# GMAT: Math 20 | Problem solving | GMAT | Khan Academy | Summary and Q&A

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December 15, 2008
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GMAT: Math 20 | Problem solving | GMAT | Khan Academy

## TL;DR

Students use ratios and equations to solve math problems.

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### Q: What is the present number of teachers in the given problem?

To find the present number of teachers, we can set up an equation using the given ratios and solve for the variable. The solution is 15.

### Q: How can we determine the smallest integer n for which 25ⁿ > 5¹²?

We can rewrite the equation using the same base, 5, and solve for the exponent. 2n > 12, so n must be greater than 6. The smallest integer greater than 6 is 7.

### Q: Why is it impossible for x and y to be prime numbers that equal 91 when added together?

Prime numbers greater than 2 are always odd. When adding two odd numbers together, the result is an even number. Since 91 is an odd number, it cannot be formed by adding two prime numbers greater than 2.

### Q: Why is the statement "x divided by y is not an integer" true?

If x divided by y were an integer, it would mean that y divides evenly into x, suggesting that x is not a prime number. However, the video states that x is a prime number, therefore making the statement true.

## Summary & Key Takeaways

• The video discusses solving math problems involving ratios and equations.

• It provides step-by-step explanations for solving various problems.

• The examples in the video cover topics such as increasing student enrollment and determining the smallest integer.