If basis points are defined so that 1 percent is equal to 100 basis points, then by how many basis points is 82.5 percent greater than 62.5 percent?

Introduction / Context:
This percentage question checks understanding of the financial term "basis points" and how to convert a difference in percentages into basis points. Basis points are widely used in banking, loans, and interest rate comparisons, so being comfortable with this conversion is very useful for aptitude exams as well as real life decisions.

Given Data / Assumptions:
- 1 percent is defined as 100 basis points.
- First value: 82.5 percent.
- Second value: 62.5 percent.
- We must find by how many basis points the first value is greater than the second value.

Concept / Approach:
The key idea is that the difference between two percentages, measured in percentage points, can be converted into basis points by multiplying by 100. One basis point is 0.01 percent, so 100 basis points make 1 percent. We first compute the difference 82.5 percent minus 62.5 percent and then express that 20 percent gap in basis points.

Step-by-Step Solution:
Step 1: Calculate the difference in percentages: 82.5 percent - 62.5 percent = 20 percent.Step 2: Recall that 1 percent = 100 basis points.Step 3: Therefore, 20 percent = 20 * 100 basis points.Step 4: 20 * 100 = 2000 basis points.So 82.5 percent is greater than 62.5 percent by 2000 basis points.

Verification / Alternative check:
You can think in terms of decimal form. The difference is 0.825 - 0.625 = 0.20. One basis point is 0.0001 in decimal form. Dividing 0.20 by 0.0001 gives 0.20 / 0.0001 = 2000. This confirms that the gap is 2000 basis points.

Why Other Options Are Wrong:
- 0.2: This is far too small; it confuses percentage with basis points scale.
- 20: This would only be correct if 1 percent equalled 1 basis point, which is not the definition.
- 200: This treats 1 percent as 10 basis points, again inconsistent with the definition.

Common Pitfalls:
A common error is to confuse percentage points with percent. The question asks for the difference in basis points, not the ratio of the two percentages. Another frequent mistake is to multiply or divide by 10 instead of 100 when converting between percent and basis points. Remember that 1 percent equals 100 basis points, not 10, so always multiply the percent difference by 100 to get basis points.

Final Answer:
The number of basis points by which 82.5 percent is greater than 62.5 percent is 2000.