Problem Solving (PS) |

Rank | Title | Topics |

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

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

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

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

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

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

7 | An integer between 1 and 300, inclusive, is chosen at random | Probability |

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

28 | Two different primes may be said to “rhyme” | Number Properties |

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

30 | How many combinations of three letters taken from letters | Combinatios |

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

32 | According to a survey, at least 70% of people like apples | Min/Max Problems |

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

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

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

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

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

38 | A scientist has a set of weights {1Kg, 2Kg, 4Kg, 8Kg, 16Kg, | Combinations |

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

40 | How many integral values of k are possible, if the lines 3x+ | Coordinate Geometry |

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

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

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

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

45 | In triangle ABC to the right, if BC = 3 and AC = 4, then | Geometry |

46 | On a race track a maximum of 5 horses can race together at | Min/Max Problems |

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

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

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

50 | If |12x−5|>|7−6x|, which of the following CANNOT be the | Absolute Values/Modules/Inequalities |

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

52 | How many 4 digit numbers are there, if it is known that the | Combinations |

53 | How many of the integers that satisfy the inequality (x+2)(x | Inequalities |

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

55 | If p and q are two different odd prime numbers, such that | Must or Could be True Questions/Number Properties |

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

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

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

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

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

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

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

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

64 | How many prime numbers n exist such that 90 < n < 106 and n | Divisibility/Multiples/Factors |

65 | The above 11 x 11 grid of dots is evenly spaced: each dot is | Combinations/Geometry |

66 | The sum of the even numbers between 1 and n is 79*80, where | Number Properties |

67 | If x is positive, which of the following could be the | Inequalities/Must or Could be True Questions |

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

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

70 | A big cube is formed by rearranging the 160 coloured and 56 | Geometry |

71 | For a nonnegative integer n, if the remainder is 1 when 2^n | Must or Could be True Questions/Remainders |

72 | A satellite is composed of 30 modular units, each of which | Fractions/Ratios/Decimals |

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

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

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

76 | Out of seven models, all of different heights, five models | Combinations |

77 | Set R contains five numbers that have an average value of 55 | Min/Max Problems/Statistics and Sets Problems |

78 | In the first quarter of 2008, Harry's Hardware Store sold 30 | Percents and Interest Problems |

79 | Each of the following equations has at least one solution | Exponents/Powers |

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

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

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

83 | In the XY co-ordinate plane, circle C has center at (8,0) an | Coordinate Geometry |

84 | A cylindrical tank of radius R and height H must be redesign | Geometry |

85 | Last Sunday a certain store sold copies of Newspaper A for | Arithmetic/Percents and Interest Problems |

86 | In the circle above, PQ is parallel to diameter OR | Geometry |

87 | When n is divided by 5 the remainder is 2. When n is divided | Remainders |

88 | A new sales clerk in a department store has been assigned to | Percents and Interest Problems/Word Problems |

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

90 | If x is positive, which of the following could be correct | Inequalities/Must or Could be True Questions |

91 | A circular rim 28 inches in diameter rotates the same number | Distance/Rate Problems/Geometry |

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

93 | Leila is playing a carnival game in which she is given 4 | Probability |

94 | T is a set of y integers, where 0 < y < 7. If the average of | Statistics and Sets Problems |

95 | The output of a factory was increased by 10% to keep up with | Percents and Interest Problems |

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

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

98 | In a room filled with 7 people, 4 people have exactly 1 | Combinations/Probability |

99 | Find the number of trailing zeros in the product of (1^1)*(5 | Geometry |

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