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# 100 Hardest Problem Solving Questions

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100 Hardest Problem Solving Questions [#permalink]

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03 Nov 2013, 13:05
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100 Hardest Problem Solving Questions

Are you familiar with the GMAT Club's timer? We have pulled timer results from our database and analyzed every question in the forum. Based on those results, we have compiled a list of the hardest questions in each of the question forums we have. Below I am presenting to you the top 100 questions from PS forum.
 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

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Re: 100 Hardest Problem Solving Questions [#permalink]

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16 Aug 2016, 10:46
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Re: 100 Hardest Problem Solving Questions   [#permalink] 16 Aug 2016, 10:46
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# 100 Hardest Problem Solving Questions

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