Unlock hundreds more features
Save your Quiz to the Dashboard
View and Export Results
Use AI to Create Quizzes and Analyse Results

OR
Sign inSign in with Facebook
Sign inSign in with Google
Quizzes > Mathematics

Hard IQ Test: Challenge Your Logic and Math Skills

Quick, free quiz of challenging IQ questions. Instant results and explanations.

Editorial: Review CompletedCreated By: Amit PandeyUpdated Aug 26, 2025
Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art brain puzzle pieces numbers math symbols geometric shapes on golden yellow background for hard IQ test quiz

This hard IQ test helps you gauge your reasoning and math skills through tricky logic, patterns, and analogies. Expect a tight mix of challenging items and instant results with brief explanations. For a broader measure, try our free online iq test, or zero in on numbers with the math iq test. Curious about extreme scores? Check out the genius test.

Which number completes the sequence: 3, 9, 27, 81, ?
162
108
324
243
undefined
A fair coin is flipped three times. The probability of exactly two heads is 3/8.
False
True
undefined
Find x if 2^(x+1) = 32.
3
6
5
4
undefined
The sum of the first n odd numbers equals n^2.
False
True
undefined
Which word does not belong: raven, crow, sparrow, bat
crow
raven
sparrow
bat
undefined
A number is divisible by 3 if the sum of its digits is divisible by 3.
False
True
undefined
If all bloops are blargs and some blargs are blings, it follows that some bloops are blings.
True
False
undefined
Which figure has the greatest number of lines of symmetry?
Regular hexagon
Square
Equilateral triangle
Regular pentagon
undefined
Which number completes the pattern: 2, 5, 11, 23, 47, ?
99
101
95
89
undefined
If A = 1, B = 2, ..., Z = 26, what is the value of CODE?
34
33
27
35
undefined
If f(x) = 3x - 2, find f(f(2)).
13
10
20
16
undefined
Among all rectangles with a fixed perimeter, the square encloses the maximum area.
True
False
undefined
In a standard 24-hour day, the minute and hour hands of a clock overlap 22 times.
False
True
undefined
All prime numbers greater than 3 are of the form 6k +/- 1.
False
True
undefined
Which arrangement has the greatest surface area for fixed volume?
Sphere
Thin sheet
Regular tetrahedron
Cube
undefined
If a polygon is regular and has each interior angle equal to 150 degrees, it has 12 sides.
False
True
undefined
What is the smallest positive integer that leaves remainder 2 when divided by 3, 4, and 5?
62
74
82
122
undefined
A graph with n nodes and more than (n-1)(n-2)/2 edges must be connected.
True
False
undefined
A simple planar graph with 5 or more vertices must have a vertex of degree at most 5.
True
False
undefined
For all real x, |x+1| + |x-1| >= 2.
True
False
undefined
0

Study Outcomes

  1. Understand Logical Reasoning Patterns -

    Identify and interpret the underlying logic structures used in our hard IQ test to improve your problem-solving methods.

  2. Analyze Complex Math Challenges -

    Break down and solve advanced mathematical problems featured in this challenging IQ quiz, refining your numerical reasoning abilities.

  3. Apply Analogy Strategies -

    Use proven techniques to tackle analogies effectively in the online IQ test free format and strengthen your comparative thinking skills.

  4. Enhance Critical Thinking Speed -

    Practice time-based exercises that boost your ability to quickly process information and make accurate decisions under pressure.

  5. Evaluate Your Cognitive Performance -

    Interpret your IQ score results to measure strengths and identify improvement areas in logical reasoning and math aptitude.

Cheat Sheet

  1. Logical Syllogisms & Deductive Reasoning -

    To excel on logic puzzles in a hard IQ test, master categorical syllogisms (e.g., "All A are B; Some B are C; therefore…") using techniques from Stanford University's Introductory Logic course. Practice with Euler diagrams to visually confirm conclusions and reduce errors. Strengthening these skills boosts performance on challenging IQ quizzes and logical reasoning tests.

  2. Mathematical Problem-Solving & Series Patterns -

    Familiarize yourself with arithmetic and geometric sequences by using the formula a_n = a_1·r^(n−1) for geometric progressions taught in MIT OpenCourseWare courses. Work through sample equations like 2, 6, 18, … to spot multiplicative patterns quickly. This approach sharpens your skills for the math challenges within an online IQ test free environment.

  3. Analogy Reasoning & Relationship Mapping -

    Develop your analogy skills by categorizing relationships - such as cause-effect or part-whole - drawing on exercises recommended by the University of Cambridge's Cognitive Science department. Use the "A is to B as C is to D" framework to articulate each term's connection before selecting the best match. Regular practice enhances accuracy on analogies in a challenging IQ quiz.

  4. Spatial Visualization & Mental Rotation -

    Improve your spatial reasoning by practicing 3D mental rotations using tools from the American Psychological Association's spatial ability research. Visualize folding or rotating shapes in your mind, then verify with paper models or apps. Mastery of spatial puzzles raises your score on the logical reasoning test sections of a hard IQ test.

  5. Working Memory & Test Strategy Techniques -

    Enhance your working memory by employing chunking methods and the dual n-back exercise supported by research from the National Institute of Mental Health. Use brief, timed drills to train focus and reduce cognitive load during an online IQ test free session. Coupling these tactics with timed practice mimics real test conditions and builds confidence.

Make a Quiz (FREE) Copy & Edit This Quiz Create a Quiz with AI

Puzzles & Riddles Quizzes

Powered by: Quiz Maker