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04 Feb 2026, 22:27
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
67% (01:35) correct
33%
(01:46)
wrong
based on 95
sessions
History
Date
Time
Result
Not Attempted Yet
The compound interest on a loan is calculated using P[(1 + r / 100 )^n – 1], where P is the principal amount borrowed, r is the annual rate of interest and n is the number of years.
The simple interest on a loan is calculated using (P * r * n) / 100 , where P is the principal amount borrowed, r is the annual rate of interest and n is the number of years.
If the same amounts are borrowed at the same rate of interest for three years, the compound interest paid will be what percentage greater than the simple interest paid?
(1) The rate of annual interest is 10%.
(2) The amount borrowed is $100,000.
The simple interest on a loan is calculated using (P * r * n) / 100 , where P is the principal amount borrowed, r is the annual rate of interest and n is the number of years.
If the same amounts are borrowed at the same rate of interest for three years, the compound interest paid will be what percentage greater than the simple interest paid?
(1) The rate of annual interest is 10%.
(2) The amount borrowed is $100,000.
nemoexplicabo
05 Feb 2026, 06:43
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This is a classic Data Sufficiency question that tests whether you truly understand the relationship between compound and simple interest formulas. I scored 725 on GMAT Focus, and this type of problem used to trip me up until I grasped the key concept.
The question asks: if the same amounts are borrowed at the same rate for three years, by what percentage will compound interest exceed simple interest?
Let me break down the formulas given:
- Compound Interest = P[(1 + r/100)^n - 1]
- Simple Interest = P × r × n / 100
Understanding What We Need:
We need to find what percentage CI is greater than SI. This means we're looking for: [(CI - SI) / SI] × 100%
Analyzing Statement 1: The rate of annual interest is 10%
Here's the critical insight that many students miss: when a Data Sufficiency question asks for a percentage or ratio, you often don't need absolute values because they cancel out.
Let's work through this with r = 10% and n = 3:
- CI = P[(1.1)3 - 1] = P[1.331 - 1] = 0.331P
- SI = P × 10 × 3 / 100 = 0.30P
Now calculate the percentage difference:
- Difference = 0.331P - 0.30P = 0.031P
- Percentage greater = (0.031P / 0.30P) × 100% = 10.33%
Notice how P cancels out! We got a specific answer (approximately 10.3%) using only the rate. Statement 1 is SUFFICIENT.
Analyzing Statement 2: The amount borrowed is $100,000
This gives us P = $100,000, but without knowing r, we cannot calculate either CI or SI. Different interest rates would yield completely different percentage differences. For example:
- At 5% for 3 years: CI exceeds SI by about 5%
- At 10% for 3 years: CI exceeds SI by about 10.3%
- At 20% for 3 years: CI exceeds SI by about 21%
Statement 2 is INSUFFICIENT.
Answer: A (Statement 1 alone is sufficient)
Common Trap Alert: The biggest mistake students make here is thinking they need both P and r to answer the question. This comes from not recognizing that when you're asked for a percentage difference or ratio, the absolute value (principal in this case) often cancels out in the calculation. This is a fundamental Data Sufficiency pattern you'll see repeatedly - whenever the question asks "what percent" or "what ratio," consider whether you actually need the absolute values or just the relative relationship.
Key Takeaway: For percentage-based questions in Data Sufficiency, always ask yourself: "Will the values I'm missing cancel out in my final calculation?" This mental check will save you from eliminating correct answers.
The question asks: if the same amounts are borrowed at the same rate for three years, by what percentage will compound interest exceed simple interest?
Let me break down the formulas given:
- Compound Interest = P[(1 + r/100)^n - 1]
- Simple Interest = P × r × n / 100
Understanding What We Need:
We need to find what percentage CI is greater than SI. This means we're looking for: [(CI - SI) / SI] × 100%
Analyzing Statement 1: The rate of annual interest is 10%
Here's the critical insight that many students miss: when a Data Sufficiency question asks for a percentage or ratio, you often don't need absolute values because they cancel out.
Let's work through this with r = 10% and n = 3:
- CI = P[(1.1)3 - 1] = P[1.331 - 1] = 0.331P
- SI = P × 10 × 3 / 100 = 0.30P
Now calculate the percentage difference:
- Difference = 0.331P - 0.30P = 0.031P
- Percentage greater = (0.031P / 0.30P) × 100% = 10.33%
Notice how P cancels out! We got a specific answer (approximately 10.3%) using only the rate. Statement 1 is SUFFICIENT.
Analyzing Statement 2: The amount borrowed is $100,000
This gives us P = $100,000, but without knowing r, we cannot calculate either CI or SI. Different interest rates would yield completely different percentage differences. For example:
- At 5% for 3 years: CI exceeds SI by about 5%
- At 10% for 3 years: CI exceeds SI by about 10.3%
- At 20% for 3 years: CI exceeds SI by about 21%
Statement 2 is INSUFFICIENT.
Answer: A (Statement 1 alone is sufficient)
Common Trap Alert: The biggest mistake students make here is thinking they need both P and r to answer the question. This comes from not recognizing that when you're asked for a percentage difference or ratio, the absolute value (principal in this case) often cancels out in the calculation. This is a fundamental Data Sufficiency pattern you'll see repeatedly - whenever the question asks "what percent" or "what ratio," consider whether you actually need the absolute values or just the relative relationship.
Key Takeaway: For percentage-based questions in Data Sufficiency, always ask yourself: "Will the values I'm missing cancel out in my final calculation?" This mental check will save you from eliminating correct answers.
07 Feb 2026, 00:30
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excellent explanation, i was thinking along the same lines. however, the frequency of compounding bugged me right when i was picking the answer choice A. i wondered what kind of compounding it is, is it annually, semiannualy or monthly? we don't know that, nor can we assume anything and neither are the details explicitly mentioned about the mode of compounding and hence went ahead and picked "E"
nemoexplicabo
nemoexplicabo
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