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100 Hardest PS questions!

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100 Hardest PS questions! [#permalink]

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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 forumh.
Problem Solving (PS)
Rank Title Topics
1On a partly cloudy day, Derek decides to walk back from work Distance/Rate Problems
2If the product of all the unique positive divisors of n, a p Divisibility/Multiples/Factorsx/Number Properties
3In the figure, point D divides side BC of triangle ABC into Geometry
4In a village of 100 households, 75 have at least one DVD Overlapping Sets
5How many even 3 digit integers greater than 700 with Combinations
6Arrow AB which is a line segment exactly 5 units along with Coordinate Geometry
7An integer between 1 and 300, inclusive, is chosen at random Probability
8How many positive integers less than 10,000 are there in Combinations
9If 10! - 2*(5!)^2 is divisible by 10^n, what is the greatest Divisibility/Multiples/Factors/Roots
10A fair coin is tossed 5 times. What is the probability of Probability
11Louie takes out a three-month loan of $1000. The lender Percents and Interest Problems
12The function g(x) is defined for integers x such that if x Arithmetic
13In racing over a given distance d at uniform speed, A can be Distance/Rate Problems
14What is the least possible distance between a point on the Coordinate Geometry
15A sequence of numbers (geometric sequence) is given by the Exponents/Powers/Sequences
16A cylindrical water tower with radius 5 m and height 8 m is Geometry/Work/Rate Problems
17Car B starts at point X and moves clockwise around Distance/Rate Problems
18What is the product of all the solutions of x^2 - 4x + 6=3 Absolute Values/Modules/Algebra
19List T consist of 30 positive decimals, none of which is an Min/Max Problems
20If x+|x|+y=7 and x+|y|-y=6 what is x+y=? Absolute Values/Modules
21If 2^x + 2^y = x^2 + y^2, where x and y are nonnegative inte Algebra
22If x represents the sum of all the positive three-digit Arithmetic/Combinations
23If x#0 and x/|x|<x, which of the following must be true? Absolute Values/Modules/Inequalities
24If an integer n is to be chosen at random from the integers Divisibility/Multiples/Factors/Probability
25Tanya prepared 4 different letters to be sent to 4 different Probability
26Tom and Linda stand at point A. Linda begins to walk in a Distance/Rate Problems
27How many values can the integer p=|x+3|-|x-3| assume? Absolute Values/Modules
28Two different primes may be said to “rhyme” Number Properties
29If a is the sum of x consecutive positive integers. b is the Statistics and Sets Problems
30How many combinations of three letters taken from letters Combinatios
31The number of straight line miles traveled downriver in one Algebra/Word Problems
32According to a survey, at least 70% of people like apples Min/Max Problems
33If a and b are distinct integers and a^b = b^a, how many Exponents/Powers/Number Properties
34It takes 6 days for 3 women and 2 men working together to Work/Rate Problems
35x/|x|<x. which of the following must be true about x ? Absolute Values/Modules/Inequalities/Must or Could be True
36Which of the following sets includes ALL of the solutions of Absolute Values/Modules
37In how many different ways can a group of 8 people be divide Combinations
38A scientist has a set of weights {1Kg, 2Kg, 4Kg, 8Kg, 16Kg, Combinations
39The elevator in an eleven-story office building travels at Distance/Rate Problems
40How many integral values of k are possible, if the lines 3x+ Coordinate Geometry
41In the diagram, points A, B, and C are on the diameter of Geometry
42In a certain sequence, every term after the first is determi Sequences
43A man cycling along the road noticed that every 12 minutes Distance/Rate Problems
44Danny is sitting on a rectangular box. The area of the front Geometry
45In triangle ABC to the right, if BC = 3 and AC = 4, then Geometry
46On a race track a maximum of 5 horses can race together at Min/Max Problems
47There are 100 freshmen at a particular college, all of whom Overlapping Sets
48Set S consists of numbers 2, 3, 6, 48, and 164. Number K is Divisibility/Multiples/Factors/Number Properties/Probability
49If x, a, and b are positive integers such that when x is Divisibility/Multiples/Factors/Must or Could be True/Remainders
50If |12x−5|>|7−6x|, which of the following CANNOT be the Absolute Values/Modules/Inequalities
51How many numbers that are not divisible by 6 divide evenly Divisibility/Multiples/Factors
52How many 4 digit numbers are there, if it is known that the Combinations
53How many of the integers that satisfy the inequality (x+2)(x Inequalities
54Two cars A and B start from Boston and New York respectively Distance/Rate Problems
55If p and q are two different odd prime numbers, such that Must or Could be True Questions/Number Properties
56How many positive integers less than 30 are either a Divisibility/Multiples/Factors/Number Properties
57If two integers are chosen at random out of the set {2, 5, 7 Number Properties/Probability
58Point (x,y) is a point within the triangle. What is the Coordinate Geometry/Probability
59How many even integers n, where 100 <= n <= 200, are divisib Divisibility/Multiples/Factors
60A cyclist travels the length of a bike path that is 225 Distance/Rate Problems/Inequalities
61If x/|x|<x which of the following must be true about x? Absolute Values/Modules/Inequalities/Must or Could be True Questions
62A man sets out to cycle from BBSR to CTC and at the same Distance/Rate Problems
63a, b, c, d are positive integers such that exactly one of Inequalities
64How many prime numbers n exist such that 90 < n < 106 and n Divisibility/Multiples/Factors
65The above 11 x 11 grid of dots is evenly spaced: each dot is Combinations/Geometry
66The sum of the even numbers between 1 and n is 79*80, where Number Properties
67If x is positive, which of the following could be the Inequalities/Must or Could be True Questions
68A man arrives at a railway station 90mins before the time at Distance/Rate Problems
69The function p(n) on non-negative integer n is defined in Exponents/Powers
70A big cube is formed by rearranging the 160 coloured and 56 Geometry
71For a nonnegative integer n, if the remainder is 1 when 2^n Must or Could be True Questions/Remainders
72A satellite is composed of 30 modular units, each of which Fractions/Ratios/Decimals
73Car B begins moving at 2 mph around a circular track with Distance/Rate Problems
74If x is an integer and |1-x|<2 then which of the following Absolute Values/Must or Could be True/Number Properties
75What is the least possible distance between a point on the Coordinate Geometry
76Out of seven models, all of different heights, five models Combinations
77Set R contains five numbers that have an average value of 55 Min/Max Problems/Statistics and Sets Problems
78In the first quarter of 2008, Harry's Hardware Store sold 30 Percents and Interest Problems
79Each of the following equations has at least one solution Exponents/Powers
80Alex and Brenda both stand at point X. Alex begins to walk a Distance/Rate Problems/Geometry
81Jerry and Jim run a race of 2000 m. First, Jerry gives Jim Distance/Rate Problems
82If N is the product of all multiples of 3 between 1 and 100 Divisibility/Multiples/Factors/Exponents/Powers
83In the XY co-ordinate plane, circle C has center at (8,0) an Coordinate Geometry
84A cylindrical tank of radius R and height H must be redesign Geometry
85Last Sunday a certain store sold copies of Newspaper A for Arithmetic/Percents and Interest Problems
86In the circle above, PQ is parallel to diameter OR Geometry
87When n is divided by 5 the remainder is 2. When n is divided Remainders
88A new sales clerk in a department store has been assigned to Percents and Interest Problems/Word Problems
89N and M are each 3-digit integers. Each of the numbers 1, 2, Arithmeticx/ Min/Max Problems
90If x is positive, which of the following could be correct Inequalities/Must or Could be True Questions
91A circular rim 28 inches in diameter rotates the same number Distance/Rate Problems/Geometry
92Eight litres are drawn off from a vessel full of water and s Mixture Problems
93Leila is playing a carnival game in which she is given 4 Probability
94T is a set of y integers, where 0 < y < 7. If the average of Statistics and Sets Problems
95The output of a factory was increased by 10% to keep up with Percents and Interest Problems
96Jerry and Jim run a race of 2000 m. First, Jerry gives Jim Distance/Rate Problems
97Points A and B are 120 km apart. A motorcyclist starts from Distance/Rate Problems / Geometry
98In a room filled with 7 people, 4 people have exactly 1 Combinations/Probability
99Find 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


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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Last edited by Bunuel on 18 Oct 2013, 04:27, edited 17 times in total.
100 Hardest PS questions!   [#permalink] 15 Jul 2013, 03:41
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100 Hardest PS questions!

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