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MCQs / Compilation of Mathematics Problems - SOLID GEOMETRY

MCQs / Compilation of Mathematics Problems - SOLID GEOMETRY

Compilation of Problems in Solid Mensuration MULTIPLE CHOICE QUESTIONS / COMPILATION OF MATH PROBLEMS SOLID MENSURATION 1. The sum ...

MCQs / Compilation of Mathematics Problems - TRIGONOMETRY

MCQs / Compilation of Mathematics Problems - TRIGONOMETRY

Compilation of Problems in Trigonometry MULTIPLE CHOICE QUESTIONS / COMPILATION OF MATH PROBLEMS TRIGONOMETRY 1. If sin A = 3/5 and ...

MCQs / Compilation of Mathematics Problems - ALGEBRA

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<tr><td class="tr-caption" style="text-align: center;">Compilations of Problems in Algebra</td></tr>
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COMPILATION OF MATH PROBLEMS</div>
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ALGEBRA</div>
 
1. Ten less than four times a certain number is 14. Determine the number. 
 
2. The hypotenuse of a right triangle is 34 cm. Find the length of the two legs if one leg is 14 cm longer than the other. 
 
3. Find the equation whose roots are the reciprocals of the roots of the equation 2x^2 - 3x – 5 = 0. 
 
4. The sum of two numbers is 21 and one number is twice the other. Find the numbers. 
 
5. For a particular experiment, you need 5 liters of a 10% solution. You find 7% and 12% solution on the shelves. How much of the 7% solution should you mix with the appropriate amount of the 12% solution to get 5 liters of a 10% solution. 
 
6. A circle with a radius of 6 has half of its area removed by a cutting border of uniform width. Find the width of the border. 
 
7. Two triangles have equal bases. The altitude of one triangle is 3 units more than its base while the altitude of the other is 3 units less than its base. Find the altitudes if the areas of the triangle differ by 21 square units. 
 
8. The roots of the quadratic equation are 1/3 and 1/4. What is the equation? 
 
9. Find the 30th term of the progression 4, 7, 10, … 
 
10. The denominator of a certain fraction is three more than twice the numerator. If 7 is added to both terms of the fraction, the resulting fraction is 3/5. Find the original fraction. 
 
11. A piece of wire is shaped to enclose a square whose area is 169 sq. cm. It is then reshaped to enclose a rectangle whose length is 15 cm. Find the area of the rectangle. 
 
12. Find the sum of 6, -2, 2/3, … 
 
13. In the expansion of (x+4y)^12, find the numerical coefficient of the 5th term. 
 
14. Find the sum of the first 10 terms of the progression 2, 4, 8, 16, … 
 
15. Find the ratio of an infinite geometric progression if the sum is 2 and the first term is 1/2. 
 
16. Find the 30th term of the sequence 4, 7, 10, … 
 
17. A man rows downstream at the rate of 5 mph and upstream at the rate of 2 mph. How far downstream should he go if he is to return in 7/4 hours after leaving? 
 
18. Find the mean proportional of 4 and 36. 
 
19. Mary is 24 years old. Mary is twice as old as Ana was when Mary was as old as Ana is now. How old is Ana now? 
 
20. Determine x so that x, 2x+7, 10x–7 will be a geometric sequence. 
 
21. Mike, Louis 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? 
 
22. Given: (x) = (x+3) (x–4) + 4. When f(x) is divided by (x–k), the remainder is k. Find k. 
 
23. The sum of the digits of a two-digit number is 11. If the digits are reversed, the resulting number is seven more than twice the original number. What is the original number? 
 
24. The time required for the examinees to solve the same problem differ by two minutes. Together, they can solve 32 problems in one hour. How long will it take for the slower problem solver to solve a problem? 
 
25. Find the sum of the roots of 5x^2 - 10x + 2 = 0. 
 
26. In a box there are 25 coins consisting of quarters, nickels and dimes with a total amount of $2.75. If the nickels were dimes, the dimes were quarters and the quarters were nickels, the total amount would be $3.75. How many quarters are there? 
 
27. A man travels in a motorized banca at the rate of 15 kph from his barrio to the poblacion and come back to his barrio at the rate of 12 kph. If his total time of travel back and forth is 3 hours, find the distance from the barrio to the poblacion. 
 
28. One leg of a right triangle is 20 cm and the hypotenuse is 10 cm longer than the other leg. Find the length of the hypotenuse. 
 
29. Three times the sine of a certain angle is twice of the square of the cosine of the same angle. Find the angle. 
 
30. A man is 41 years old and his son is 9. In how many years will the father be three times as old as his son? 
 
31. A tank is filled with an intake pipe that fills it in 2 hours and an outlet pipe that empty it in 6 hours. If both pipes are left open, how long will it take to fill the empty tank? 
 
32. A piece of wire of length 50 m is cut into two parts. Each part is then bent to form a square. It is found that the total area of the square is 100 m^2. Find the difference in length of the sides of the two squares. 
 
33. A purse contains $11.65 in quarters and dimes. If the total number of coins is 70, find how many dimes are there? 
 
34. How many liters of water must be added to 35 liters of 89% HCl solution to reduce its strength to 75%? 
 
35. Find the value of m that will make 4x^2 - 4mx + 4m + 5 a perfect square trinomial. 
 
36. Ana is 5 yrs. older than Beth. In 5 yrs., the product of their ages is 1.5 times the product of their present ages. How old is Beth now? 
 
37. Find the coefficient of the term involving b^4 in the expansion of (a^2 - b^2)^10. 
 
38. The seating section in a Coliseum has 30 seats in the first row, 32 seats in the second row, 34 seats in the third row, and so on, until the tenth row is reached, after which there are ten rows each containing 50 seats. Find the total number of seats in the section. 
 
39. Pedro started running at a speed of 10 kph. Five minutes later, Mario started running in the same direction and catches up with Pedro in 20 minutes. What is the speed of Mario? 
 
40. The sum of two numbers is 35 and their product is 15. Find the sum of their reciprocals. 
 
41. The ten’s digit of a certain two digit number exceeds the unit’s digit by four and is one less than twice the unit’s digit. Find the number. 
 
42. One pipe can fill a tank in 6 hours and another pipe can fill the same tank in 3 hours. A drain pipe can empty the tank in 24 hours. With all three pipes open, how long will it take to fill in the tank? 
 
43. A piece of paper is 0.05 inch thick. Each time the paper is folded into half, the thickness is doubled. If the paper was folded twelve times, how thick in feet the folded paper be? 
 
44. A man invested part of Php 20,000 at 18% and the rest at 16%. The annual income from 16% investment was Php 620 less than three times the annual income from 18% investment. How much did he invest at 18%? 
 
45. If 3^x=9^y  and 27^y=81^z, find x/z. 
 
46. It takes an airplane one hour and forty five minutes to travel 500 miles against the wind and covers the same distance in one hour and fifteen minutes with the wind. What is the speed of the airplane? 
 
47. An airplane travels from points A and B with a distance of 1500 kms and a wind along its flight line. If it takes the airplane 2 hours from A to B with the tailwind and 2.5 hours from B to A with the headwind, what is the velocity? 
 
 
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MCQs / Compilation of Mathematics Problems - ALGEBRA

Compilations of Problems in Algebra COMPILATION OF MATH PROBLEMS ALGEBRA 1. Ten less than four times a certain number is 14. Determ...

LET Reviewer for GENERAL EDUCATION (MATHEMATICS) Part 3

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LET Reviewer in General Education</div>
 
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PRACTICE TEST FOR GENERAL EDUCATION 
MATHEMATICS 
 
1. Give the factors of 2x3 + 9x2 + 9x 
a. x (2x – 3)(x + 3) 
b. x (2x + 3)(x + 3) 
c. x (3x – 2)(x + 3) 
d. x (2x + 3)(x – 3) 
 
2. Which of the following is/are TRUE? 
I. x3 - y3 = (x – y)(x2 + y2) 
II. (5x – 2y)(5x – 2y) = 25x2 – 20xy+4y2 
III. x2 + y2 = (x + y)(x + y) 
 
a. I only 
b. I and III 
c. II only 
d. I and II 
 
3. If f(x) = x4 – x2 and g(x) = x3 – 3x2 + 2x, then for all values of x for which g(x) ≠ 0, f(x)/g(x) 
a. 2(x + 1) / (x – 2) 
b. x(x – 1)/ (x – 2) 
c. x(x + 1) / (x – 2) 
d. x(x – 1)/ (x + 2) 
 
4. If x =-5, what is the value of (x^2-9)/(x+3) ? 
a. -8 
b. -6 
c. 5 
d. 7 
 
5. Divide (x^2-9)/y ÷ (2x+6)/8 
a. 4(x-3)/y 
b. 4(x+3)/y 
c. 4(x-9)/y 
d. 4(x+9)/y 
 
6. What value of x will satisfy the equation 0.2(2x+1470) = x? 
a. 490 
b. 560 
c. 1470 
d. 2130 
 
7. Three times the first of three consecutive odd integers is 3 more than twice the third. Find the third integer. 
a. 9 
b. 13 
c. 11 
d. 15 
 
8. The product of 2 whole numbers is 36, and their ratio is 1:4. Which of these is the smaller number? 
a. 9 
b. 3 
c. 2 
d. 12 
 
9. A, B, and C are consecutive numbers. If A>B>C, what is the value of (A-B) (A-C) (B-C)? 
a. -2 
b. -1 
c. 1 
d. 2 
 
10. Charlie was 40 years when his son Adam was born. How old was Charlie when he was 5 times as old as Adam? 
a. 40 
b. 45 
c. 50 
d. 60 
 
11. In 2001, Lior was four times as old as Ezra, and in 2003, Lior was twice as old as Ezra. How many years older than Ezra is Lior? 
a. 1 
b. 2 
c. 3 
d. 4 
 
12. A man started painting a wall at 9:00 AM and was able to finish painting 3/5 of it at 10:30 AM. Continuing at this rate, at what time will he finish painting the wall? 
a. 11:35 AM 
b. 11:30 AM 
c. 12:30 AM 
d. 12:15 AM 
 
13. If Mary can address a box of envelopes in 5 hours and Jane can address the same box of envelopes in 10 hours, how many minutes will it take Mary and Jane working together to address all the envelopes in the box? 
a. 80 
b. 160 
c. 200 
d. 450 
 
14. A father and son working together can finish painting a room in 6 hours. Working alone, a father takes 9 hours to do the painting. How many painting hours will it take the son, working alone, to finish painting the room? 
a. 18 
b. 75 
c. 15 
d. 12 
 
15. How much water must be added to 100 cc of 80% solution of punch to reduce it to 50%? 
a. 18 cc 
b. 1540 cc 
c. 36 cc 
d. 60 cc 
 
16. How many ounces of pure acid must be added to 20 ounces of a solution that is 5% acid to strengthen it to a solution that is 24% acid? 
a. 5 
b. 6 
c. 10 
d. 2 ½ 
 
17. Two buses leave the same station at 9:00 pm. One bus travels north at the rate of 30 kph and the other travels east at 40 kph. How many kilometers apart are the buses at 10 pm? 
a. 50 km 
b. 70 km 
c. 100 km 
d. 140 km 
 
18. Kath’s grades in three math quizzes are 82, 78, 86. What grade should get in her next quiz to raise her average to 85? 
a. 94 
b. 90 
c. 88 
d. 87 
 
19. In the playground for kindergarten kids, 18 children are riding tricycles or bicycles. If there are 43 wheels in all, how many tricycles are there? 
a. 7 
b. 8 
c. 9 
d. 11 
 
20. At an amusement park, Lance bought 3 hamburgers and 4 sodas for a total of PhP 150. While paying the same prices, Karen bought 2 hamburgers and 3 sodas for PhP 105. What is the total cost of 1 hamburger and 1 soda? 
a. PhP 15 
b. PhP 40 
c. PhP 30 
d. PhP 45 
 
21. What day follows the day before yesterday if 2 days from now will be Sunday? 
a. Wednesday 
b. Thursday 
c. Friday 
d. Saturday 
 
22. If July 12, 2003 fell on a Tuesday, on what day will July 12, 2005 fall? 
a. Monday 
b. Thursday 
c. Sunday 
d. Friday 
 
23. If January 1, 2008 is a Wednesday, on what day does Christmas day of the same year fall? 
a. Thursday 
b. Friday 
c. Wednesday 
d. Saturday 
 
24. What are the missing terms in the series 5, 10, 20 _____, 80, ____320? 
a. 40, 160 
b. 40, 120 
c. 50, 120 
d. 35, 135 
 
25. The first 5 numbers in a sequence are 5,6,8,11 and 15. What are the 8th and 10th numbers in the sequence? 
a. 27 and 42 
b. 26 and 49 
c. 33 and 50 
d. 32 and 49 
 
26. What is the 500th digit to the right of the decimal point when 15/37 is expressed as a decimal? 
a. 0 
b. 4 
c. 5 
d. 7 
 
27. What is the sum of all the two digit numbers which are divisible by 5? 
a. 945 
b. 950 
c. 960 
d. 1050 
 
28. What is the 10th term in the progression -8, 4, -2, … ? 
a. 1/66 
b. 1/65 
c. 1/63 
d. 1/64 
 
29. In the progression 18, 12, 8…, which term is 512/729? 
a. the 8th 
b. the 6th 
c. the 9th 
d. the 7th 
 
30. Which is the sum of the infinite progression 3/2, 1, 2/3, 4/9…? 
a. 6 ½ 
b. 5 ½ 
c. 4 ½ 
d. 7 ½ 
 
31. If the ratio of sec x to csc x is 1:4, then the ratio of tan x to cot x is ___________ 
a. 1:4 
b. 1:1 
c. 4:1 
d. 1:16 
 
32. The shadow of an electric pole is 5 meters long when the angle of elevation if the sun is 60°. What is the length of the shadow when the angle of elevation of the sun is 45°? 
a. 5√3 meters 
b. √3 meters 
c. 10√3meters 
d. 5 meters 
 
33. A car is parked 120 feet from a building that is 350 feet tall. What is the measure of the angle of depression from the top of the building to the car? 
a. 18.9° 
b. 37.8° 
c. 64.2° 
d. 71.1° 
 
34. In triangle ABC, with right angle at B, the sine of A is 4/5. What is the cosine of A? 
a. 2/5 
b. 4/3 
c. 3/5 
d. ¾ 
 
35. I sin ϴ = 3/5 and 0 ≤ ϴ ≤ Π/2, then tan ϴ = 
a. 3/2 
b. 4/3 
c. 5/4 
d. 3/4 
 
36. Find the equation of the line whose slope is 4 and passing through the point (2, -3) 
a. 4x – y – 11 = 0 
b. 4x – y + 11 = 0 
c. 4x + y – 11 = 0 
d. 4x + y + 11 = 0 
 
37. What is the equation of the line passing through the points (3,1) and (-5, 4)? 
a. 3x + 8y + 17 = 0 
b. 3x – 8y + 17 = 0 
c. 3x + 8y – 17 = 0 
d. 3x – 8y – 17 = 0 
 
38. What is the equation of the line whose x – intercept is 6 and y – intercept is -8? 
a. 3x – 4y – 24 = 0 
b. 4x – 3y – 24 = 0 
c. 3x – 4y + 24 = 0 
d. 4x – 3y + 24 = 0 
 
39. If the lines whose equation are y = ax + b and x = cy + d are parallel, which statement must be true? 
a. a = -(1/c) 
b. c = a 
c. a = (1/c) 
d. c = - a 
 
40. What is the slope of the perpendicular bisector of line segment AB if A is the point (0, -3) and B is the point (4,0)? 
a. –(4/3) 
b. –(3/4) 
c. 3/4 
d. 4/3 
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LET Reviewer for GENERAL EDUCATION (MATHEMATICS) Part 3

LET Reviewer in General Education LET Reviewer for General Education PRACTICE TEST FOR GENERAL EDUCATION MATHEMATICS 1. Give the f...

LET Reviewer for GENERAL EDUCATION (MATHEMATICS) Part 2

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LET Reviewer in General Education</div>
 
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<tr><td class="tr-caption" style="font-size: 12.8000001907349px;">LET Reviewer for General Education</td></tr>
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PRACTICE TEST FOR GENERAL EDUCATION 
MATHEMATICS 
 
1. The perimeter of an isosceles triangle is 42 in. The 2 equal sides are each 3 times as long as the third side. What are the lengths of these sides? 
a. 18, 21, 3 
b. 21, 21, 21 
c. 6, 6, 8 
d. 18, 18, 6 
 
2. What is the volume of a cube whose surface area is 54? 
a. 54 
b. 81 
c. 27 
d. 729 
 
3. How many gallons of water will fill a fish tank that is 18 inches by 12 inches by 48 inches? (There are 231 cubic inches per gallon). Round your answer to the nearest gallon. 
a. 45 gallons 
b. 38 gallons 
c. 47 gallons 
d. 40 gallons 
 
4. A box is 12 inches wide, 16 inches long and 6 inches high. How many square inches of paper would be needed to cover it on all sides? 
a. 192 sq. in. 
b. 900 sq. in. 
c. 360 sq. in. 
d. 720 sq. in. 
 
5. Find, in feet, the amount of framing needed to frame a picture 8 ½ inches by 11 inches? 
a. 3 ¼ ft 
b. 2 ¼ ft 
c. 4 ¼ ft 
d. 5 ¼ ft 
 
6. Which of these weights is heaviest? 
a. 2250 g 
b. 2.5 kg 
c. 4200 mg 
d. 5 pounds 
 
7. Which of the following is equal to 1000nm? 
a. 1 mm 
b. 1 cm 
c. 1 µm 
d. 1 dm 
 
8. What is 3 m + 28 dm when converted to centimeters? 
a. 480 
b. 580 
c. 4800 
d. 5800 
 
9. If a car travels 35 miles for every gallon of gasoline, how many kilometers will it travel for every liter of gasoline? 
a. 14.9 km/L 
b. 86.9 km/L 
c. 9.26 km/L 
d. 21.8 km/L 
 
10. The readings on water meter in April and May are 417.8m3 and 430.4m3. If there is a basic charge of 23 pesos and the cost per m3 is 20 pesos, how much is the billing for water consumption between the two months? 
a. P2,520 
b. P272 
c. P2,543 
d. P275 
 
11. The hypotenuse of a right triangle is 25 feet. If one leg is 24 feet, what is the length of the other leg? 
a. 6 ft 
b. 5 ft 
c. 7 ft 
d. 20 ft 
 
12. What is the length of the diagonal BD of the rectangle pictured below? 
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a. 50 
b. 40 
c. 30 
d. 20 
 
13. A rectangular lot is 5 meters wide and 12 meters long. How long is a path that cuts diagonally across the lot? 
a. 13 meters 
b. 15 meters 
c. 17 meters 
d. 7 meters 
 
14. A dinner menu offers choices of 7 appetizers, 12 main dishes, and 6 desserts. How many ways can you choose one of each course? 
a. 72 
b. 504 
c. 25 
d. 84 
 
15. How many four-digit numbers are there in which the tens digit is 8 and none of the digits is 9? 
a. 210 
b. 392 
c. 504 
d. 648 
 
16. A certain bank issues 3-letter identification codes to its customers. If each letter can be used only once per code, how many different codes are possible? 
a. 326 
b. 78 
c. 15,600 
d. 17,576 
 
17. Find the number of distinct permutations of the letters of the word ‘ANNUAL’. 
a. 180 
b. 270 
c. 360 
d. 720 
 
18. In how many ways can 7 people seated around a circular table? 
a. 49 
b. 720 
c. 5,040 
d. 14 
 
19. Anthony has 5 action figures. In how many ways can he arrange the figures in his shelf? 
a. 20 
b. 25 
c. 100 
d. 120 
 
20. A student has ten posters to pin up on the wall of her room, but there is space or only seven. In how many ways can she choose the posters to be pinned up? 
a. 5040 
b. 604,800 
c. 120 
d. 7 
 
21. How many ways can a committee of 4 people be selected from a group of 7 people? 
a. 35 
b. 70 
c. 140 
d. 210 
 
22. In a candy jar, there are 15 lemons, 12 chocolates, and 3 mints. If a candy is picked at random, what is the probability of not getting a mint? 
a. 1/2 
b. 9/10 
c. 1/6 
d. 1/10 
 
23. If five fair coins are flipped, what is the probability that all five land on heads? 
a. 1/32 
b. 1/25 
c. 1/5 
d. 1/2 
 
24. An integer between 100 and 999, inclusive, is chosen at random. What is the probability that all three digits of the number are different odd numbers? 
a. 1/3 
b. 1/15 
c. 3/5 
d. 1/10 
 
25. A committee of 3 is to be selected from a group of 5 girls and 3 boys. What is the probability that two boys are selected? 
a. 15/56 
b. 8/56 
c. 3/56 
d. 5/56 
 
26. What is the value of (16^(1/2))(16^(1/3))(16^(1/6)) 
a. 16^(1/36) 
b. 2 
c. 4 
d. 16 
 
27. The simplest expression for (2^40)/(4^20) is _____________. 
a. 1 
b. 4 
c. (1/2)^20 
d. 2^20 
 
28. Which of the following is equivalent to 7^77 - 7^76? 
a. 7^77 + 76 
b. 7^77 – 76 
c. 7^76 (6) 
d. 7(77 -76) 
 
29. Evaluate: 3^0 + 3^(-2) (3^4) 
a. 82 
b. 10 
c. 9 
d. 81 
 
30. If 23x – 1 = 16, then x = 
a. 1/3 
b. 1/2 
c. 1 
d. 5/3 
 
31. An online shop sells a certain calculator for P850 and charges P250 for shipping within Manila, regardless of the number of calculators ordered. Which of the following equations shows the total cost(y) of an order as a function of the number of calculators ordered (x)? 
a. y= 850x + 250 
b. x= 850y + 250 
c. y= (850 + 250)x 
d. y= 250x + 850 
 
32. What is the domain of the function f(x) =((x-2)^3)/((x+2)^2)? 
a. All real numbers. 
b. {x | -2 < x < 2} 
c. {x | x ≠ 2} 
d. {x | x ≠ - 2} 
 
33. What is the range of the function f(x) = √(x^2 - 4)? 
a. All real numbers 
b. All real numbers greater than or equal to 0. 
c. All real numbers greater than or equal to 2. 
d. All real numbers greater than or equal to 2 or less than or equal to -2 
 
34. f(x) = -2x^2 – 3x, f(-5) = 
a. -65 
b. -35 
c. 35 
d. 85 
 
35. If f(x) = x^2 – 5 and g(x) = x^2 + 5, what is the value of f(g(5))? 
a. 50 
b. 405 
c. 600 
d. 895 
 
36. If f(x) = (4-3x)/2, then f^-1(x)= 
a. (4-2x)/3 
b. (2x-4)/3 
c. (3x-4)/2 
d. (2-3x)/4 
 
37. Write the expression 4x^3 + x in factored form. 
a. 4 (x^3 + 1) 
b. 4x^2 (x + 1) 
c. x (4x^2 + 1) 
d. 4x (x^2 + 1) 
 
38. Which of the following could be a factor of n (n+1) if n is a positive integer less than 3? 
a. 3 
b. 5 
c. 8 
d. 9 
 
39. Which of the following is a factor of the equation x^2 – 2x – 24 = 0? 
a. x – 4 
b. x + 2 
c. x + 4 
d. x + 6 
 
40. Write the following in factored form: 65y^3 – 35y^2 + 15y 
a. 5 (13y^3 – 7y^2 + 3y) 
b. 5 (13 – 7y^2 + 3y) 
c. 5y (13y^2 – 7y + 3) 
d. 5y (13 – 7y + 3) 
 
 
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LET Reviewer for GENERAL EDUCATION (MATHEMATICS) Part 2

LET Reviewer in General Education LET Reviewer for General Education PRACTICE TEST FOR GENERAL EDUCATION MATHEMATICS 1. The perime...

LET Reviewer for GENERAL EDUCATION (MATHEMATICS) Part 1

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LET Reviewer in General Education</div>
 
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PRACTICE TEST FOR GENERAL EDUCATION 
MATHEMATICS 
<div class="separator" style="clear: both; text-align: center;">
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1. Which of the following is not an irrational number? 
a. π 
b. √(π^2) 
c. (π^3)/(π^3) 
d. (π^0)/π 
 
2. Simplify: 6 – {3 – 2 [5 – (– 10)] + 7} 
a. -16 
b. 16 
c. -14 
d. 26 
 
3. How many integers between 1 and 150 are divisible by both 4 and 5? 
a. 7 
b. 8 
c. 9 
d. 10 
 
4. If x/2 – x/6 is an integer, which of the following statements is true? 
a. x is a multiple of 6 
b. x is even 
c. x is a multiple of 3 
d. x is odd 
 
5. Which of the following is the smallest prime number greater than 200? 
a. 214 
b. 205 
c. 201 
d. 211 
 
6. What is the sum of the prime factors of 140? 
a. 9 
b. 12 
c. 14 
d. 15 
 
7. What is the greatest number that can divide 48, 12 and 32 without a denominator? 
a. 2 
b. 4 
c. 3 
d. 6 
 
8. What is the smallest positive integer that has 6, 8 and 10 as factors? 
a. 300 
b. 240 
c. 80 
d. 120 
 
9. What is the smallest number which can be exactly divided by 18, 27 and 15? 
a. 900 
b. 27 
c. 270 
d. 3 
 
10. John and Bob are cycling on a track. Bob completes one lap every 12 seconds, and John completes one lap every 15 seconds. When will Bob lap John, assuming that they started together? 
a. after 45 seconds 
b. after 3 minutes 
c. after 2 minutes 
d. after 1 minute 
 
11. ││-3│-│-4│-│-5││= 
a. 2 
b. 4 
c. 6 
d. 12 
 
12. What is the sum of the product and quotient of -5 and 5? 
a. -26 
b. -24 
c. -1 
d. 0 
 
13. What part of an hour has passed from 2:48 pm. to 3:20 pm? 
a. 7/8 
b. 1/3 
c. 8/15 
d. 8/25 
 
14. Which of the following numbers satisfies the inequality 2/3 < 1/x < 3/4? 
a. 3/5 
b. 5/3 
c. 7/10 
d. 10/7 
 
15. Which of the following lists the numbers 3/8, 4/11, and 5/13 in increasing order? 
a. 3/8, 4/11, 5/13 
b. 4/11, 3/8, 5/13 
c. 5/13, 4/11, 3/8 
d. 4/11, 5/13, 3/8 
 
16. What is the value of? 
a. 21 
b. 21 
c. 21 
d. 22 
 
17. Mr. Jimenez owns a 10 ½ hectare tract of land. He plans to subdivide this tract into ¼ hectare lots. He must first set aside of the total land for roads. How many lots will this tract yield? 
a. 32 
b. 35 
c. 42 
d. 45 
 
18. If the price of round-trip fare to Malolos, Bulacan is P285, how much will it cost a family of four if the husband pays full fare, the wife pays ⅔ of full fare, and the two children each pay ½ of the regular price? 
a. P 475 
b. P 570 
c. P 760 
d. P 1140 
 
19. A carpenter wanted three pieces of wood each 1 5/8 feet long. If he planned to cut them from a 6-foot piece of wood, how much of the piece would be left? 
a. 4 7/8 ft 
b. 1 1/8 ft 
c. 4 5/8 ft 
d. 3 ft 
 
20. In one senior class, ⅓ of the students are honor students. Of these honor students, 2/7 are varsity athletes. If there are four athletes in the class, how many students are there in the class? 
a. 42 
b. 52 
c. 60 
d. 84 
 
21. Julie spent one-sixth of her money in one store. In the next store, she spent three times as much as she spent in the first store, and had 80 pesos left. How much money did she have at the start? 
a. P 240 
b. P 252 
c. P 300 
d. P 360 
 
22. If dosage of medicine is ⅔ milliliter, how many dosages can be given from a bottle containing 20 milliliters? 
a. 13⅓ 
b. 19⅓ 
c. 20 
d. 30 
 
23. What is the average of ½, ¼, and ⅓? 
a. 13/24 
b. 13/29 
c. 13/36 
d. 13/27 
 
24. A scale replica of a building is 18 inches tall. If the actual height of the building is 36 feet, then the scale used between the model and the actual building is 1 inch = __________. 
a. 1.5 ft 
b. 2 ft 
c. 18 ft 
d. 24 ft 
 
25. A certain pole cast a shadow 24 feet long. At the same time another pole 3 feet high casts a shadow 4 feet long. How high is the first pole, given that the heights & shadows are in proportion? 
a. 24 ft 
b. 21 ft 
c. 18 ft 
d. 20 ft 
 
26. Four mangoes cost P29.00. At what price will 2 ½ dozen mangoes cost? 
a. P 217.50 
b. P 188.50 
c. P 348.50 
d. P 870.00 
 
27. If a car travels 96 miles on 8 liters of gas, how far can the car travel on a full tank of gas that holds 20 liters? 
a. 230 miles 
 b. 235 miles 
c. 240 miles 
d. 245 miles 
 
28. A recipe which is good for 4 persons calls for 2/3 cup of milk. How much milk will be needed by a recipe for 6 persons? 
a. 1 cup 
b. 2 cups 
c. 4 cups 
d. 8 cups 
 
29. If a baseball player hits 10 home runs in the first 45 games, at the same rate how many home runs can he expect to hit during the 162-game season? 
a. 38 
b. 42 
c. 36 
d. 40 
 
30. If a certain job can be finished by 18 workers in 26 days, how many workers are needed to finish the job in 12 days? 
a. 24 
b. 30 
c. 39 
d. 45 
 
31. A meter stick was cut into two pieces at the 64-cm mark. What is the ratio of the smaller piece to the largest piece? 
a. 9:16 
b. 16:25 
c. 13:50 
d. 9:25 
 
32. In a certain school, the ratio of boys to girls is 3 to 7. If there are 150 boys and girls in the school, how many boys are there? 
a. 45 
b. 105 
c. 75 
d. 90 
 
33. If P75.00 is shared among three children in the ratio of 3:7:15. What is the size of the smallest share? 
a. P 35 
b. P 25 
c. P 15 
d. P 9 
 
34. An artist ordered cans of red paint, white paint, and green paint in the ratio 2 : 4 : 6, respectively. If he ordered a total of 24 cans of paint, how many cans of white paint did he order? 
a. 4 
b. 8 
c. 12 
d. 16 
 
35. Three brothers inherited a cash amount of P 120,000 and they divided it among themselves in the radio of 5:2:1. How much more is the largest share than smallest share? 
a. P15,000 
b. P30,000 
c. P60,000 
d. P75,000 
 
36. What percent of 4 is 3/5 of 8? 
a. 48% 
b. 80% 
c. 83% 
d. 120% 
 
37. If 50% of x is 20, what is 30% of x? 
a. 30 
b. 12 
c. 20 
d. 16 
 
38. What percent of P340.00 is P30.60? 
a. 9% 
b. 8% 
c. 7% 
d. 6% 
 
39. What percent is 3/4 of 5/6? 
a. 65% 
b. 90% 
c. 80% 
d. 75% 
 
40. If the area of one circle is twice of another circle, what is the ratio in percent, of the smaller to larger circle? 
a. 25% 
b. 50% 
c. 70% 
d. 75% 
 
41. In a group of 250 students, 40 are freshmen. What percentage of the group are freshmen? 
a. 15 
b. 16 
c. 30 
d. 40 
 
42. A senior class of 50 girls and 70 boys sponsored a dance. If 40% of the girls and 50% of the boys attended the dance approximately what percent attended? 
a. 44 
b. 46 
c. 42 
d. 40 
 
43. Employees at Highwire Musictown get a 20% discount on all purchases. If Luis buys three tapes at P7.49 each, how much will he have to pay after his employee discount? 
a. P 16.98 
b. P 17.98 
c. P 18.98 
d. P 19.98 
 
44. An employee earning P9,200 a month will receive a 15% increase next month. How much will his/her new salary be? 
a. P10,500 
b. P10,530 
c. P10,580 
d. P10,560 
 
45. The school cafeteria raised the price of a plate of rice from P8 to P10. If the same rate of increase was applied to a regular order of viand which used to cost P20, how much does an order of viand cost now? 
a. P 22 
b. P 24 
c. P 25 
d. P 26 
 
46. A store reduced the price of a computer by 20% and sold it for P56,400. How much did the computer originally for? 
a. P 60,400 
b. P 65,000 
c. P 70,500 
d. P 72,500 
 
47. How much interest would be paid on a bank loan of P30,000 for 8 months at 12% annual interest? 
a. P2,400 
b. P2,800 
c. P3,240 
d. P3,600 
 
48. You buy a refrigerator for P12,800.00 and make a down payment of P2,500.00. If you finance the remainder at 8% annually for three years, how much will you actually pay for the refrigerator? 
a. P 12,190.00 
b. P 10,300.00 
c. P 15,272.00 
d. P 12,772.00 
 
49. P8,000 is invested at 12% simple interest. What is the amount at the end of 2 years? 
a. P 8,960 
b. P 8,240 
c. P 9,600 
d. P 9,920 
 
50. How long will it take P10,000 to grow to P12,000 if it is invested at 9% compounded monthly? 
a. 25 months 
b. 18 months 
c. 20 months 
d. 15 months 
 
 
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LET Reviewer for GENERAL EDUCATION (MATHEMATICS) Part 1

LET Reviewer in General Education LET Reviewer for General Education PRACTICE TEST FOR GENERAL EDUCATION MATHEMATICS 1. Which of...

LET Reviewer for GENERAL EDUCATION (MATHEMATICS)

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LET Reviewer in General Education</div>
 
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PRACTICE TEST FOR GENERAL EDUCATION 
MATHEMATICS 
 
1. If the price of round-trip fare to Malolos, Bulacan is P285, how much will it cost a family of four if the husband pays full fare, the wife pays ⅔ of full fare, and the two children each pay ½ of the regular price? 
A. P 475 
B. P 570 
C. P 760 
D. P 1140 
 
2. What number subtracted from each of 71 and 58 will result in two perfect squares? 
A. 22 
B. 33 
C. 35 
D. 42 
 
3. Jessica has 6 red t-shirts and 9 yellow t-shirts. If she picks one t-shirt at random, what is the probability that it will not be yellow? 
A. 2/5 
B. 9/15 
C. 2/3 
D. 3/15 
 
4. The simplest expression for (2^40)/(4^20) is _____________. 
A. 1 
B. 4 
C. (½)^20 
D. 2^20 
 
5. What percent of 4 is 3/5 of 8? 
A. 48 % 
B. 80 % 
C. 83 1/3 % 
D. 120 % 
 
6. Three times the first of three consecutive odd integers is 3 more than twice the third. Find the third integer. 
A. 9 
B. 13 
C. 11 
D. 15 
 
7. Which of the following is/are TRUE? 
I. x^3 - y^3 = (x – y)(x^2 + y^2) 
II. (5x – 2y)(5x – 2y) = 25x^2 – 20xy + 4y^2 
III. x^2 + y^2 = (x + y)(x + y) 
 
A. I only 
B. I and III 
C. II only 
D. I and II 
 
8. How many members of Set A are factors of any members of Set B? 
SET A = {0,1,2,3,4,5} 
SET B = {1,2,7,9,10} 
 
A. 6 
B. 5 
C. 4 
D. 3 
 
9. A meter stick was cut into two pieces at the 64-cm mark. What is the ratio of the smaller piece to the largest piece? 
A. 9:16 
B. 16:25 
C. 13:50 
D. 9:25 
 
10. The product of 2 whole numbers is 36, and their ratio is 1:4. Which of these is the smaller number? 
A. 9 
B. 3 
C. 2 
D. 12 
 
11. Find, in feet, the amount of framing needed to frame a picture 8 ½ inches by 11 inches? 
A. 3 ¼ ft 
B. 2 ¼ ft 
C. 4 ¼ ft 
D. 5 ¼ ft 
 
12. If a certain job can be finished by 18 workers in 26 days, how many workers are needed to finish the job in 12 days? 
A. 24 
B. 30 
C. 39 
D. 45 
 
13. Which of these weights is heaviest? 
A. 2250 g 
B. 2.5 kg 
C. 4200 mg 
D. 5 pounds 
 
14. A certain pole cast a shadow 24 feet long. At the same time another pole 3 feet high casts a shadow 4 feet long. How high is the first pole, given that the heights & shadows are in proportion? 
A. 24 ft 
B. 21 ft 
C. 18 ft 
D. 20 ft 
 
15. What is the median of the following numbers 8, 5, 7, 5, 9, 9, 1, 8, and 10? 
A. 5 
B. 7 
C. 8 
D. 9 
 
16. Which is the 10th term of the progression -8, -4, -2, ..., ___? 
A. 1/66 
B. 1/65 
C. 1/63 
D. 1/64 
 
17. Two buses leave the same station at 9:00 pm. One bus travels north at the rate of 30 kph and the other travels east at 40 kph. How many kilometers apart are the buses at 10 pm? 
A. 50 km 
B. 70 km 
C. 100 km 
D. 140 km 
 
18. A park has a triangular shape. It has a base of 12m and a height of 9m. What is its area? 
A. 122 m^2 
B. 108 m^2 
C. 42 m^2 
D. 54 m^2 
 
19. Joel repacks a 60 kg sack of sugar into small packs of 750g. How many small packs can be made? 
A. 90 
B. 45 
C. 75 
D. 80 
 
20. What is the value of (12 1/6) - (2 3/8) - (7 2/3) + (19 3/4)? 
A. 21 
B. 21 1/8 
C. 21 7/8 
D. 22 
 
21. An employee earning P9,200 a month will receive a 15% increase next month. How much will his/her new salary be? 
A. P10,500 
B. P10,530 
C. P10,530 
D. P10,560 
 
22. What is 3 m +.28 dm when converted to centimeters? 
A. 480 
B. 580 
C. 4800 
D. 5800 
 
23. What is the smallest positive integer that has 6, 8 and 10 as factors? 
A. 300 
B. 240 
C. 80 
D. 120 
 
24. If dosage of medicine is ⅔ milliliter, how many dosages can be given from a bottle containing 20 milliliters? 
A. 13⅓ 
B. 19⅓ 
C. 20 
D. 30 
 
25. A box is 12 inches wide, 16 inches long and 6 inches high. How many square inches of paper would be needed to cover it on all sides? 
A. 192 sq. in. 
B. 900 sq. in. 
C. 360 sq. in. 
D. 720 sq. in. 
 
26. If x^2 is odd, which of these statements is true? 
I. x is odd 
II. x^2 is odd 
III. x^2 + 1 is odd 
 
A. I and III only 
B. I and II only 
C. I only 
D. II only 
 
27. What are the missing terms in the series 5, 10, 20 _____, 80, ____320? 
A. 40, 160 
B. 40, 120 
C. 50, 120 
D. 35, 135 
 
28. Michael is 15 years older than his brother Rafael. However, y years ago Michael was twice as old as Rafael. If Rafael is now x years old and x > y, find the value of x-y. 
A. 13 
B. 14 
C. 15 
D. 16 
 
29. Which of the following sets of numbers can be sides of a right triangle? 
A. 4, 5, 6 
B. 6, 6, 2, 3 
C. 3, 6, 3 
D. 2, 2, 3 
 
30. Which of the following could be a factor of n (n+1) if n is a positive integer less than 3? 
A. 3 
B. 5 
C. 8 
D. 9 
 
31. In a certain school, the ratio of boys to girls is 3 to 7. If there are 150 boys and girls in the school, how many boys are there? 
A. 45 
B. 105 
C. 75 
D. 90 
 
32. In one senior class, ⅓ of the students are honor students. Of these honor students, 2/7 are varsity athletes. If there are four athletes in the class, how many students are there in the class? 
A. 42 
B. 52 
C. 60 
D. 84 
 
33. If the variance of distribution is 25, then the standard deviation is ________. 
A. 12.5 
B. 30 
C. 625 
D. 5 
 
34. How long will it take P10,000 to grow to P12,000 if it is invested at 9% compounded monthly? 
A. 25 months 
B. 18 months 
C. 20 months 
D. 15 months 
 
35. The school cafeteria raised the price of a plate of rice from P8 to P10. If the same rate of increase was applied to a regular order of viand which used to cost P20, how much does an order of viand cost now? 
A. P 22 
B. P 24 
C. P 25 
D. P 26 
 
36. A 737-model plane has 29 rows with 5 seats per row, except for the last three rows which had 3 seats each. What is the seating capacity of the plane? 
A. 144 
B. 145 
C. 142 
D. 139 
 
37. The perimeter of an isosceles triangle is 42 in. The 2 equal sides are each 3 times as long as the third side. What are the lengths of these sides? 
A. 18,21,3 
B. 21,21,21 
C. 6,6,8 
D. 18,18,6 
 
38. Julie spent one-sixth of her money in one store. In the next store, she spent three times as much as she spent in the first store, and had 80 pesos left. How much money did she have at the start? 
A. P 240 
B. P 252 
C. P 300 
D. P 360 
 
39. How many ounces of pure acid must be added to 20 ounces of a solution that is 5% acid to strengthen it to a solution that is 24% acid? 
A. 5 
B. 6 
C. 10 
D. 2 1/2 
 
40. If 50% of x is 20, what is 30% of x? 
A. 30 
B. 12 
C. 20 
D. 16 
 
41. Kath’s grades in three math quizzes are 82, 78, 86. What grade should get in her next quiz to raise her average to 85? 
A. 94 
B. 90 
C. 88 
D. 87 
 
42. P8,000 is invested at 12% simple interest. What is the amount at the end of 2 years? 
A. P 8,960 
B. P 8,240 
C. P 9,600 
D. P 9,920 
 
43. Anthony has 5 action figures. In how many ways can he arrange the figures in his shelf? 
A. 20 
B. 25 
C. 100 
D. 120 
 
44. Which of these numbers is greater than 1/4? 
A. .04 
B. (1/2)^2 
C. 1/8 
D. 1/0.04 
 
45. A senior class of 50 girls and 70 boys sponsored a dance. If 40% of the girls and 50% of the boys attended the dance approximately what percent attended? 
A. 44 
B. 46 
C. 42 
D. 40 
 
46. Give the factors of 2x^3 + 9x^2 + 9x 
A. x(2x – 3)(x + 3) 
B. x(2x + 3)(x + 3) 
C. x(3x – 2)(x + 3) 
D. x(2x + 3)(x – 3) 
 
47. Joseph has more money than Mila but less than Billy. If the amounts held by Joseph, Mila and Billy are x, y and z respectively, which of the following is TRUE? 
A. Z < X < Y 
B. X < Z < Y 
C. Y < X < Z 
D. Y < Z < X 
 
48. If x =-5, what is the value of (x^2 - 9)/(x + 3)? 
A. -8 
B. -6 
C. 5 
D. 7 
 
49. What percent is 3/4 of 5/6? 
A. 65% 
B. 90% 
C. 80% 
D. 75% 
 
50. A man started painting a wall at 9:00 AM and was able to finish painting 3/5 of it at 10:30 AM. Continuing at this rate, at what time will he finish painting the wall? 
A. 11:35 AM 
B. 11:30 AM 
C. 12:30 AM 
D. 12:15 AM 
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LET Reviewer for GENERAL EDUCATION (MATHEMATICS)

LET Reviewer in General Education LET Reviewer for General Education PRACTICE TEST FOR GENERAL EDUCATION MATHEMATICS 1. If the pri...

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