Express 6.72% as a simplified ratio.

Introduction / Context:
This question asks to convert a percentage into a ratio. Conversions between percentages, fractions and ratios are very common in quantitative aptitude, as they allow a value to be interpreted in different forms depending on the problem. Expressing a percentage as a ratio often requires writing it as a fraction and then simplifying to lowest terms.

Given Data / Assumptions:

We are given the percentage 6.72%.
We need to express 6.72% as a ratio of two integers in simplest form.
Ratios are usually written as a : b, where a and b are whole numbers with no common factor other than 1.

Concept / Approach:
First convert the percentage to a fraction over 100. Then remove the decimal by multiplying numerator and denominator by an appropriate power of 10. After that, simplify the resulting fraction by dividing numerator and denominator by their greatest common divisor. Finally, interpret the simplified fraction as a ratio in the form a : b.

Step-by-Step Solution:
Step 1: Write 6.72% as a fraction. 6.72% = 6.72 / 100. Step 2: Remove the decimal by multiplying numerator and denominator by 100. 6.72 / 100 = 672 / 10,000. Step 3: Simplify the fraction 672 / 10,000. First, divide both numerator and denominator by 16. 672 / 16 = 42, and 10,000 / 16 = 625. So 672 / 10,000 simplifies to 42 / 625. Step 4: Check if 42 / 625 can be reduced further. 42 factors into 2 * 3 * 7. 625 factors into 5 * 5 * 5 * 5. There is no common factor except 1, so the fraction is in simplest form. Step 5: Write the simplified fraction as a ratio. 42 / 625 corresponds to the ratio 42 : 625.

Verification / Alternative check:
To verify, convert the ratio 42 : 625 back into a percentage. First interpret it as the fraction 42 / 625. Compute 42 / 625, which equals 0.0672. Now convert this decimal to a percentage by multiplying by 100: 0.0672 * 100 = 6.72%. This matches the original percentage given in the question, confirming that the ratio 42 : 625 is correct.

Why Other Options Are Wrong:
Ratios like 65 : 124 or 21 : 125 correspond to different fractions and therefore different percentages when converted back.
37 : 442 and 168 : 2500 also simplify to values that are not equal to 0.0672 and hence do not represent 6.72%.
Only 42 : 625 converts exactly back to 6.72%.

Common Pitfalls:
Learners sometimes treat 6.72% as 0.672 or 6.72 directly without dividing by 100, which gives incorrect fractions. Another error is to stop simplifying too early, leaving the fraction in non-simplest form. Some may also incorrectly cancel digits instead of factors when simplifying. Always convert the percentage to a fraction over 100, clear the decimals properly, and then systematically reduce numerator and denominator by their greatest common divisor.

Final Answer:
6.72% expressed as a ratio is 42 : 625.