**Math Practice Problems Module 2**

1. Evaluate the determinant

½1 6 0½

½4 2 7½

½0 5 3½

a. 011

b. 101

c. –001

d. –101

2. Find the value of a so that 1+a, 7+a, and 25+a forms a geometric progression

a. 3

b. 4

c. 2

d. 5

3. Mel gave Lea ½ of her mystery books. Lea gave Benjie ½ of the books she got form Mel. Benjie gave Badong ½ of the books he got from Lea. Badong got only 4 books. How many books did Mel start with?

a. 8.5

b. 7.5

c. 8

d. 32

4. If the first and tenth terms of an arithmetic sequence are 3 and 30 respectively, find the fiftieth term of the sequence.

a. 150

b. 75

c. 50

d. 100

5. What is the remainder if x

^{55}+3x^{47}-5x^{31}-8x^{24}+2x^{18}-4 is divided by x + 1.a. 10

b. 9

c. –9

d. –10

6. The equation y = a

^{m}is equivalent to the equationa. m = log

_{y}ab. m = log

_{a}yc. m = yloga

d. m = alogy

7. A chemical storeroom has a 90% acid solution and a 40% acid solution. How many centiliters of solution must be taken from each to obtain 25 centiliters of a 50% acid solution?

a. 6 and 19

b. 4 and 21

c. 5 and 20

d. 3 and 22

8. Find the sum of the sequence ½ +1/4 + 1/8 +1/16 ….

a. 2

b. 4

c. 1

d. 3

9. If you place one cent on the first square of the chessboard, two cents on the second square, four cents on the third, and so on, continuing to double the amount until all 64 squares are covered, how much money will there be in the last square board?

a. 9 x 10

^{15}b. 9.22 x 10

^{16}c. 9.22 x 10

^{15}d. 9.22 x 10

^{18}10. ________ is the set, which has no elements.

a. universal set

b. infinite set

c. empty set

d. finite set

11. There are 2n persons at a dinner dance party of which the number of males equals the number of females. If the two persons are selected at random, what is the probability that the two persons selected at random are of opposite sex?

a. n

^{2}/2n-1b. n/2n-1

c. n/n-1

d. n/2n+1

12. How many four-digit number can be written using the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 if no digit is repeated in any number?

a. 3020

b. 3022

c. 3024

d. 3042

13. How many cars can be given license plates having 5-digit number using the digit 1, 2, 3, 4, 5, 6, 7, 8, 9 with no digit repeated in any license plate.

a. 15120

b. 15400

c. 16020

d. 15020

14. Find the number of permutation of the letters in the word “ENGINEER”?

a. 33600

b. 3360

c. 3860

d. 3630

15. How many three-digit numbers between 100 and 1000 can be made with the digits 0, 1, 2, 3, and 4 if no digit is repeated in any number?

a. 48

b. 49

c. 46

d. 45

16. How many of the arrangements of the letter of the word “VOLTAGE” begins with a vowel and end with a consonant.

a. 1440

b. 1490

c. 1460

d. 1450

17. Find n if P(n+2, 2) = 5 P((n-1, 2)

a. 6

b. 9

c. 4

d. 3

18. How many different teams of 5 players can be chosen out of 12 applicants?

a. 730

b. 718

c. 792

d. 719

19. How many different committees of 5 members can be formed from 8 men and 6 women if each committee is to have exactly 3 men?

a. 830

b. 840

c. 860

d. 820

20. In how many ways can 2 or more ties can be selected out of 8 ties.

a. 235

b. 240

c. 247

d. 245

21. Find n if P(n, 3) = 6C(n,5).

a. 8

b. 9

c. 10

d. 7

22. A committee of three is to be chosen from a group of 5 men and 4 women. If the selection is made at random, find the probability that two are men.

a. 10/21

b. 9/10

c. 5/9

d. 11/21

23. A bag contains nine balls numbered 1 to 9. Two balls are drawn at random. Find the probability that one is even and the other is odd.

a. 5/9

b. 9/10

c. 10/21

d. 7/9

24. A bag contains nine balls numbered 1 to 9. Two balls are drawn at random. Find the probability that both are even.

a. 3/18

b. 5/18

c. 1/3

d. 7/18

25. A bag contains nine balls numbered 1 to 9. Two balls are drawn at random. Find the probability that both are odd.

a. 3/18

b. 3/8

c. 1/3

d. 820

26. A bag contains 4 white and 5 black balls. If 4 balls are drawn, what is the probability that the first two balls are white and the last two are black?

a. 4/5

b. 5/63

c. 4/53

d. 3/5

27. One bag contains 4 white and 6 black balls; a second bag contains 2 white and 8 black balls; a third bag contains 5 white and 5 black balls. One ball is drawn from each bag. Find the probability that all are white.

a. 1/25

b. 5/19

c. 3/19

d. 3/25

28. What is probability of throwing a 6 in single throw of two dice?

a. 1/6

b. 5/36

c. 9/51

d. 5/6

29. Find the probability of throwing a 4 with a die exactly 3 times in 7 trials.

a. 0.00781

b. 0.781

c. 0.0781

d. 0.0871

30. A coin is tossed 6 times. Find the probability of getting 4 heads.

a. 15/64

b. 3/8

c. 4/36

d. 13/64

31. A card is drawn from a deck of 52 cards. What is the probability that the card drawn is a king or a heart?

a. 16/52

b. 4/52

c. 13/52

d. 15/52

32. Two person A and B work independently on a puzzle. If the probability that A can solve the puzzle is 0.60 and that B is 0.75. What is the probability that the puzzle will be solved?

a. 0.90

b. 0.80

c. 0.75

d. 0.65

33. There are three applicants A, B, and C to an EE position in an electric firm. The odds that A will get the position are 7:5 and the odds that B will get the same position are 1:3. What is the probability that either A or B will be employed?

a. 3/7

b. 5/6

c. 3/5

d. 2/7

34. What are the odds in favor of C in problem 33?

a. 1:5

b. 2:5

c. 3:5

d. 4:5

35. Six red blocks and 4 white blocks are placed at random in a row. Find the probability that the two blocks in the middle are of the same color.

a. 2/11

b. 1/5

c. 7/15

d. 4/15

36. In the series of nos. 2, 5, 8, 11…41, the sum is

a. 301

b. 302

c. 303

d. 304

37. Johnny and Louie can clean a room in 3 hrs. After working for 2 hrs., Johnny has his snack while Louie cleaned the room alone for 2 more hrs. How long Louie takes to clean the room alone?

a. 5 hrs

b. 6 hrs

c. 7 hrs

d. 8 hrs

38. Five times Greggy’s age is 10 more than his grandfather’s age. If the sum of their ages is 86, what is grandfather’s age?

a. 50

b. 60

c. 70

d. 80

39. Seven times a number is 3 more that 5 times another. If the sum of the numbers is 9, what are the numbers?

a. 2 and 7

b. 3 and 6

c. 4 and 5

d. 1 and 8

40. Train B is 5 mph faster than Train A and can travel a distance of 105 miles, ½ hour faster than A. What are the rates of the two trains?

a. 20 and 25

b. 30 and 35

c. 40 and 45

d. 50 and 55

41. The denominator of a fraction exceeds the numerator by 4. If the numerator was tripled, the denominator doubled, the resulting fraction’s denominator is 1 less than the numerator of the resulting fraction. What is the original fraction?

a. 7/11

b. 8/12

c. 9/13

d. 10/14

42. Richard can finish off a gallon of ice cream in one hour while Philip can eat it in 45 mins. How long would it take both of them to consume the gallon of ice cream?

a. 15.51 min

b. 20.61 min

c. 25.71 min

d. 30.81 min

43. Annie, Betty, Carol and Dina can finish ½, ¼, 1/8, and 1/6 of a job respectively in one day. How many hours will it take them to do the whole job if they work together?

a. 17.01 hrs

b. 19.02 hrs

c. 21.03 hrs

d. 23.04 hrs

44. In 5 years, a boy will be 7/6 times as old as his uncle. A year ago, he will be 4/13 times as old. How old is the boy?

a. 8

b. 9

c. 10

d. 11

45. A fraction becomes equal to 1 when 9 is added to the numerator and becomes 1 ¼ when 16 is subtracted from the denominator. What is the fraction?

a. 35/44

b. 37/46

c. 39/48

d. 41/50

46. The sum of the digits of a 2-digit number is 17. if 9 is added to the number, the order of the digits will be reversed. Find the number.

a. 69

b. 79

c. 89

d. 99

47. Barry can walk at a rate of 5 km/hr and his brother Alfie can walk at a rate of 15 km/hr. How long would it take them to be 60 km apart if they are walking at opposite directions?

a. 2 hrs

b. 3 hrs

c. 4 hrs

d. 5 hrs

48. Two pipes can fill a tank in 5 and 6 hours respectively while another pipe can empty it in 6 hours. If the 3 pipes were used at the same time, how many hours would it take to fill the tank?

a. 2 hrs

b. 3 hrs

c. 4 hrs

d. 5 hrs

49. A woman divides P18, 000 among her 3 daughters in 2:3:4 ratios. How much did each daughter receives?

a. P4, 000, P6, 000, P8, 000

b. P5, 000, P6, 000, P7, 000

c. P2, 000, P7, 000, P9, 000

d. P5, 000, P6, 000, P7, 000

50. A balcony section of a convention hall has 12 seats in the 1

^{st}row, 14 in the 2^{nd}, 16 in the 3^{rd}, and so on. If there are only 15 rows in the said balcony section, how many seats are there in the 15^{th}row?a. 35

b. 40

c. 45

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