IQ Test #15: Tricky Mathematical Problem-Solving Excellence

🧠 Test Your Tricky Mathematical Problem-Solving Skills!

Warning: Deceptive Mathematical Puzzles Ahead! This test features counterintuitive problems, mathematical paradoxes, and clever puzzles that require deep analytical thinking. Only those who can see beyond surface-level solutions will excel!

Analyze each tricky mathematical puzzle carefully - these require recognizing hidden patterns, avoiding common traps, and applying creative problem-solving. Click Check My Tricky Mathematical IQ to evaluate your advanced quantitative reasoning skills!

1) A bat and ball cost $1.10 total. The bat costs $1.00 more than the ball. How much does the ball cost?

A) $0.05 B) $0.10 C) $0.05 D) $0.15

2) If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?

A) 100 minutes B) 5 minutes C) 20 minutes D) 1 minute

3) In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half the lake?

A) 24 days B) 36 days C) 42 days D) 47 days

4) A man is looking at a portrait. Someone asks him, "Who are you looking at?" He replies: "Brothers and sisters I have none, but this man's father is my father's son." Who is in the portrait?

A) His son B) His father C) Himself D) His brother

5) You are running a race and overtake the second person. What position are you in now?

A) First B) Second C) Second D) Third

6) How many times can you subtract 5 from 25?

A) 5 times B) Once C) Infinite times D) 25 times

7) If 2 is company and 3 is a crowd, what are 4 and 5?

A) Friends B) Family C) Party D) 9

8) A farmer has 17 sheep. All but 9 die. How many are left?

A) 9 B) 8 C) 17 D) 0

9) I am an odd number. Take away one letter and I become even. What number am I?

A) 5 B) 3 C) 7 D) 9

10) What is the next number in this sequence: 1, 11, 21, 1211, 111221, ...?

A) 13112221 B) 312211 C) 21111221 D) 221121

Your Tricky Mathematical Problem-Solving Results! 🌟

Score: 0 / 10

Strong tricky mathematical problem-solving skills demonstrate your ability to think critically, avoid cognitive traps, and solve problems from multiple perspectives!

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Answers and Clarifications

Understand the clever reasoning behind each tricky solution. Click on any question below to view its detailed explanation.

Question 1: The Bat and Ball Problem

Correct Answer: C) $0.05

This classic puzzle tests whether you fall for the intuitive but wrong answer:

• Common wrong answer: $0.10 (because $1.10 - $1.00 = $0.10)
• But if ball = $0.10, then bat = $1.10, total = $1.20 (wrong)

Correct algebraic approach:

• Let ball = x dollars
• Then bat = x + 1.00 dollars
• Total: x + (x + 1.00) = 1.10
• 2x + 1.00 = 1.10
• 2x = 0.10
• x = 0.05

The ball costs $0.05 and the bat costs $1.05, totaling $1.10 with the bat costing exactly $1.00 more.

Question 2: Machine Rate Problem

Correct Answer: B) 5 minutes

This tests understanding of rates and scaling:

• 5 machines make 5 widgets in 5 minutes
• This means each machine makes 1 widget in 5 minutes
• Therefore, 100 machines would make 100 widgets in the same 5 minutes

The key insight is that the number of machines and number of widgets scale together, so the time remains constant.

Common wrong answers:

• 100 minutes (linear scaling without understanding rates)
• 20 minutes (incorrect proportional thinking)

Question 3: Lily Pad Growth Problem

Correct Answer: D) 47 days

This tests understanding of exponential growth and working backwards:

• The patch doubles in size every day
• On day 48, the patch covers the entire lake
• Therefore, on day 47, the patch covers half the lake
• Because it doubles from half to full in one day

Common wrong answers:

• 24 days (assuming linear growth)
• 36 days (various incorrect proportional calculations)

This demonstrates the counterintuitive nature of exponential growth.

Question 4: Family Riddle

Correct Answer: A) His son

This tests logical reasoning and careful parsing of the statement:

"Brothers and sisters I have none" - the speaker has no siblings

"This man's father is my father's son" - let's break this down:

• "My father's son" - since the speaker has no brothers, this must refer to the speaker himself
• So "this man's father is me"
• Therefore, the man in the portrait is the speaker's son

The portrait shows the speaker's son, and the speaker is looking at his own child.

Question 5: Race Position Puzzle

Correct Answer: C) Second

This tests careful thinking about positions and overtaking:

• If you overtake the second person, you take their position
• You were behind the second person
• After overtaking them, you are now in second place
• The first person is still ahead of you

Common wrong answers:

• First (thinking you're now ahead of everyone)
• Third (miscounting positions)

Visualize the race: [First] [Second] [You] → after overtaking: [First] [You] [Former Second]

Question 6: Subtraction Trick Question

Correct Answer: B) Once

This is a linguistic trick rather than a mathematical one:

• After you subtract 5 from 25 once, you get 20
• The question asks how many times you can subtract 5 from 25
• After the first subtraction, you're no longer subtracting from 25
• You're subtracting from 20, then 15, then 10, etc.

The trick is in the wording "from 25" - you can only do this once before the number changes.

If the question was "how many times can you subtract 5 from 25 until you reach 0," the answer would be 5 times.

Question 7: Wordplay Puzzle

Correct Answer: D) 9

This tests pattern recognition in wordplay:

• "2 is company" - this is a common saying
• "3 is a crowd" - another common saying
• The pattern is mathematical: 4 and 5 make 9

The puzzle switches from interpreting numbers as group sizes to treating them as numbers to be added.

This demonstrates the importance of recognizing when a pattern changes or when a puzzle requires switching perspectives.

Question 8: Farmer's Sheep

Correct Answer: A) 9

This tests careful reading and logical interpretation:

• "All but 9 die" means all sheep except 9 die
• If 17 sheep total, and all but 9 die, then 9 sheep remain alive
• 8 sheep died (17 - 9 = 8)

Common wrong answers:

• 8 (misinterpreting "all but 9" as 9 died)
• 17 (ignoring that some died)
• 0 (extreme misinterpretation)

The phrase "all but X" means "everything except X."

Question 9: Letter Removal Puzzle

Correct Answer: C) 7

This tests thinking about numbers as words:

• The number is "seven"
• Remove the letter "s" and you get "even"
• "Even" can mean both "smooth/level" and refers to even numbers

Other numbers don't work:

• 5 (five) → remove "f" = "ive" (not a number)
• 3 (three) → remove any letter doesn't make "even"
• 9 (nine) → remove any letter doesn't make "even"

This puzzle requires thinking about numbers in their written form rather than as numerical values.

Question 10: Look-and-Say Sequence

Correct Answer: B) 312211

This tests pattern recognition in the famous "look-and-say" sequence:

• 1 → "one 1" → 11
• 11 → "two 1s" → 21
• 21 → "one 2, one 1" → 1211
• 1211 → "one 1, one 2, two 1s" → 111221
• 111221 → "three 1s, two 2s, one 1" → 312211

Each term describes the digits of the previous term in order:

Count how many of each digit appear consecutively, then write the count followed by the digit.

This sequence was studied by mathematician John Conway and has fascinating mathematical properties.

Select a Question to View Its Answer

Click on any of the question tabs above to see the detailed reasoning behind each tricky solution.

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These tricky mathematical puzzles test your ability to avoid cognitive traps, think critically, and solve problems from unexpected angles.

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Why Master Tricky Mathematical Problem-Solving?

Tricky mathematical problem-solving develops critical thinking and cognitive flexibility. These skills enable you to:

• Recognize and avoid common cognitive biases and logical fallacies
• Solve problems from multiple perspectives and approaches
• Think creatively when standard methods don't work
• Detect patterns and hidden structures in complex situations
• Excel in fields requiring innovative problem-solving and analysis

These abilities are crucial for research, innovation, strategy development, and any field requiring out-of-the-box thinking.

What This Test Measures

This Tricky Mathematical Problem-Solving IQ Test evaluates several key cognitive abilities:

• Cognitive Reflection: Overcoming intuitive but incorrect answers
• Lateral Thinking: Solving problems through unconventional approaches
• Pattern Recognition: Identifying hidden patterns and sequences
• Logical Analysis: Parsing complex statements and relationships
• Mental Flexibility: Switching between different problem-solving strategies

These skills collectively contribute to your overall ability to solve novel and deceptive problems effectively.