Problem Solving (PS) |

Rank | Title | Topics |

1 | How many even 3 digit integers greater than 700 with | Combinations |

2 | If the product of all the unique positive divisors of n, a p | Number Properties/Divisibility/Multiples/Factors |

3 | Set S consists of numbers 2, 3, 6, 48, and 164. Number K is | Probability/Number Properties/Divisibility/Multiples/Factors |

4 | Arrow AB which is a line segment exactly 5 units along with | Coordinate Geometry |

5 | If 10! - 2*(5!)^2 is divisible by 10^n, what is the greatest | Divisibility/Multiples/Factors/Roots |

6 | A big cube is formed by rearranging the 160 coloured and 56 | Percents and Interest Problems/Geometry |

7 | In the figure, point D divides side BC of triangle ABC into | Geometry |

8 | The function g(x) is defined for integers x such that if x | Arithmetic |

9 | Louie takes out a three-month loan of $1000. The lender | Percents and Interest Problems |

10 | If two integers are chosen at random out of the set {2, 5, 7 | Probability/Number Properties |

11 | How many numbers that are not divisible by 6 divide evenly | Divisibility/Multiples/Factors |

12 | On a partly cloudy day, Derek decides to walk back from work | Distance/Rate Problems |

13 | a, b, c, d are positive integers such that exactly one of | Inequalities |

14 | A sequence of numbers (geometric sequence) is given by the | Exponents/Powers/Sequences |

15 | How many values can the integer p=|x+3|-|x-3| assume? | Absolute Values/Modules |

16 | A man arrives at a railway station 90mins before the time at | Distance/Rate Problems |

17 | An integer between 1 and 300, inclusive, is chosen at random | Probability/Number Properties |

18 | A cyclist travels the length of a bike path that is 225 | Inequalities/Distance/Rate Problems |

19 | In racing over a given distance d at uniform speed, A can be | Distance/Rate Problems |

20 | In the diagram, points A, B, and C are on the diameter of | Geometry |

24 | How many positive integers less than 10,000 are there in | Combinations |

25 | Twenty metres of wire is available to fence off a flower bed | Geometry/Min/Max Problems/Out of Scope - Too Hard |

26 | In a certain sequence, every term after the first is determi | Sequences |

27 | List T consist of 30 positive decimals, none of which is an | Min/Max Problems |

28 | In a village of 100 households, 75 have at least one DVD | Overlapping Sets |

29 | Points A and B are 120 km apart. A motorcyclist starts from | Distance/Rate Problems/Geometry |

30 | A cylindrical water tower with radius 5 m and height 8 m is | Geometry/Work/Rate Problems |

31 | If integer C is randomly selected from 20 to 99, inclusive. | Probability |

32 | If an integer n is to be chosen at random from the integers | Probability/Divisibility/Multiples/Factors |

33 | If 2^x + 2^y = x^2 + y^2, where x and y are nonnegative inte | Algebra |

35 | If |12x5|>|76x|, which of the following CANNOT be the | Inequalities/Absolute Values/Modules/Word Problems |

36 | Consider a regular polygon of p sides. The number of values | Number Properties/Geometry |

38 | It takes 6 days for 3 women and 2 men working together to | Work/Rate Problems/Poor Quality |

40 | If x represents the sum of all the positive three-digit | Arithmetic/Combinations |

41 | Of a group of people, 10 play piano, 11 play guitar, 14 play | Overlapping Sets |

43 | In the xy-coordinate system, rectangle ABCD is inscribed wit | Geometry/Coordinate Geometry |

44 | How many triangles with positive area can be drawn on the | Geometry/Coordinate Geometry |

45 | 3 cooks have to make 80 burgers.They are known to make 20 | Work/Rate Problems |

46 | A man cycling along the road noticed that every 12 minutes | Distance/Rate Problems |

47 | Eight litres are drawn off from a vessel full of water and s | Mixture Problems |

48 | How many positive integers less than 30 are either a | Number Properties/Divisibility/Multiples/Factors |

49 | If N is the product of all multiples of 3 between 1 and 100 | Number Properties/Exponents/Powers/Divisibility/Multiples/Factors |

50 | Tom and Linda stand at point A. Linda begins to walk in a | Distance/Rate Problems |

51 | Two kinds of Vodka are mixed in the ratio 1:2 and 2:1 and | Mixture Problems |

52 | If a is the sum of x consecutive positive integers. b is the | Statistics and Sets Problems |

53 | A dessert recipe calls for 50% melted chocolate and 50% rasp | Mixture Problems |

54 | How many positive integers between 200 and 300 (both inclusi | Divisibility/Multiples/Factors |

55 | How many combinations of three letters taken from letters | Combinations |

56 | If the probability of rain on any given day is 50%, what is | Probability |

57 | x is the sum of y consecutive integers. w is the sum of z | Statistics and Sets Problems |

59 | In how many different ways can a group of 8 people be divide | Combinations |

60 | If x#0 and x/|x|<x, which of the following must be true? | Inequalities/Absolute Values/Modules |

61 | The sum of four consecutive odd numbers is equal to the sum | Sequences |

62 | If a and b are distinct integers and a^b = b^a, how many | Number Properties/Exponents/Powers |

63 | A fair coin is tossed 5 times. What is the probability of | Probability |

64 | If x+|x|+y=7 and x+|y|-y=6 what is x+y=? | Absolute Values/Modules |

65 | Which of the following sets includes ALL of the solutions of | Absolute Values/Modules |

66 | If x is an integer and |1-x|<2 then which of the following | Absolute Values/Modules/Must or Could be True Questions/Number Properties |

67 | What is the product of all the solutions of x^2 - 4x + 6=3 | Absolute Values/Modules/Algebra |

68 | The expression x[n]y is defined for positive values of x and | Exponents/Powers/Functions and Custom Characters |

69 | There are 100 freshmen at a particular college, all of whom | Overlapping Sets |

70 | The elevator in an eleven-story office building travels at | Distance/Rate Problems |

71 | Two different primes may be said to rhyme | Number Properties |

72 | The number of straight line miles traveled downriver in one | Algebra/Word Problems |

73 | If x is the smallest positive integer that is not prime and | Divisibility/Multiples/Factors |

74 | Car B begins moving at 2 mph around a circular track with | Distance/Rate Problems |

75 | On planet Simplon, each year has 12 months, each of which | Fractions/Ratios/Decimals |

76 | Car B starts at point X and moves clockwise around | Distance/Rate Problems |

77 | |x+3| - |4-x| = |8+x|. How many solutions does the equation | Absolute Values/Modules |

78 | How many even integers n, where 100 <= n <= 200, are divisib | Number Properties/Divisibility/Multiples/Factors |

79 | A wall clock gains 2 mins in 12 hrs, while a table clock | Distance/Rate Problems |

80 | Jane gave Karen a 5 m head start in a 100 race and Jane was | Distance/Rate Problems |

82 | Ax(y) is an operation that adds 1 to y | Functions and Custom Characters |

83 | N and M are each 3-digit integers. Each of the numbers 1, 2, | Arithmetic/Min/Max Problems |

85 | Two cars A and B start from Boston and New York respectively | Distance/Rate Problems |

86 | A cyclist travels the length of a bike path that is 225 | Word Problems/Min/Max Problems |

87 | Jerry and Jim run a race of 2000 m. First, Jerry gives Jim | Distance/Rate Problems |

88 | Of the three-digit integers greater than 700, how many have | Combinations |

90 | A man sets out to cycle from BBSR to CTC and at the same | Distance/Rate Problems |

91 | A firm's annual revenue grows twice as fast as its costs. In | Percents and Interest Problems |

92 | At a local beach, the ratio of little dogs to average dogs | Percents and Interest Problems/Fractions/Ratios/Decimals |

93 | The function p(n) on non-negative integer n is defined in | Exponents/Powers |

94 | This year Henry will save a certain amount of his income | Word Problems/Fractions/Ratios/Decimals |

95 | The positive value of x that satisfies the equation (1 + 2x) | Algebra/Exponents/Powers |

96 | Point (x,y) is a point within the triangle. What is the | Coordinate Geometry/Probability |

98 | Danny is sitting on a rectangular box. The area of the front | Geometry |

99 | A bus from city M is traveling to city N at a constant speed | Distance/Rate Problems |

100 | Each day a man meets his wife at the train station after | Distance/Rate Problems |

101 | How many different combinations of outcomes can you make by | Combinations |

102 | Tanya prepared 4 different letters to be sent to 4 different | Probability |

103 | If x, a, and b are positive integers such that when x is | Remainders/Divisibility/Multiples/Factors/Must or Could be True Questions |

104 | In the diagram, triangle PQR has a right angle at Q and a | Geometry |

105 | Rita and Sam play the following game with n sticks on a | Word Problems |

106 | What is the least possible distance between a point on the | Coordinate Geometry |

107 | Tanks X and Y contain 500 and 200 gallons of water respectiv | Work/Rate Problems |

108 | Brenda and Sally run in opposite direction on a circular tra | Distance/Rate Problems |

109 | Alex and Brenda both stand at point X. Alex begins to walk a | Distance/Rate Problems/Geometry |

110 | There are 5 bags three of which contains 5 white and 2 black | Probability/Poor Quality |

111 | If x/|x|<x which of the following must be true about x? | Absolute Values/Modules/Inequalities/Must or Could be True Questions |

112 | For any integer k > 1, the term length of an integer | Number Properties |