Algebra Puzzle – Critical Thinking 15
Algebra Puzzle - Critical Thinking 15: this Effortless Math guide explains the topic in plain language, shows how it works through solved examples, and gives you free practice to try immediately, so the idea sticks instead of staying abstract.
Critical thinking challenges like this one can be as much a part of a math class as learning concepts, computations, and formulas.
Challenge:
What is the smallest positive integer p such that 1080p is a perfect cube number?
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The correct answer is 25.
First, find the factor of 1080p. The prime factors of 1080p are:
(2^3×3^3×5×p)
In order for (2^3×3^3×5×p) to be a perfect cube, each prime factor must come in sets of triples. Since, we have (2^3×3^3×5), thus, we only need to change 5 to (5^3). Therefore, p equals to (5^2) or 25.
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Mastering Algebra Puzzles
Algebra puzzles develop your logical thinking. Read carefully, define variables, translate to equations, and solve systematically. This approach works for number puzzles, age problems, and work-rate scenarios.
Example
I think of a number, double it, add 5, and get 17. What’s the number? Set 2n + 5 = 17. Solve: 2n = 12, so n = 6. Check: 2(6) + 5 = 17. ✓
Common Errors
- Not reading carefully
- Misinterpreting word relationships
- Forgetting to check if answers make sense
Related Topics
Review one-step equations and multi-step equations for foundations.
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