in the matrix
  32 16 
d.  9  1 5 2
  17 22  28  A   3  6 4

74. Given the matrices  8 0 7 
  5 3 6 5 2
 A  
3 0 6  3  b. 
and  B   , find
a.
4  8 0 6 4
1 5
 8  5 2 3 6
c. d. 
 A B  6 4 8 0
52 33
a.   b.  
33 52
82. Find the cofactor of 4 in the matrix 87. Find the determinant of the matrix
2 4 1  90 37 
1  2 5    22 16 
   
5 2 6 a. -626 b. -2, 254
1 5 1 2 c. 2,254 d. 626
a. b. 88. Find the determinant of the matrix
5 6 5 2
1 5 1 2
3  3 1 
c.  d.  1 5 2
5 6 5 2  
83. Find the cofactor of A31 in the 
4  2 4 
 1 5 2 a. 46 b. -32 c. 29 d. 38
 A  3  6 4 89. Find the determinant of the matrix
matrix  4 3 1 
 8 0 7  10  6  16 
3 6 5 2  
a. b.  
 6 7 1 

8 0 6 4
5 2 3 6 a. 108 b. 0 c. 10 d. -54
c. d.  90. Find the determinant of the matrix
6 4 8 0
2 3 5 1 
Transpose of a Matrix 4 2 3 5
[A].  A   .
84. Find the transpose of the matrix  3 1 4 2
 4 3  
 2 5 4 2 3
 5 a. 116 b. 119 c. 124 d. 132
 4 3   4 2 91. Find the determinant of the matrix
a.   b. 
 2 5  3 5  4  1 2 3
2 0 2 1
  4 3  A  
c.   d. [A]. .
 2 5 10 3 0 1
 
  4 2 14 2 4 5

 3 5 a. 36 b. -44 c. -28 d. 26
85. Find the transpose of the matrix Adjoint of Matrix

 A  
2 0 4
 92. Determine the adjoint of the
5  3 8  1 4
  2  5 matrix  A    .
 3 5
a.  0 3  b.
  5  4

  4  8 
 a.   b.
 3  1
2 5  5 4
0  3 3
   1

4
 8 
  4
 5  5 4
c.   d.  3
 2 5  2  5
  3 1    1

0 3   3
c.   d.  0  93. Determine the adjoint of the

 4 8 
 4  8
   15 44
matrix  A   .
Determinant of a matrix  28 59 

86. Find the determinant of the matrix

 4 3
 2 5

a. -26 b. -14 c. 26 d. 14
  59 44  59  44 1   5  4
a.   b.  b. 
 28  15 28  15  19   1 3 
  59 44  1 5  4
c.  d. c. d.
  28  15 19 
  1  3

 59  44  1  5  4
 28  15  19   1 3 
 
Inverse of a Matrix 95. Find the eigenvalues of the matrix
 3  2  5
94. Determine the inverse of the  A   4  1  5

  3 4  2  1  3
matrix  .
 1 5
a. -2. -2, 5 b. 2, -5, -5
1 5  4 c, 2, 2, -5 d. -2, 5, 5
a. 
19   1  3



102. Solve for x in the equation

Quadratic Equation 10
96. Solve for x in the equation x2 – 4 x 7
x
= 0. a. -2 and 5 b. 2 and -5
a. 1 and 4 b. 2 and -2 c. -2 and -5 d. 2 and 5
c. 1 and -4 d. 2 and 2 103. Solve for x in the equation
97. Solve for x in the equation 4x2 + 9 2 3 13
= 0.  
a. 2i/3 and -2i/3 x 2 x5 4
b. 3/2i and -3/2i a. 6 and 19/13
c. 3i/2 and -3i/2 b. 6 and -19/13
d. 2/3i and -2/3i c. -6 and 19/13
d. -6 and -19/13
98. Solve for x in the equation x2 – 104. Solve for x in the equation
13x + 36 = 0. 5 x  3 2 x  7 632
  .
a. 3 and 12 b. 4 and 9 x 1 2x  3 63
c. 2 and 18 d. 1 and 36 a. -4/5 and -111/76
99. Solve for x in the equation 2x2 – b. -4/5 and 111/76
7x – 15 = 0. c. 4/5 and -111/76
a. -5 and 3/2 b. 5 and -3/2 d. 4/5 and 111/76
c. 5 and 3/2 d. -5 and -3/2 105. Solve for x in the equation
100. Solve for x in the equation x2 – 7 x  3 2 x  5 481
6x + 34 = 0.   .
2 x  1 7 x  3 240
a. 3 ± 5i b. 5 ± 3i a. 3/2 and 125/73
c. 2 ± 5i d. 5 ± 2i b. -3/2 and -125/73
101. Solve for x in the equation 9x2 + c. 3/2 and -125/73
x+2=0 d. -3/2 and 125/73
 1   17 1   17 106. Solve for x in the equation 3x2 –
a. b.
18 18 4ix + 4 = 0
 1   71 a. -2i and -2i/3 b. -2i and
c. d. 2i/3 c. 2i and -2i/3 d. 2i and
18
2i/3
1   71 107. Solve for x in the equation x4 + x2
18 – 56 = 0
a. 3 2 b. 2 2
c. 2i 2 d. 3i 2
108. Solve for x in the equation a. 3/2 b. -2/3
x  3 2( x  5)
2 2 c. 2/3 d. -3/2
 2 3 119. Find the product of the roots of
x2  5 x 3 the equation 15x2 + 2x – 8 = 0
a.  13 b.  15 a. -8/15 b. -15/8
c.  17 d.  4 c. 8/15 d. 15/8
109. Solve for x in the equation 120. What is the product of the roots
x  3 x  18  0 . of the equation 15x2 + 2x – 8 = 0
a. 16 b. 25 c. 36 d. 9 a. ¾ b. -1/4
110. Solve for x in the equation x4/3 – c. -3/4 d. ¼
14x2/3 – 48 = 0. 121. Find the value of k in the
a. -4.18i b. -4.81i quadratic equation 7x2 + (2k + 5)x –
c. -8.14i d. -8.41i 5k + 1 = 0 so that the sum and the
111. Solve for x in the equation in (x2 product of the roots are equal.
+ 8x + 3) = In (3x) + In (x + 1). a. 2 b. -3 c. -2 d. 3
a. -1/2 b. 3 c. -2 d. 1/3 122. In a quadratic equation, the sum
112. Solve for x in the equation of the identical roots is 2  7i . Find
1 the product of the roots.
x  1
1  3  4 7i
1 a. b.
1 4
1
1  ...  4  3 7i
a. 1.390 b. 1.483 4
c. 1.521 d. 1.618  3  4 7i  4  3 7i
113. Find a quadratic equation whose c. d.
4 4
roots are 3 and -9. 123. A quadratic equation has two
a. x2 – 6x – 27 = 0 identical roots. When 2 are added to
b. x2 + 6x – 27 = 0 both of the roots the product of the
c. x2 + 12x – 27 = 0 roots is tripled. Find the roots of the
d. x2 – 12x – 27 = 0 original quadratic equation.
114. Find a quadratic equation whose
a. 1  5 b. 2  3
roots are  3i .
c. 2  5 d. 1  3
a. x2 – 9 = 0 b. x2 + 6 = 0
c. x2 – 6 = 0 d. x2 + 9 = 0 124. If the roots of the quadratic
115. Find a quadratic equation whose equation Ax2 + Bx + C = 0 are h and
roots are 3 + 5i and 3 – 5i. k, which of the following are the roots
a. x2 – 6x + 73 = 0 of the equation Cx2 + Bx + A = 0
b. x2 + 16x + 73 = 0 a. h2 and k2 b. 2h and 2k
c. x2 + 6x – 34 = 0 c. 1/h and 1/kd. h + k and hk
d. x2 – 6x – 34 = 0 125. In a quadratic equation problem,
116. If one of the roots of a quadratic one student made a mistake in
equation is 8 – 3i, find the quadratic copying the coefficient of x and got the
equation roots 5 and -3/2. Another student also
a. x2 – 16x + 73 = 0 made a mistake in copying the
b. x2 + 16x + 73 = 0 constant term and got the roots 2/3
c. x2 + 16x – 73 = 0 and ¼. Find the correct quadratic
d. x2 – 16x – 73 = 0 equation.
117. If ¼ and -7/2 are the roots of the a. 12x2 + 11x + 90 = 0
quadratic equation Ax2 + Bx + C = 0, b. 12x2 – 11x + 90 = 0
what is the value of B? c. 12x2 + 11 – 90 = 0
a. -28 b. 4 c. -7 d. 26 d. 12x2 – 11x – 90 = 0
118. Find the sum of the roots of the
equation 15x2 + 2x – 8 = 0 Binomial Theorem
126. Find the 4th term in the expansion 137. Find the sum of the coefficients in
of (x + y)5 the expansion of (x + y – z)8.
a. 5x2y3 b. 10x2y3 a. 3 b. 2 c. 0 d. 1
3 2
c. 5x y d. 10x3y2 138. Find the sum of the exponents in
th
127. Find the 6 term in the expansion the expansion of (x + y)3.
of (2x – 3y)6 a. 6 b. 10 c. 8 d. 12
a. -90,720x3y5 139. Find the sum of the exponents in
b. -108,864x3y5 the expansion of (2x3 – y5) 7.
c. -81,648x3y5 a. 210 b. 224 c. 56 d. 180
d. -48,384x3y5 140. Find the sum of the exponents in
128. Find the 5th term in the expansion  2
12
7 the expansion of  x 2   .
 2y 2
  x
of  x  
3

 x2  a. 56 b. 96 c. 78 d. 84
a. 280x6y6 b. -280x6y6 Number/ Digit Problems
6
c. 560xy d. -560xy8
129. Find the middle term in the 141. Three times the first of three
expansion of (x + 3y)6. consecutive odd integers is three more
a. 1,215x3y3 b. 1,458x3y3 than twice the third. Find the third
c. 135x3y3 d. 540x3y3 integer.
130. Find the term involving x9 in a. 9 b. 11 c. 13 d. 15
12 142. The sum of five consecutive even
 2 2 integers is 1,280. Find the product of
x  
 x the lowest and the largest integers.
a. 32,168x9 b. 25,344x9 a. 64,512 b. 65,024
c. 6,987x9 d. 512x9 c. 65,532 d. 65,520
131. Find the term in (3x – y1/2)13 that 143. A number is less than 100 and its
involves y4. tens digit is 2 more than its units
a. 173,745x5y4 digits. If number with the digits
b. 312,741x5y4 reversed is subtracted from the
c. 416,988x5y4 original number remainder is 3 times
d. 104,247x5y4 the sum of the digits. Find the
132. Find the term in (x – y + z)11 that number.
involves x3y5 a. 42 b. 53 c. 75 d. 64
a. 9,240x3y5z2 144. The square of the tens digit of a
b. 9,240x3y5z3 two digit number is 7 less than the
c. -9,240x3y5z3 sum of the digits. If the digits are
d. -9,240x3y5z2 transposed the number is increased by
133. Find the term in (a + 2b – c)10 63, Find the number.
that involves a4c3. a. 47 b. 56 c. 38 d. 29
a. 33,600a4b4c3 145. the sum of the digits a 2 digit
b. 33,600a4b3c3 number is 10. IF the number is divided
c. -33,600a4b4c3 by the digit, the quotient is 3 and the
d. -33,600a4b3c3 remainder is 4. Find the number.
134. The middle term in the expansion a. 37 b. 28 c. 46 d. 19
of (a3 + 2b2)n is Camb12. Find m. 146. Divide 224 into two parts such
a. 19 b. 20 c. 17 d. 18 that when the larger part is divided by
135. Find the sum of the coefficients in the smallest part, the quotient is 2 and
the expansion of (2x – 3y)35. the remainder is half of the smaller
a. -1 b. 1 c. -2 d. 2 part. Find the larger part.
136. Find the sum of the coefficients in a. 150 b. 180 c. 170 d. 160
the expansion of (3x +1)4. 147. The sum of the digits of a three
a. 256 b. 254 c. 255 d. 257 digit number is 17. If the digits are
reversed the resulting number is c. 6.57 km d. 6.75 km
added to the original number, the 157. The scale of a certain map is
result is 1,474. If the resulting number 1:100,000. The distance between two
is subtracted from the original points on the map is 3 units. How
number, the result is 396. Find the many units will these two points
original number. measure on another map with scale of
a. 935 b. 845 c. 854 d. 953 1:60,000?
148. The sum of the digits of a three a. 9 units b. 5 units
digit number is 12. When the hundreds c. 18 units d. 6 units
and tens digits are interchanged, the 158. the time of travel of a free falling
number is reduced by 630. But when body varies directly as the square root
the hundreds and units digits are of the distance it falls. If a body falls
interchanged, the number is reduced 78.48 meters in 4 seconds, how far
only by 495. Find the sum the squares will it travel in 8 seconds?
of the digits. a. 313.92 m b. 117.72 m
a. 70 b. 74 c. 68 d. 72 c. 627.84 m d. 156.96 m
149. When 3 is added to both 159. At constant temperature, the
numerator and the denominator of a resistance of a wire varies directly as
certain fraction, its value is decreased its length and inversely as the square
by 9/40. However, when 3 is of its diameter. If a piece of wire 0.10
subtracted from both, its value is inch in diameter and 50 feet long has
increased by 9/10. Find the a resistance of 0.10 ohms, what is the
denominator of the original fraction. resistance of another piece of wire of
a. 3 b. 4 c. 5 d. 6 the same material, 2,000 feet long,
150. Find the remainder when 37 0.20 inch diameter?
raised to 1,810 is divided by 7. a. 0.50 ohms b. 4 ohms
a. 1 b. 2 c. 3 d. 4 c. 1 ohms d. 2 ohms
Proportion/Variation 160. The quantity of water discharged
over a rectangular weir is directly
151. If y varies directly as x and equal proportional to the crest length and
to 3 when x is equal to 10, find the three halves the power of the head
value of y when x is equal to 25. (height of water above the crest). If
a. 80 b. 75 c. 60 d. 90 the rate of discharge over a weir
152. z varies directly as x and having a crest length of 3m and a
inversely as the square root of y. It is head of 0.70 m is 3.23 m3/sec, find
equal to 3 when x is 13 and y is 16. the rate of discharge over a weir
Find the value of z when x is 52 and y having a crest length of 6 m and a
is 9. head of 1.40 m.
a. 24 b. 20 c. 25 d. 16 a. 18.72 m3/s b. 7.82 m3/s
153. Find the fourth proportional to c. 17.28 m3/s d. 18.27 m3/s
33,22 and 27. 161. Coulomb’s Law states that the
a. 21 b. 18 c. 15 d. 20 electrical force between two point
154. Find the third proportional to 16 charges varies directly as the product
and 12. of the charges and inversely as the
a. 9 b. 10 c. 12 d. 15 square of the distance between them.
155. Find the mean proportional If the electrical force between two
between 8 and 392. points charges 25x10-9 coulombs and
a. 80 b. 72 c. 60 d. 56 75x10-9 coulombs and 0.03 meters
156. The scale of a certain map is apart is 0.019 N, find the electrical
1.250,000 mm. If two points on the force between two point charges
map is 27mm, find its actual ground 30x10-9 coulombs and 120x10-9
measurement. coulombs and 0.10 meters apart.
a. 5.67 km b. 5.76 km
 a. 0.0033 N b. 0.0044 N as his son. How old was the father
c. 0.0055 N d. 0.0066 N when his son was born?
162. The relative angle of twist a. 26 years old
between the ends of a solid circular b. 30 years old
rod varies directly the product of the c. 42 years old
applied torque and the length, and d. 36 years old
inversely as the fourth power of the 168. Elmer is 36 years old and his
diameter. If the angle of twist of a daughter is 8 years old. In how may
circular rod is 2.23 radians, find the years will Elmer’s age be twice his
angle of twist on another rod of the daughter’s age?
same material when the length, A 20 years b. 24 years
diameter, and applied torque were c. 18 years d. 22 years
halved. 169. Allan is 28 years old when his son
a. 4.46 rad b. 1.12 rad is born. In how many years will Allan
c. 8.92 rad d. 0.56 rad be thrice as old as his son?
163. If three cats can kill three mice in a. 14 years b. 16 years
three minutes, in how many minutes c. 18 years d. 12 years
can twelve cats kill twelve mice? 170. The quotient of the ages of a
a. 12 min b. 6 min mother and her daughter is 2 with
c. 4 min d. 3 min remainder 5. Five years ago, the
164. If 2 typist can type 2 pages in 2 mother was thrice as old as her
minutes, in how many seconds will it daughter then. How old is the mother
take 5 types to type 19 pages? now?
a. 516s b. 456s a. 35 years old
c. 576s d. 396s b. 32 years old
165. Ten students from Pampanga c. 36 years old
decided to stay in Manila for a regular d. 30 years old
review preparation for the CE Board 171. At present, Gilbert’s age is 30%
Exam. To minimize their expenses, of his father’s age. Thirty years from
they agreed bring 18 sacks of rice that now, Gilbert’s age will be 60% of his
will last for 4 months. After their father age. How old is Gilbert now?
regular review, students went back to a. 18 years old
Pampanga. Only the remaining b. 16 years old
students enrolled in the refresher for 1 c. 12 years old
month. How much more rice will the d. 14 years old
remaining students need to their 172. Two years ago, the ratio of the
extended stay in Manila? (1 sack = 50 ages of a boy and a girl was 3 s to 4.
kg) In 8 years their ages will be in the
a. 120 kg b. 135 kg ratio 4 is to 5. Find the sum of their
c. 150 kg d. 175 kg ages now.
Age Problems a. 74 years b. 70 years
c. 72 years d. 80 years
166. A doctor’s age 8 years ago is two 173. Richard is 5 years older than
thirds his age 13 years hence. How old Paul. The product of their ages is 21
is he now? years less than 15 times the sum of
a. 42 years old their ages. How old is Paul now?
b. 45 years old a. 30 years old
c. 50 years old b. 32 years old
d. 40 years old c. 25 years old
167. Two years ago, a father was four d. 27 years old
times as old as his son. In 3 years, the 174. Ryan is 5 years older than Jake.
father will only be three times as old In 5 years, the product of their ages
will be 1.5 times the product of their youngest was born, the sum of the
present ages. How old is Jake now? parent’s ages was 70. In 38 years, the
a. 25 years old sum of the parent’s ages will be equal
b. 20 years old to the sum of the children’s ages. How
c. 15 years old old is the second child?
d. 30 years old a. 22 years old
175. Noel is 5 years older than Dennis b. 24 years old
and 10 years younger than Hilda. In 8 c. 20 years old
years their combined ages will be 65. d. 26 years old
How old is Noel? 181. A man lived his life for “x” years.
a. 18 years old When he was at his midlife, his first
b. 12 years old child was born. When he was at his
c. 7 years old two thirds of his life, his second child
d. 15 years old was born. When the man died, the
176. A boy is one half as old as his sum of the ages of his children is 60.
brother and 6 years younger than his How long did the man live?
sister sum of their ages is 38. How old a. 66 years b. 72 years
is the boy? c. 78 years d. 84 years
a. 14 years old 182. Diophantus is one of the brilliant
b. 8 years old Greek mathematicians born around
c. 16 years old 250 A.D. His age from birth until death
d. 7 years old may be determined from a epitaph
177. Twenty two years ago, Sherly revealing the fact that he passed a
was twice as old as Pinky and eight sixth of his life in childhood, a twelfth
times as old as Roy. That same year, in adolescence, and seventh more as a
the sum of their ages was 26. How old bachelor. Five years after he got
is Pinky now? married, a son was born to him who
a. 30 years old died four years before Diophantus at
b. 28 years old one half his father’s final age. How old
c. 38 years old is Diophantus when his son was born?
d. 24 years old a. 38 years old
178. A is 50%older than B 40% b. 44 years old
younger than C. If the sum of their c. 42 years old
ages is 110 how old is A? d. 40 years old
a. 36 years old 183. Peter is 36 years old. Peter is
b. 32 years old twice as old as Jun was when Peter
c. 33 years old was as old as Jun is now How old is
d. 30 years old Jun?
179. The sums of the parent’s ages is a. 30 years old
twice the sum of the children’s ages. b. 27 years old
Four years ago, the sum of the c. 24 years old
parent’s ages was thrice the sum of d. 32 years old
the children’s ages. In 16 years, the 184. When John was as old as Paul is
sum of the ages of the parents and now, the sum of their ages was 51.
children will be equal. How many When Paul will be as old as John is
children are there? now, the sums of their ages will 103.
a. 4 b. 7 c. 5 d. 6 John is older than Paul by how many
180. The sum of the ages of the years?
parents and the three children is 9 a. 25 years b. 19 years
decades over a century. The father is c. 13 years d. 32 years
twice as old as the eldest child. When 185. In an organization, there are
the eldest child was born sum of the engineers, accountants and doctors.
parent’s ages was 54.When the The sum of their ages is 2,160; the
average age is 36. The average age of a. 51 m b. 20m
the engineers and doctors, 36 and 2/3. c. 43 m d. 38 m
If each engineer were 1 year older, 192. Two circles are tangent to a third
each accountant 6 years older, and circle internally and are tangent to
each doctor 7 years older, their each other externally. The distances
average age would be 41. Determine between their centers are 10 m, 13 m,
the number of engineers, accountants, and 19 m. Find the radius of the
and doctors. largest circle.
a. 24 engineers, 20 a. 21 cm b. 25 cm
accountants,16 doctors c. 11 cm d. 15 cm
b. 16 engineers, 24 193. A cardboard box manufacturer
accountants, 20 doctors wishes to make boxes from
c. 20 engineers, 16 rectangular pieces of cardboard 30 cm
accountants, 24 doctors by 40 cm by cutting squares with 5 cm
d. 20 engineers, 24 sides from four corners. Find the
accountants, 16 doctors volume contained by each box.
Geometric Problems a. 4,375 cm3 b. 3,600cm3
c. 3,000 cm3 d. 2,800 cm3
186. The base of an isosceles triangle 194. The total surface area of two
is 6 cm shorter than its equal sides. If cubes is 1,732 cm3. The total length of
the perimeter is 87 cm, find the length their edges is 276 cm. Find the edge of
of the base. the smaller cube.
a. 27 cm b. 25 cm a. 8 cm b. 12 cm
c. 28 cm d. 31 cm c. 10 cm d. 15 cm
187. The width of a rectangle is 9 cm. 195. A lizard traveled from corner A to
The length is 1 cm shorter than the corner B of the rectangular room
diagonal. Find the length of the shown. Determine its shortest distance
diagonal. covered.
a. 41 cm b. 42 cm
c. 40 cm d. 39 cm
188. The hypotenuse of a right triangle
is 25 cm longer than one leg and 32
cm longer than the other leg. Find the
area of the triangle.
a. 2,340 cm2 b. 2,430 cm2 a. 5.39 m b. 7.28 m
c. 3,240 cm2 d. 3,420 cm2 c. 6.40 m d. 6.71 m
189. A vertical pole was broken by the Clock Problems
wind. The upper part, still attached,
reached a point on the level ground 15 196. At what time between 4:00 Pm
feet from the base. If the upper part is and 5:00 Pm will the hands of the
9 feet longer than the lower part, how clock coincident?
tall was the pole? a. 4:21.82 b. 4:22.27
a. 20 feet b. 17 feet c. 4:23.64 d. 4:21.64
c. 15 feet d. 25 feet 197. In how many minutes after 2
190. A circular rose bed is bordered by o’clock will the hands of the clock
a 2 meter walk. The area planted is extend in opposite directions for the
16/25 of the area of the bed. Find the first time?
radius of the bed a. 40.64 min b. 41.64 min c.
a. 7 m b. 8 m c. 9 m d. 10 m 42.64 min d. 43.64 min
191. Three circles are tangent 198. At approximately what time
externally. The distances between between 6 and 7 o’clock will the
their centers are 58 m, 63 m, and 81 minute and hour hands coincide?
m. Find the radius of the largest circle.
 a. 27 min and 41 sec after 6 c. 5:17.27 d. 5:16.55
o’clock 208. A man left his home at past 3
b. 32 min and 0.73 sec after 6 o’clock P.M as indicated in his wall
o’clock clock. Between two to three hours
c. 25 min and 38 sec after 6 after, he returned home and noticed
o’clock that the hands of the clock
d. 32 min and 44 sec after 6 interchanged. At what time did he
o’clock leave his home?
199. In how many minutes after 10 a. 3:33.47 b. 3:31.47
o’clock will the hands of the clock be c. 3:32.47 d. 3:34.47
perpendicular for the second time? 209. At what time after 7 o’clock will
a. 39.18 min b. 38.18 min the second hand bisect the hour and
c. 37.18 min d. 36.18 min the minute hands for the first time?
200. How many times will the hands of a. 7:00:16.66 b. 7:00:17.66
the clock coincide in one day? c. 7:00:18.66 d. 7:00:19.66
a. 22 b. 21 c. 23 d. 24 210. If it were eight hours later, it
201. How many times will the hands of would be half as long until midnight as
the clock be at right angles with each it would be it was two hours later.
other in one day? What time is it now?
a. 24 b. 48 c. 22 d. 44 a. 9:00 am b. 12:00 pm
202. At what time after 3 o’clock will c. 8:00 am d. 10:00 am
the hour and the minute hands be 80° Mixture Problems
with each other for the second time?
a. 3:32.91 b. 3:33.91 211. A 50 mL 40% acid solution is
c. 3:30.91 d. 3:31.91 added to a 150 mL 30% acid solution.
203. Find the angle between the hands What will the concentration of the
of the clock at 3:43 P.M. resulting mixture?
a. 148.50o b. 147.50o a. 25% b. 27.50%
o
c. 145.50 d. 146.50o c. 30% d. 32.50%
204. Determine the obtuse angle 212. How much of a 90% solution of
between the hour and the minute insect spray must a farmer add to 200
hands at 2:51 P.M. cc of a 40% insect spray to make a
a. 208.50o b. 220.50o 50% solution of insect spray?
o
c. 139.50 d. 151.50o a. 30cc b. 40cc
205. What time between 2 and 3 c. 50cc d. 60cc
o’clock will the angle between the 213. A 500 mL of 0.40 g/mL salt
hands of the clock be bisected by the solution is added to a 900 mL of 0.65
line connecting the center of the clock g/mL salt solution. What will be the
and the 3 o’clock mark? concentration of the resulting mixture?
a. 2:21.27 b. 2:18.46 a. 0.74 g/mL b. 0.47 g/mL
c. 2:23.54 d. 2:19.54 c. 0.65 g/mL d. 0.56 g/mL
206. It is now between 9 and 10 214. How much water must be added
o’clock. In 4 minutes, the hour hand to 1.45 liters, 80 proof liquor to make
will be exactly opposite the position it 65 proof?
occupied by the minute hand 3 a. 0.29 L b. 0.33 L
minutes ago. What is the time now? c. 0.38 L d. 0.42 L
a. 9:22 b. 9:21 215. A 700 pound alloy containing
c. 9:20 d. 9:19 50% tin and 25% lead is to be added
207. It is between 5 and 6 o’clock. In with amounts of pure tin and pure lead
20 minutes, the minute hand will be to make an alloy which is 60% tin and
ahead of the hour hand as it was 20% lead. Determine how much pure
behind it. What time is it now? tin must be added.
a. 5:18.36 b. 5:19.45 a. 150 lb b. 175 lb
 c. 200 lb d. 225 lb a. 8.75 gal b. 11.25 gal
216. A vat contains a mixture of acid c. 8.44 gal d. 11.56 gal
and water. If 25 gallons of acid are Motion Problems
added, the mixture will be 80% acid. If 221. If the speed of a racing car is
25 gallons of water are added, the increased by 20 kph, it will cover in 7
mixture will be 60% acid. Find the hours the same distance it can
percentage of acid in the mixture. ordinarily cover in 8 hours. What is its
a. 65% b. 70% ordinary speed?
c. 75% d. 72% a. 140 kph b. 150 kph
217. How much water must be c. 160 kph d. 170 kph
evaporated from 12 Liters of 3kg/L salt 222. A plane flew at 20/27 of its usual
solution until the concentration rate in a 3,000 km course due to
becomes 3.60 kg/L? inclement weather; thereby taking an
a. 1L b. 2L c. 3L d. 4L additional 1-1/2 hours to its usual time
218. A container is filled with 70 liters required for the trip. What is the usual
which is 40% alcohol by volume. How trip of the plane?
much of a mixture must be taken and a. 600 kph b. 700 kph
then replaced with equal amount of c. 800 kph d. 900 kph
water so that the resulting solution is 223. When the speed of a car is
30% alcohol by volume? increased by 36 kph, it passes thrice
a. 17.50L b. 15L as many light posts as it was at
c. 20L d. 22.50L ordinary speed. Find the ordinary
219. A contractor is required to secure speed of the car.
his 200 m3 if materials for a subbase a. 21 kph b. 15 kph
from three pit with the following soil c. 18 kph d. 12 kph
analyses. From the first pit, the 224. Two airplanes left airports which
analysis is comprised of 55% coarse are 960 km apart and flew toward
aggregate, 35% fine aggregate, and each other. One plane flew 32 kph
10% mineral filter. The second pit faster than the other. If they passed
comprised of 65% coarse aggregate, each other at the end of an hour and
20% fine aggregate, and 15% mineral 12 minutes, what was the rate of the
filter. The third pit comprised of 10% faster plane?
coarse aggregate, 50% fine aggregate, a. 352 kph b. 384 kph
and 40% mineral filter. The volumetric c. 416 kph d. 448 kph
composition of the combined materials 225. Two cars run toward each other.
as desired is set at 50% coarse Their speeds are 30 kph and 40 kph.
aggregate, 35% fine aggregate, and At the moment when they are 105 km
15% mineral filter. How much soil apart, a bee files at 50 kph from the
must be taken from the first pit to bumper of the slower car to the
produce the desired design mix? bumper of the other and shuttles back
a. 102.19 m3 b. 48.72 m3 and forth until the vehicles collide.
c. 142.86 m3 d. 28.57 m3 Find the total distance traveled by the
220. A container is filled with 20 bee.
gallons of pure water. Five gallons of a. 75 km b. 85 km
water is taken from the container and c. 90 km d. 100 km
is replaced by 5 gallons of pure acid 226. Car A can travel around a circular
then thoroughly mixed. Another 5 track in 120 seconds while car B in 80
gallons is taken from the mixture and seconds. If they started from the same
is replaced again by 5 gallons of pure point but travel in opposite direction at
acid. If this process is done the same time in how many seconds
repeatedly, find the amount f water in will they meet for the first time?
the container after doing the process 3 a. 42 sec b. 48 sec
times. c. 56 sec d. 60 sec
227. It took a certain vehicle 3 hours After biking for 10 km, he was
to travel a distance of 120 km. On its detained due to bad weather for half
way back, it took him only 2 hours in an hour. As a result, he had to speed
traveling the same path. What was his up 2 kph faster. What was his original
average speed? speed?
a. 44 kph b. 48 kph a. 8.50 kph b. 8 kph
c. 50 kph d. 56 kph c. 7.50 kph d. 9 kph
228. A motorboat can travel 4 km 234. Allan and Manjo joined in a race.
upstream in the same time it can After the signal, they started running
travel 9 km downstream. If the from the same position in the same
velocity of the current is 8 kph, find direction. It takes Allan 3 leaps while
the velocity of the boat in still water. Manjo takes 2 leaps, but 5 leaps of
a. 16 kph b. 18.50 kph Allan is equal to 4 leaps of Manjo.
c. 20.80 kph d. 24.60 kph When Allan reached the finished line,
229. A boat propelled to move at 25 Manjo is behind by 48 of his own
kph in still water, travels 4.20 km leaps. How many leaps did Allan take
against the river current in the same during the race?
time that it can travel 5.80 km with a. 300 leaps b. 200 leaps
the current. Find the speed of the c. 360 leaps d. 240 leaps
current. 235. A thief is being pursued by a
a. 5 kph b. 6 kph policeman. He is ahead by 30 of his
c. 4 kph d. 3 kph own pace. How many paces must the
230. The boat travels downstream in policeman take if he takes 4 paces
two thirds the time as it does while the thief takes 5, but 3 of the
upstream. If the speed of the river policeman’s paces is as long as 4 of
current is 8 kph, determine the the thief’s paces.
velocity of the boat in still water. a. 420 paces b. 360 paces
a. 30 kph b. 40 kph c. 480 paces d. 450 paces
c. 50 kph d. 60 kph 236. A commuter returning by train
231. A man walks from his house to from his office ordinarily reaches his
the office. If he leaves at 8:00 A.M. suburban station at 5 o’clock. His
and walks at the rate of 2 kph, he will chauffeur leaves his home with a car
have arrived 3 minutes earlier, but if just in time to meet him when the
he leaves at 8:30 A.M. and walks at 3 train arrives, and drives him back
kph, he will have arrived 6 minutes home. On a certain day the man takes
late. What time should he arrive at the a train which arrives at the station an
office? hour earlier. He walks toward home
a. 9:06 am b. 9:12 am until he meets his chauffeur car. The
c. 8:54 am d. 8:43 am chauffeur turns and drives the man
232. The average vertical speed of an the rest of the way home, arriving
experimental rocket is 1,200 kph home 10 minutes earlier than usual.
during its flight. Upon reaching its Find the time that the man walks.
maximum height, it released a capsule a. 55 min b. 50 min
which descended at an average c. 60 min d. 45 min
vertical speed of 630 kph. If the 237. Cid and Jojo travels from point A
capsule touched the earth 90 minutes to point B and back. Cid starts 3 hours
after the rocket was launched, find the after Jojo started. Cid overtakes Jojo
height reached by the rocket. at a point 4.20 km from B. IF Cid
a. 619.67 km b. 550.29 km reaches A 5 hours and 20 minutes
c. 640.82 km d. 581.36 km ahead of Jojo, find the distance AB.
233. A man started on his mountain a. 12 km b. 18 km
bike for Manila, a distance of 30 km c. 15 km d. 16km
intending to arrive at a certain time. Work Problems
 c. 6.62 hrs d. 7.45 hrs
238. A steel man can saw a piece of 245. A and B working together can
bar into 5 pieces in 16 minutes. In finish the job in 10 days. If A works 4
how many minutes can the steel man days and B works 3 days, one-third of
saw the same bar into 10 pieces? the job shall be finished. How many
a. 30 min b. 32 min days will it take A to finished the job
c. 34 min d. 36 min alone?
239. A can do a piece of work along in a. 30 days b. 15 days
30 days, B in 20 days, and C in 60 c. 20 days d. 45 days
days. If they work together, how many 246. Josie can type 100 words in the
days would it take them to finish the same time that it takes Jane to type
work. 75 words. If Jane’s typing rate in 8
a. 15 days b. 8 days words per minute less than that of
c. 10 days d. 12 days Josie’s, find Jane’s typing rate.
240. If Paolo can do his chores in ¾ of a. 32 words/min
an hour, and if Miriam and Paolo b. 24words/min
together do the in ½ on an hour, how c. 16 words/min
long will it take Miriam to do it alone? d. 20 words/min
a. 60 min b. 90 min 247. A swimming pool is filled through
c. 75min d. 120 min its inlet pipe and them emptied
241. Working together, A and B can through its outlet pipe in a total of 8
finish a painting job in 20/3 days. B, hours. If water enters through its inlet
working alone, can finish the job in 3 and simultaneously allowed to leave
days less than A. How long will it take through its outlet, the pool is filled in 7
A to finish the job alone? ½ hours. How long will it take to fill
a. 15 days b. 12 days the pool with the outlet closed?
c. 21 days d. 18 days a. 2.50 hours b. 3 hours
242. A gardener can mow a lawn in 3 c. 3.50 hours d. 3.75 hours
hours. After 2 hours, it rained and he 248. Eight men can excavate 50 m of
discontinue to work. In the afternoon, canal in 7 hours. Three men can
a girl completed the rest of the work in backfill 30 m of the excavated canal in
1 hour and 15 minutes. How long 4 hours. How long would it take 10
would it take the girl to mow the lawn men to dig and backfill 100 m of
alone? canal?
a. 3 hrs b. 3.50 hrs a. 12.50hrs b. 15.20hrs
c. 3.75 hrs d. 4 hrs c. 21.50hrs d. 25.10hrs
243. Two pipes running simultaneously 249. Twenty eight men can finish the
can fill a tank in 2 hours and 40 job in 60 days. At the start of the 16th
minutes. After the larger pipe had run day, 5 men were laid off and after 45th
for 3 hours the smaller pipe was also day, 10 more men were hired. How
turned on and the tank was full 40 many days were they delayed in
minutes later. How long would it take finishing the job?
the smaller pipe to fill the tank alone? a. 2.27 days b. 2.45 days
a. 10 hours b. 6 hours c. 2.97 days d. 3.67 days
c. 4 hours d. 8 hours 250. Group A consisting of 6 members
244.John, Paul and George can finish a can paint antenna tower in 80 hours
job in 12, 16 and 19 hours, while group B of 8 member can paint it
respectively. John and Paul work in 120 hours. If another group C is to
together for 4 hours. Paul got tired so be formed consisting of 3 members
George worked in place of him until from both groups, in how many hours
the job is finished. How long did John can they finished the job?
work? a. 112.67 hrs b. 106.67 hrs c.
a. 7.06 hrs b. 6.86 hrs 109.67 hrs d. 116.67 hrs
251. A three man maintenance crew investment which yields 18%. How
could clean the campus in 4 hours; much was the total annual income?
whereas, a four man maintenance a. P47, 520 b. P47,880
crew do it in 3 hours. If one member c. P42,480 d. P42,120
of the four man crew was an hour late, 257. A sum of money of simple
how long did it take the entire cleaning interest amounted to P7, 800 after five
of the campus? years and P8, 840 after nine years.
a. 1.92 hrs b. 2 hrs Find the amount of the money after 15
c. 1.86 hrs d. 1.68 hrs years.
252. Candle A and candle B of equal a. P10, 140 b. P9,820
length are lighted at the same time c. P9,600 d. P10,400
and burning until candle A is twice as 258. A man wants to invest a sum of
long as candle B. Candle A is designed P500 in two investments. The first
to fully burn in 8 hours while candle B investments earn a rate of interest 4
for 4 hours. How long will they be times that of the second investment.
lighted? In 3 years, the first investment grows
a. 3hrs and 30 min to P372. In 10 years, the second
b. 2 hrs and 40 min investment grows to P240. Find the
c. 3 hrs amount of his money after 15 years.
d. 2 hrs a. P780 b. 920
Money Related Problems c. P870 d. P830
259. The cost for building a
253. A couple does not wish to spend rectangular vat with a square base
more than P700 for dinner at a was P12,800. The base cost P30/m2
restaurant. If sales tax of 6% is added and the sides cost P20/m2. Find the
to the bill they plan to tip 15% after height of the vat if the combined area
the tax has been added, what is the of the base and sides was 512m2.
most they can spend for the meal? a. 2m b. 3 m c. 4 m d. 5 m
a. P660.38 b. P559.30 260. In what ratio must a peanut
c. P608.70 d. P574.24 costing P240.00 per kg be mixed with
254. The price of 8 calculator ranges a peanut costing P340.00 per kg so
from P200 to P1,000. If their average that a profit of 20% is made by selling
price is P950, what is the lowest the mixture at P360.00 per kg?
possible price of any one of the a. ½ b. ¾ c. 2/3 d. 1/3
calculators? 261. Mrs. Reyes planned to spend
a. P500 b. P550 P39,000 for fabric for her store. She
c. P600 d. P650 found her fabric on sale at 20% less
255. A retired government employee per yard than she had expected and
invested P25, 000 of his retirement was able to buy 40 extra yards for a
pay at 16% per annum. He found total cos to P41,600. What was the
another investment opportunity at original cost per yard?
20% per annum where he invested the a. P250/yd b. P275/yd
rest of his retirement pay. If he c. P300/yd d. P325/yd
realized a total yearly income of 19% 262. A consumer is trying to decide
on his two investments, what was his whether to purchase car A or car B.
retirement pay? Car A costs P500,000, has an mpg
a. P100, 000 b. P75, 000 rating of 30 and has an insurance of
c. P96, 000 d. P125, 000 P27,500 per year. Car B costs P600,
256. A man speculating in real estate, 000 has an mpg rating of 50, and has
invested P300, 000 in two land an insurance of P40, 000 per year.
development. One investment yields Assuming that the consumer drives
12% and the yearly income from this 15, 000 miles per year and that the
is P3, 600 more than the other price of gas remains constant at
P62.50 per gallon, determine the 273. How many numbers between 20
minimum number of years it will take and 1, 056 are exactly divisible by 14?
for the total cost of car B to become a. 73 b. 74 c. 75 d. 76
less than that of car A. 274. Find the sum of all the odd
a. 12 years b. 15 years numbers between 100 and 1, 000
c. 10 years d. 11 years a. 472,500 b. 427,500
Arithmetic Progression c. 247,500 d. 274,500
275. Find the sum of the numbers
263. Find the 19th term of the between 361 and 589 that are divisible
arithmetic 4, 15, 26, …. by 19.
a. 180 b. 191 c. 202 d. 213 a. 6,175 b. 5225
264. Find the 25th term of the c. 5,510 d. 5,890
arithmetic progression 29, 16, 3…. 276. The nth term of a sequence is
a. -283 b. -296 given by 5n – 32. Find the sum of the
c. -309 d. -322 first 20 terms.
265. Find the sum of the first 11 terms a. 415 b. 416 c. 410 d. 401
of the arithmetic progression -22, -14, 277. The sum of the first n terms of a
-6… sequence is given by the expression
a. 140 b. 198 17n2-11n. Determine the 20th term.
c. 264 d. 338 a. 625 b. 652 c. 526 d. 562
266. Find the sum of the first 90 terms 278. The 8th term of an arithmetic
of the arithmetic progression -5, 3, 11, sequence is 112 and the common
… difference is -33. Find the expression
a. 29, 493 b. 30, 184 for the nth term.
c. 30, 883 d. 31, 590 a. 376 – 33n b. 376 + 33n
267. Find the sum of the first 30 terms c. 367 – 33n d. 367 + 33n
of the arithmetic progression 53/4 , 279. The first term of a sequence is
367/12, 675/12… -61 and the common difference is 16.
a. 13,885 b. 13,855 Find the expression for the sum of the
c. 13,585 d. 13,558 first n terms.
268. The first term of an arithmetic a. 8n2 – 68n b. 8n2 + 68n
progression is 8 and the last term is c. 8n2 – 69n d. 8n2 + 69n
62. If the sum of all the terms is 210, 280. The fourth term of an arithmetic
find the number of terms. sequence is equal to 1, and the
a. 5 b. 6 c. 7 d. 8 difference between the 20th and the
269. The first term of an arithmetic 14th terms is 54. Determine the sum of
progression is 7 and the 17th term is the first 10terms.
89. Find the 50th term. a. 146 b. 164 c. 145 d. 154
a. 2581/8 b. 2851/8 281. Determine x so that 2x + 1, 10x
3
c. 258 /8 d. 2853/8 – 15, 2x2 + 9 will be an arithmetic
270. There are 20 arithmetic means progression.
between -38 and 3. Find the common a. 5 b. 6 c. 7 d. 8
difference. 282. If the terms 3(x2 – 1), x2 – 4x +
a. 15/21 b. 120/21 5, 11 – 9x form an arithmetic
c. 23/19 d. 218/19 progression, find the sum of the first 8
271. There are 8 arithmetic means terms.
between 5 and 64. Find the 6th term. a. -144 b. -168
a. 374/9 b. 375/9 c. -160 d. -152
7
c. 37 /9 d. 378/9 283. The sum of three number in an
272. Find the sum of the seven arithmetic progression is 66. The sum
arithmetic means between 34 and 68. of the square is 1, 790. Find the third
a. 425 b. 357 c. 255 d. 459 number.
a. 64 b. 46 c. 35 d. 53
284. The sum of four numbers in an 292. A rectangular plate is submerged
arithmetic progression is 98. The sum vertically with its upper edge in the
of their squares is 3,006. Find the surface of the water. The force on the
third number. first meter of the rectangle on one side
a. 30 b. 27 c. 35 d. 32 is 14.70 kN and every meter below the
285. The arithmetic mean of six first experiences a force 29.40 kN
numbers is 17. If numbers are added more than the preceding meter. How
to the progression the new arithmetic high is the rectangle if the total force
mean is 21. What are the two numbers on one side is 2,116.80 kN?
if the difference is 4? a. 12 m b. 10 m
a. 32 and 36 b. 31 and 35 c. 14 m d. 16 m
c. 34 and 38 d. 33 and 37 Geometric Progression
286. Find the value of x if 3x – y, 2x +
y, 4x +3, and 3x + 3y are consecutive 293. Find the 16th term of the
terms of an arithmetic sequence. geometric progression 2, 6, 18,…
a. 2 b. 3 c. 4 d. 5 a. 28, 697,814
287. In a pile of logs, each layer b. 258,280,326
contains one more log than the layer c. 86, 093,442
above and the top contains just one d. 9,565,938
log. If there are 105 logs in the pile, 294. Find the 9th term of the geometric
how many layers are there? progression 72, -12, 2….
a.11 b. 12 c. 13 d. 14 a. -1/139,968
288. How many times will a clock b. -1/23,328
strike in 24 hours if it strikes only at c. 1/23,328
the hours, and strikes once at 1 twice d. 1/139,968
at 2, thrice at 3…? 295. Find the sum of the first 8 terms
a. 224 b. 112 c. 156 d. 78 of the geometric progression 7, 28,
289. A particle moves along a straight 112,…
path. For the first second, it travels 16 a. 38,272 b. 152, 951
m. In every second after the first, it c. 152,915 d. 38,227
travels 2 m farther than it did in the 296. Find the sum of the first 10 terms
preceding second. How far will it travel of the geometric progression -343,
after 10 seconds? 49,-7..
a. 250 m b. 34 m a. -400.17 b. -300.12
c. 180 m d. 92 m c. 400.17 d 300.12
290. A man owns pigs in his barn. He 297. The first term of a geometric
had purchased feed that will last for 75 progression is -8 and the 12th term is
days for his livestock. The pigs were 1/256. Find the 7th term.
then infested with disease. If the man a. -1/16 b. 1/16
has 4, 950 pigs initially and 25 pigs did c. 1/8 d. -1/8
each day, for how long will it feed last? 298. There are 20 geometric means
a. 85 days b. 100 days between 512 and 36. Find the
c. 125 days d. 297 days common ration.
291. In the recent “Gulf War” in the a. 0.8812 b. 0.8782
Middle East, the allied forces captured c. 0.8757 d. 0.8691
6, 390 of Saddam’s soldiers with 299. The first term of a geometric
provisions on hand that will last for progression is 375 and the fourth term
216 meals taking 3 meals a day. The is 192. Find the common ratio.
provisions lasted 9 more days because a. 0.60 b. 0.70
of daily deaths. At an average how c. 0.80 d. 0.90
many died per day? 300. There are 8 geometric mean
a/ 15 b. 16 c. 17 d. 18 between 64/3, 125 and 625/8. Fin the
6th term.
 a. 125/4 b. 25/3 b. P23,803.11
c. 5 d. 2 c. P25, 707.36
301. The first term of a geometric d. P22, 489.80
progression is 256 and the last term is 309. An equipment costing P5, 000,
6,561. If the sum of all the terms is 000 depreciates in value 16% a year.
19, 171, find the number of terms. Find its worth after 5 years.
a. 7 b. 8 c. 9 d. 10 a. P2, 091,059.71
302. Find the sum of the geometric b. P1, 475,451.73
progression 2x, 4x + 14, 20x – 14, …. c. P1, 756,490.16
Up to the 10th term. d. P2,489,356.80
a. 566,579 b. 312,228 310. A container is filled with 20
c. 617,774 d. 413336 gallons of pure water. Five gallons of
303. Find the geometric means of 18 water is taken from the container and
and 1,458. is replaced by 5 gallons of pure acid
a. 126 b. 162 then thoroughly mixed. Another 5
c. 216 d. 261 gallons is taken from the mixture and
304. Find the geometric mean of is replaced again by 5 gallons of pure
2.138, 6.414, 19.242, and 57.726. acid. If this process is done
a. 10.367 b. 10.995 repeatedly, find the amount of water
c. 11.109 d. 12.607 in the container after doing the
305. The sum of three numbers in process 15 times.
arithmetic progression is 45. If the a. 0.672gal b. 0.267gal
first number decreased by 4, the c. 0.276gal d. 0.627gal
second number decreased by 3, and 311. The side of a square is 36 cm. A
the third number increased by 14, the second square is formed by joining, in
new numbers will be in geometric the proper order, the third points of
progression. Find the fifth term of the the sides of the first square. A third
geometric progression. square is formed by joining the third
a. 360 b. 310 points of the second square, and so
c. 324 d. 256 on. Find the side of the 25th square.
306. The half life of a certain a. 0.0129 cm b. 0.0232 cm
radioactive substance is 2 years. Find c. 0.0173 cm d. 0.0311 cm
the amount that will be left from a 420 312. Find the “sum” of the infinite
gram substance after 22 years. geometric progression 36, 24, 16, …
a. 0.10g b. 0.82g a. 108 b. 180
c. 0.21g d. 0.41g c. 160 d. 116
307. In a family, the three children’s 313. Find the limiting value of
ages are in geometric progression. 0.38444…
When the youngest child was born, the a. 317/450 b. 371/450
oldest was thrice as old as the second c. 173/450 d. 137/450
child. In 3 years, the sum of the ages 314. The sum of an infinite geometric
of the second and the youngest child series is 8. Each term in the series is
will be equal to the age of the oldest. four times the sum of all the terms
How old was the oldest child when the that follows it. Find the fourth term.
youngest child was born? a. 8/625 b. 16/625
a. 3yearsold b. 27yearsold c. 32/625 d. 64/625
c. 12yearsold d. 9yearsold 315. A ball is dropped from a height of
308. An amount of money worth P15, 48 ft and rebounds two thirds of the
000 was borrowed at a rate of interest distance it falls. If it continues to fall
of 8% per year. If the interest is added and rebound in this way, how far will it
to the principal every years, how much travel before coming to rest?
must be repaid after 6 years? a. 120 ft b. 192 ft
a. P20,407.33 c. 240 ft d. 200 ft
316. A man borrowed a certain arithmetic progression. If the third
amount of money and promised to pay number were decreased by 3 they
his dept with equal monthly payments would be in geometric progression.
at an interest rate of 12% per month. Find the third term of the harmonic
At the end of the month, he is paying progression.
P6,720 which is just the interest of his a. 0 b. 18 c. 16 d. 12
debt. If he continues to pay this way, 324. It took a certain vehicle 3 hours
will he be able to repay all his debt? to travel a distance of 120 km. On its
How much did he borrow? way back, it took him only 2 hours to
a. Yes, P56,000 travel the same path. What was his
b. Yes,P65,000 average speed?
c. No, P65, 000 a. 44 kph b. 48 kph
d. No, P56, 000 c. 50 kph d. 56 kph
317. The side of a square is 36 cm. A 325. A car travels from P to Q at 36
second square is formed by joining, in kph and returns from Q to P at 24 kph.
the proper order, the third points of Find its average velocity.
the sides of the first square. A third a. 30.22 kph b. 30.00
square is formed by joining the third c. 28.80 kph d. 29.39 kph
points of the second square, and so 326. A race is scheduled for four laps.
on. Find the area of the squares. The velocities of a car for these laps
a. 3,402.77 cm2 are 60 kph, 56 kph, 52 kph, and 63
b. 2,916.00 cm2 kph, consecutively. Find its average
c. 5,089.46 cm2 velocity for the whole race.
d. 4,223.83 cm2 a. 57.30 kph b. 57.45 kph
Harmonic Progression c. 57.60 kph d. 57.75 kph
327. If a carpenter spends P1,000 in
318. Find the 20th term of the one month for nails costing P200 per
harmonic progression ½, 1/5, 1/8,… carton and spends another P1,000 a
a. 1/50 b. 1/53 month later for the same kind of nails
c. 1/56 d. 1/59 that now cost P300 per carton, how
319. Find the 52nd term of the much did he pay per carton on the
harmonic progression 9/8, 45/13, average for the nails he purchased?
-45/14,… a. P240 b. P260
a. -45/1,733 b. -45/1,337 c. P280 d. P250
c. -1,733/45 d. -1,337/45 Sequence and Series
320. The 3rd term of a harmonic
progression is 15 and the 9th term is 6. 328. The sum of the first n terms of a
Find the 11th term. sequence is given by the expression
a. 4 b. 5 c. 6 d. 7 17n2 – 11n. Determine the 20th term.
321. The arithmetic mean and a. 625 b. 652
geometric mean of two numbers are 4 c. 526 d 562
and 18, respectively. Find their 329. Find the nth term for the
harmonic mean. sequence 1/3, 2/5, 3/7, 4/9…
a. 96 b. 81 c. 84 d. 72 a. n/(2n + 1) b. n/(n + 1)
322. The geometric mean and the c. n/(2n – 1) d. n/(n – 1)
arithmetic mean of two numbers are 8 330. The sequence -1, -4, 2,… is
and 17 respectively. Find the harmonic a. AP b. GP c. HP d. IGP
mean. Diophantine Equation
a. 3.45 b. 3.76
c. 3.54 d. 3.67 331. Find the value of x in the
323. Three numbers are in harmonic equation 14x + 35y = 91. Assume x
progression. If the third number were and y are both positive integers.
decreased by 4 they would be in a. 5 b. 3 c. 6 d. 4
332. A combination of pennies, dimes, digits were reversed, the number is
and quarters amount to $0.99. Find reduced 297. Find the sum of the
the minimum number of coins for the digits.
given amount. a. 15 b. 10 c. 13 d. 17
a. 8 b. 9 c. 10 d. 11 339. Find the sym of the digit of the
333. A man bought 20 chickens for smallest positive integer that when
P20.00. The cocks cost P3.00 each, divided by 5 the remainder is 3, and
the hens P1.50 each, an the chicks at when divided by 7 the remainder is 5.
P0.50 each. How many hens did he a. 8 b. 9 c. 5 d. 6
buy? 340. A purse contains $8.85 in
a. 10 b. 13 c. 16 d. 5 quarters and dimes. Another purse
334. A merchant has three items on contains dimes as many as the
sale: namely, a radio for P50.00, a quarters and quarters as many as the
clock for P30.00 and a flashlight for dimes contained in the purse. How
P1.00. At the end of the day, he has much is in the second purse?
sold a total of 100 of the three items a. $13.10 b. $15.30
and has taken exactly P1,000.00 on c. $16.25 d. $14.35
the total sales. How many radios did 341. The sum of a certain number of
he sell? consecutive integers is 63. The largest
a. 80 b. 4 c. 16 d. 20 integer is twice the smallest. Find the
335. Three items A, B and C were sold smallest integer.
in a store. Item A cost P10.00 each, a. 4 b. 5 c. 6 d. 7
item B cost P1.00 each, and three Venn Diagram
pieces of item C cost P1.00. The total
sales at the end of the day were 342. IN a certain group of consumers,
P100.00 and a total of 100 items were each one may drink beer, and/or
sold. How many of items B were sold? brandy, and/or whisky, or all. Also 155
a. 42 b. 40 c. 54 d. 49 drink brandy, 173 drink beer, 153
336. A man is thinking of buying drink whiskies, 53 drink beer and
chocolates, nougats, and candies. brandy, 79 drink beer and whisky, 66
Chocolates cost P10.00 a piece, drink brandy and whisky. 21 of them
nougats P1.00 for 3 pieces, and drink beer, brandy and whisky. How
candies P2.00 for 7 pieces. He wants many are there in the group?
to buy a variety of 100 of these items, a. 302 b. 303
enough for his budget of P60.00. How c. 304 d. 305
many nougats must he buy? 343. Prior to the last IBP elections
a. 54 b. 42 c. 48 d. 60 survey was conducted in a certain
337. A basketball match is to be held barangay in Metro Manila to find out
in a coliseum with a seating capacity which of the three political parties they
of 2, 500. Three types of tickets are like bEst. The results indicated that
produced and it is expected that they 320 liked KBL, 250 liked LABAN and
will all be sold. Class A tickets cost 180 liked INDEPENDENT. But23of
P1,000 each, class B P750 and class C these 160 liked Both KBL and LABAN,
P400. It happened that the sold tickets 100 liked bOth LABAN and
were only half, ¾ and 4/5 of classes A, INDEPENDENTS, and 70 liked both
B and C respectively, thereby reducing KBL and INDEPENDENTS. Only 30 said
the expected total receipts by they liked all three parties and none
P559,000. How many class C tickets aDmitted that they did23not like any
were sold? party. How many voters are there in
a. 1,200 b. 960 the barangay?
c. 1,050 d. 840 a. 450 b. 420
338. The units digit of three digit c. 485 d. 510
number is twice the tens digit. If the
344. The President recently appointed and B, 20% smoke cigarettes A and C
25 generals of the AFP. Of these 12% smoke cigarette B and C only,
14 have already served in the and 10% smoke all three cigarettes.
encounter in Jolo What percent smoke exactly two
12 have already served in the brands of cigaretTes?
encounter in Basilan a. 42% b. 32%
10 have already served in the c. 7% d. 20%
encounter in Sultan Kudarat 349. I discovered that my cAt Sweenie
There were also had a taste for lizards. He chases
6 who served in the encounter them, plays with them, and then eats
in Jolo and Basilan them afterwards. One day, hE
3 who served in the encounter deposited lizard on my carpEt 6 gray
in Basilan and Sultan Kudarat lizards, 12 lizards that had dropped
4 who served in the encounter their tails in an effort to escape
in Jolo and Sultan Kudarat capture, and 15 lizards that he’d
How may general served in all chewed on A little. Only one of the
three counters? lizards was gray cHewed on, and
a. 1 b. 2 c. 3 d. 4 tailless; two were gray and tailless but
345. The probability of the students not chEwed on; two were gray and
passing Chemistry and Physics are chewed on but not tailless. If there
70% and 50% respectively. None of were a total of 24 lizards, how many
the students failed in both subjects. If were tailless ad chewed on but not
8 of them passed both subjects, how gray?
many students took the exam? a. 4 b. 6 c. 5 d. 3
a. 30 b. 50 c. 40 d. 60 350. A survey concerning the
346. The probability of the students preferences of a group of persons on
passing Chemistry and Physics are different brands of shows the
40% and 55% respectively. If there following:
are 260 students who took the exam 31 who drink Matador and
and 37 of them failed in both subjects, Chivas Regal do not like Emperador
how many students passed both 140 drink Matador
subjects? 152 drink Emperador
a. 20 b. 28 c. 27 d. 24 160 drink Chivas Regal
347. A survey concerning a group of The ratio of those who drink
TV viewers shows the following: Emperador and Chivas Regal to those
56% watch sports who drink Emperador and Matador is 4
39% watch movie to 5. Twelve of those who prefer
51% watch news Emperador and Chivas Regal only
16% watch sports and movies changed their brand and decided to
19% watch movies and news drink Emperador, Matador only
30% watch sports and news because Chivas Regal is expensive for
11% watch sports, movies and them. The ratio of those who drink
news Emperador and Chivas Regal to those
The rest are children who like who drink Emperador and Matador
watching cartoons only. How many of then becomes 1 to 2. If 63 drink
the TV viewers are children? Emperador only, how many
a. 15% b. 12% respondents are there?
c. 8% d. 10% a. 251 b. 286 c. 290 d. 313
348. In a survey concerning the 351. Experts Review Center gave an
smoking habits of consumer, it was examination of Geometry, Calculus,
found that 50% smoke cigarette B, Probability and Engineering Economy
55% smoke cigarette A, 40% smoke to its students. The results are as
cigarette C, 30% smoke cigarette A follows:
 178 passed Engineering 354. The salary of an employee’s job
Economy has five levels, each one 5% greater
172 passed Probability than the one below it. Due to
177 passed Calculus circumstances, the salary of the
161 passed Geometry employee must be reduced from the
65 passed Probability and top (fifth) level to the second level,
Engineering Economy which means a reduction of P6, 100.00
63 passed Calculus and per month. What is the employee’s
Engineering Economy present salary per month?
56 passed Calculus and a. P22, 502.47b. P28, 546.08
Probability
49 passed Geometry and c. P34, 672.48d. P44, 799.44
Engineering Economy 355. During dinner, the guests were
60 passed Geometry and told to share dishes with one another.
probability Every two of them share a dish for
51 passed Geometry and rice, every three a dish for broth, and
Calculus every four a dish for meat. If there are
19 passed Calculus, Probability, 65 dishes in all, how many guests
and Engineering Economy were there?
20 passed Geometry, a. 84 b. 48 c. 60 d. 72
probability and Engineering Economy 356. A son in the family says “I have
15 passed Geometry, calculus, sisters twice as many as brothers. A
and Engineering Economy daughter in the same family says “I
16 passed Geometry, Calculus have brothers two thirds as many as
and Probability sisters”. How many children are there
6 passed all subjects in the family?
IF there are 93 students who did not a. 18 b. 12 c. 15 d. 16
pass in any subject, how many 357. A traffic check counted 390 cars
students does Experts Review Center passing a certain spot on one day and
have? 430 cars at the same spot on the
a. 498 b. 499 c. 500 d. 501 following day. During the first day
Miscellaneous Problems there were 3 times as many cars going
East and half as many going West as
352. In a certain electronics factory, on the second days was the total
the ratio of the number of male to number of eastbound cars and the
female workers is 2:3. If 100 new total number of westbound cars for the
female workers are hired, the number two days?
of female workers will increase to 65% a. Eastbound = 280 cars,
of the total number of workers. Find Westbound = 540 cars
the original number of workers in the b. Eastbound = 240 cars,
factory. Westbound = 580 cars
a. 960 b. 420 c. 700 d. 540 c. Eastbound = 580 cars,
353. Twelve cubic yards of crushed Westbound = 240 cars
stone for surfacing three private roads d. Eastbound = 540 cars,
of different lengths is to be distributed Westbound = 280 cars
in three piles so that the second pile 358. If there is a bird on every branch,
has 20 cubic feet less than the first there will be an excess bird. But if
and the third pile has 8 cubic feet there will two birds per branch, there
more than twice as much as the first. will be an excess branch. How many
How much material should go into the branches are there?
first pile? a. 2 b. 3 c. 4 d. 5
a. 176 b. 104 c. 84 d. 64 359. An Argentine air Armanda was
engaged in an air battle by British RAF
planes superior in number with a ratio
of 11 to 9. After the battle, the total
count of planes destroyed on both
sides was 35% of which 15 belong to
the British and the surviving strength
is in proportion of 8 British to 5
Argentines. Find the original strength
of the British.
a. 55 b. 60 c. 50 d. 45
360. During the last election, the total
number of votes recorded in a certain
municipality was 12, 400. Had 2/5 of
the supporters of a LABAN candidate
stayed away from the polls and ½ of
the supporters of a GAD candidate
behaved likewise, the LABAN
candidate’s majority over the other
would have been reduced by 100. How
many votes did LABAN receive?
a. 6,300 b. 5,400
c. 7,000 d. 8,100
361. The total number of voters in a
certain barangay is 640. Two
candidates A and B run for barangay
chairman with A emerging as a winner.
Had 42 candidates A’s supporters
changed their minds and voted instead
for candidate B, candidate A would
have been lost by half of his previous
majority over candidate B’s
supporters. How many votes did
candidate A had?
a. 322 b. 368 c. 348 d. 270