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Basic Math Problems: 1.) A certain luxury ship cruses Cebu to Manila at 21 knots. If it will take 21 hours to reach Manila from Cebu, the distance travel by the ship is nearly a. 847.5 km b. 507.15 statute mile c. 441 statute mile d. 414 nautical mile Solution: Solving for distance, D = Vt V = 21 knots = 21 D = 21(21) = 441 nautical miles x = 507.15 statute mile 2.) Carry out the following multiplication and express your answer in cubic meter: 8cm x 5mm x 2m a. 8 x 10 – b. 8 x 10^2 c. 8 x 10- d. 8 x 10- Solution: 8 cm x = 0.8 m 5 mm x =0.005 m 0.08(0.005)(2) = 8 x 10-4^ m^3 3.) Which of the following is equivalent to 1 hectare? a. 100 ares b. 2 acres c. 1000 square meters d. 50000 square feet Solution: 1 hectare = 100 ares = 10,000 sq. meters 4.) A 7kg mass is suspended in a rope. What is the tension in the rope in SI? a. 68.67 N b. 70 N c. 71 N d. 72 N Solution: The unit of force (tension) in the SI system is newtons (N). Tension = 7 kg = 68.67 N
5.) A 10 liter pail is full of water. Neglecting the weight of the pail, how heavy is its water content? a. 5 kg b. 6.67 kg c. 10 kg d. 12.5 kg Solution: Density of water () is 1000 or 1 W = • V W = 1 x 10 liters = 10 kg 6.) If 16 is 4 more than 4x, find 5x – 1. a. 14 b. 3 c. 12 d. 5 Solution: 16 = 4x + 4 x = 3 5x – 1= 5(3) – 1 = 14 7.) Solve for the value of x and y. 4x + 2y = 5 13x – 3y = 2 a. y = ½ , x = 3/ b. y = 3/2 , x = ½ c. y = 2 , x = 1 d. y = 3 , x = 1 Solution: 4x + 2y = 5 y = - 2x 13x – 3y = 2 Substitute (1) in (2): 13x - 3 = 2 18x = 2 + = x = = y = - 2 =
anm^ = (an)m^ = 1000000 (1000)m^ = 100, m = 2 Substitute m = 2, in (3): a^2 = 1000 a = 10 12.) Give the factors of the a^2 – x^2. a. 2a – 2x b. (a + x)(a - x) c. (a + x)(a + x) d. 2x – 2a Solution: a^2 – x^2 = (a+x)(a-x) 13.) Solve value of k so that 4x^2 + 6x + k is a perfect square. a. 36 b. 2. c. 9 d. 2. Solution: x^2 + 1.5x + 0.25k = 0 = 0 since it is perfect square, then (1.5 / 2)^2 = 0.25k k = 2. 14.) If x to the ¾ power equals 8, x equals a. – b. 6 c. 9 d. 16 Solution: x = (8)4/3^ = 16 15.) If f(x) = 2x^2 + 2x + 4, what is f(2)? a. 4x + 2 b. 16 c. x^2 + x + 2 d. 8
Solution: f(x) = 2x^2 + 2x + 4 f(2) = 2(2)^2 + 2(2) + 4 = 16 16.) Find the quotient 3x^5 - 4x^3 + 2x^2 + 36x + 48 divided by x^3 - 2x^2 + 6 a. 3x^2 - 4x – 8 b. 3x^2 + 4x + 8 c. 3x^2 - 6x – 8 d. 3x^2 + 6x + 8 Solution: 17.) Find the mean proportional of 4 and 36. a. 72 b. 24 c. 12 d. 20 Solution: Let: x = the mean proportion of 4 and 36 = x^2 = 144 x = 18.) In the equation x^2 + x = 0, one root is equal to a. 1 b. 5 c. ¼ d. none of these Solution: x(x + 1) = 0 x = 0 x = - 19.) Determine k so that the equation 4x^2 + kx + 1 = 0 will have just one real solution. a. 3 b. 4 c. 5 d. 6 Solution:
Solution: loga 10 = 0. = 0. log 10 a = = 4 24.) If log (^) b 1024 = 5/2. Find b. a. 2560 b. 16 c. 4 d. 2 Solution: logb 1024 = = logb b = = 1. b = antilog (1.204) = 16 25.) Find the value of x if log 12 x = 2. a. 144 b. 414 c. 524 d. 425 Solution: log 12 x = 2 x = (12)^2 = 144 26.) The sum of Kim’s and Kevin’s ages is 18. in 3 years, kim will be twice as old as Kevin. What are their ages now? a. 4, 13 b. 5, 13 c. 7, 11 d. 6, 12 Solution: x + y = 18 y = 18 – x (y + 3) = 2(x + 3) Substitute y in equation (2): (18 –x) + 3 = 2x + 6 21 – x = 2x + 6 x = 5 years old y = 18 – 5
y = 13 years old 27.) A father tells his son , “I was your age now when you were born.” If the father is now 38 years old, how old was his son 2 years ago? a. 15 b. 17 c. 19 d. 21 Solution: 38 – x = x - 0 x = 19 years old Two years ago, the son was (19 – 2) = 17 years old 28.) A pump can pump out water from a tank in 11 hours. Another pump can pump out water from the same tank in 20 hrs. how long will it take both pumps to pump out the water in the tank? a. 7 hours b. 6 hours c. 7 ½ hours d. 6 ½ hours Solution: Let: x = time needed to complete the work
- = x = 7.096 hours 29.) Glenn can paint a house in 9 hours while Stewart can paint the same house in 16 hours. They work together for 4 hours. After 4 hours, Stewart left and Glenn finished the job alone. How many more days did it take Glenn to finish the job? a. 2.75 hours b. 2.50 hours c. 2.25 hours d. 3 hours Solution: Note: (rate)(time) = 1(complete job) 4 + (x) = 1 0.6944 + 0.111x = 1 x = 2.75 hours 30.) Mike, Loui and Joy can mow the lawn in 4, 6 and 7 hours respectively. What fraction of the yard can they mow in 1 hour if they work together? a. 47/ b. 45/ c. 84/
34.) Find the fraction such that if 2 is subtracted from its terms its becomes ¼, but if 4 is added to its terms it becomes ½. a. 3/ b. 5/ c. 5/ d. 6/ Solution: Let: = the fraction = 4x – 8 = y – 2 y = 4x – 6 = 2x + 8 = y + 4 Substitute (1) in (2): 2x+8 = (4x – 6) + 4 10 = 2x x = 5 y = 4(5) – 6 = 14 Thus the fraction is. 35.) Find the product of two numbers such that first added to the second equals to 19 and three times the first is 21 more than the second. a. 24 b. 32 c. 18 d. 20 Solution: Let: x = the first number y = the second number 2x + y = 19 y = 19 – 2x 3x = y + 21 Substitute (1) in (2): 3x = (19 – 2x) + 21 5x = 40 x = 8 y = 19 – 2(8) = 3 36.) A man rows downstream at the rate of 5mph and upstream at the rate of 2mph. How far downstream should he go if he return in 7/4 hours after leaving? a. 2.5 miles b. 3.3 miles c. 3.1 miles d. 2.7 miles Solution:
Note: time = t 1 + t 2 = ttotal
- = 0.7(S) = 1.75 S = 2.5 miles 37.) An airplane flying with the wind, took 2 hours to travel 1000km and 2.5 hours in flying back. What was the wind velocity in kph? a. 50 b. 60 c. 70 d. 40 Solution: Let: V 1 = velocity of airplane V 2 = velocity of wind V 1 + V 2 = = 500 V 1 - V 2 = = 400 Subtract (2) from (1): (V 1 +V 2 ) – (V 1 -V 2 ) = 500 – 400 2V 2 = 100 V 2 = 50 kph 38.) On a certain trip, Edgar drive 231 km in exactly the same time as Erwin drive 308 km. If Erwin’s rate exceeded that of Edgar by 13 kph, determine the rate of Erwin. a. 39 kph b. 44 kph c. 48 kph d. 52 kph Solution: Let: V = rated of Erwin V – 13 = rate of Edgar t 1 =^ t 2 = 231V = 308V – 4004 V = 52 kph 39.) In how many minutes after 7 o’clock will the hands be directly opposite each other for the first time? a. 5.22 min b. 5.33 min c. 5.46 min d. 5.54 min Solution:
d. Php 400 Solution: Let: x = selling price without discount 0.8x = new selling price (with discount) Profit = Income – Expenses 0.3 (0.8x) = 0.8x – 200 0.24 x = 0.8x – 200 x = P 357. 43.) The sum of three arithmetic means between 34 and 42 is a. 114 b. 124 c. 134 d. 144 Solution: 34, a 2 , a 3 , a 4 , 42 a 5 = a 1 + 4d Thus, a 2 = 36, a 3 = 38 and a 4 = 40 42 = 34 + 4d sum = 36 + 38 + 40 = 114 d = 2 44.) A stack of bricks has 61 bricks in the bottom layer, 58 bricks in the second layer, 55 bricks in the third layer, and so on until there are 10 bricks in the last layer. How many bricks are there al together? a. 638 b. 637 c. 639 d. 640 Solution: a 1 = 61; a 2 = 58; a 3 = 55; an = 10 By inspection, d = -3 an = a 1 + (n-1)d 10 = 61 + (n-1)(-3) 10 = 61 – 3n + 3 n = 18 S = = S = 639 logs 45.) Once a month, a man puts some money into a cookie jar. Each month he puts 50 centavos more into the jar than the month before. After 12 years, he counted his money, he had Php 5,436. how much money did he put in the jar in the last month? a. Php 73. b. Php 75. c. Php 74. d. Php 72. Solution: d = 0.50; n = 12(12) = 144
S =
5436 = a 144 = a 1 + 143d 5436 = 144a 1 + 5148 = 2 + 143(2) a 1 = 2 a 144 = P 73. 46.) How many times will a grandfather’s clock strikes in one day if it strikes only at the hours and strike once at 1 o’clock, twice at 2 o’ clock and so on? a. 210 b. 24 c. 156 d. 300 Solution: a 1 = 1; a 2 = 2; a 3 = 3; ……. a 12 = 12 S = = (1+12) S = 78 Note: One day is equivalent to 24 hours. Thus, total = 2(78) = 156 times 47.) When all odd numbers from 1 to 101 are added, the result is a. 2500 b. 2601 c. 2501 d. 3500 Solution: a 1 = 1; an=101; d= an = a 1 + (n-1) d 101 = 1 + (n-1)(2) S = = = 2601 101 = 1 + 2n – 2 n = 51 48.) The fourth term of a Geometric Progression is 216 and the 6th^ term is 1944. find the 8 th^ term. a. 17649 b. 17496 c. 16749 d. 17964 Solution: a 4 = 216; a 6 = 1994 a 4 = a 1 r^3 a 6 = a 1 r^3 216 = a 1 r^3 1994 = a 1 r^3 Divide (2) by (1): = r^2 = 9 r = 3 Substitute r in (1): 216 = a 1 (3)^3
c. 18 d. 21 Solution: Total spheres = 10 + 6 + 3 + 1 = 20 spheres 53.) A club 0f 40 executives, 33 like to smoke Marlboro and 20 like to smoke Philip Morris. How many like both? a. 10 b. 11 c. 12 d. 13 Solution: Let: x = number of executives who smoke both brand of cigarettes (33-x)+x+(20-x) = 40 33 + 20 – x = 40 x = 13 executives 54.) How many four letter words beginning and ending with the vowel without any letter repeated can be formed from the word “personnel”? a. 40 b. 480 c. 20 d. 312 Solution: Note: “PERSONNEL” Number of vowels = 2(E&O) Number of consonants = 5 (P,R,S,N & L) Two vowels can be filled in this section Five consonants can be filled in this section Four consonants can be filled in this section One vowel can be filled in this section 2 5 4 1 Let: N = number of words N = 2(5)(4)(1) = 40 words 55.) What is the number of permutations of the letters in the word BANANA? a. 36 b. 60 c. 52 d. 42 Solution: Note: “BANANA” Number of A’s = 3 = = =60 ways
Number of N’s = 2 56.) Four different colored flags can be hung in a row to make coded signal. How many signals can be made if a signal consists of the display of one or more flags? a. 64 b. 66 c. 68 d. 62 Solution: N = 10(8)(6) N = 180 ways 57.) In how many ways can 4 boys and 4 girls be seated alternately in a row of 8 seats? a. 1152 b. 2304 c. 576 d. 2204 Solution: Number of ways the 4 boys can be arranged = 4! Number of ways the 4 girls can be arranged = 4! N = (4! 4!)2 = 1152 ways 58.) In how many ways can you invite one or more of your five friends in a party? a. 15 b. 31 c. 36 d. 25 Solution: 5 C1,2.. = 2 5 – 1^ = 31 combinations 59.) There are 50 tickets in a lottery in which there is a first and second prize. What is the probability of a man drawing a prize if he owns 5 tickets? a. 50% b. 25% c. 20% d. 40% Solution: P = probability of the man to win a prize P = number of tickets he bought x probability of winning the lottery P = 5 = 60.) A coin is tossed 3 times. What is the probability of getting 3 tails up? a. 1/ b. 1/ c. ¼ d. 7/
b. 8/ c. 3/ d. 2/ Solution: Numbers from 1 to 20, which is divisible by 3=6 numbers (3,6,9,12,15,18) Numbers from 1 to 20, which is divisible by 7 = 2 numbers (7,4) Total numbers from 1 to 20, which is divisible by 3 or 7 = 8 numbers Let: P = probability that the ticket number is divisible by 3 or 7 P = P = =
- Find each interior angle of a hexagon. A. 90° C. 150° B. 120° D. 180° Solution: = Note: A hexagon has 6 sides, thus n=6. = = 120°
- The sides of a triangle are 8 cm, 10cm and 14 cm. Determine the radius of the inscribed circle. A. 2.25 cm C. 2.45 cm B. 2.35 cm D. 2.55 cm Solution: A = = = = 16 A = A = 39.19 cm^2 A = r s 39.19 = r(16) r = 2.45 cm
- A circle with radius 6 cm has half its area removed by cutting off a border of uniform width. Find the width of the border. A. 1.76 cm C. 1.98 cm B. 1.35 cm D. 2.03 cm Solution: Note: Since half of the area was removed, then the area (A) left is also one-half of the total area. A = = =18 But “A” is also equal to the area of the small circle. A = r^2
- The area of a circle is 89.42 sq. inches. What is its circumference? A. 32.25 in. C. 35.33 in. B. 33.52 in. D. 35.55 in.
Solution: A = r^2 Let: C = circumference of the circle 89.42 = r^2 C = 2r = (2)(5.335) = 33.52 in. r = 5.335 in
- What is the area in sq. cm. Of the circle circumscribed about an equilateral triangle with a side 10 cm long? A. 104.7 C. 106. B. 105.7 D. 107. Solution: Note: Since an equilateral triangle. A = B = C = 60°. A = bc sin A = (10)^2 sin 60° A = 43.3 cm^2 A = = 43.3 = r = 5.774 cm Solving for area of cirle: A = r^2 = (5.774)^2 A = 104.7 cm^2
- The angle of a sector is 30° and the radius is 15 cm. What is the area of the sector in cm^2? A. 59.8 C. 58. B. 89.5 D. 85. Solution: A = r^2 where: A = area pf the sector r =radius of the circle = included angle in radians A = (15)^2 = 58.9 cm^2
- The arc of a sector is 9 units and its radius is 3 units. What is the area of the sector in square units? A. 12.5 C. 14. B. 13.5 D. 15. Solution: A = rC where: r = radius of the circle C = length of arc A = (3)(9) A = 13.5 sq. units
- What is the area in sq. m of the zone of a spherical segment having a volume of 1470.265 cu. m if the diameter of the sphere is 30m? A. 465.5 m^2 C. 665.5 m^2 B. 565.5 m^2 D. 656.5 m^2 Solution: V = (3r-h)
