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 |