Algebra Puzzle – Critical Thinking 15

Challenge:

What is the smallest positive integer p such that 1080p is a perfect cube number?

The Absolute Best Book to Challenge Your Smart Student!

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.

The Absolute Best Books to Ace Algebra

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.