Directions: Each of the questions given below consists of a statement and/or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the given question. Read both the statements and: Give answer (a) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question; Give answer (b) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question; Give answer (c) if the data either in Statement I or in Statement II alone are sufficient to answer the question; Give answer (d) if the data even in both Statements I and II together are not sufficient to answer the question; Give answer (e) if the data in both Statements I and II together are necessary to answer the question. What is the rate of compound interest on a sum of money? (Bank P.O., 2009) I. The total simple interest at the same rate on ₹ 6000 at the end of 3 years is ₹ 1800. II. The total compound interest on ₹ 6000 at the end of 2 years is ₹ 1260.
Verbal Reasoning
Data Sufficiency
Difficulty: Medium
Choose an option
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Aif the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question;
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Bif the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question;
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Cif the data either in Statement I or in Statement II alone are sufficient to answer the question;
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Dif the data even in both Statements I and II together are not sufficient to answer the question;
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Eif the data in both Statements I and II together are necessary to answer the question.
Answer
Correct Answer: if the data either in Statement I or in Statement II alone are sufficient to answer the question;
Explanation
### Concept & Logic
To determine the rate of interest, we can use the formulas for Simple Interest and Compound Interest if other variables (Principal, Time, Amount/Interest) are known.
$$S.I. = \frac{P \times R \times T}{100}$$
$$C.I. = P\left[\left(1 + \frac{R}{100}\right)^T - 1\right]$$
### Step-by-Step Solution
From Statement I:
* Given: $P = 6000$, $T = 3$, $S.I. = 1800$
* We can find $R$ using $1800 = \frac{6000 \times R \times 3}{100}$. This simplifies to $R = 10\%$.
* Therefore, Statement I alone is sufficient.
From Statement II:
* Given: $P = 6000$, $T = 2$, $C.I. = 1260$
* We can find $R$ using $1260 = 6000\left[\left(1 + \frac{R}{100}\right)^2 - 1\right]$. This yields an equation with only $R$ as the unknown variable.
* Therefore, Statement II alone is sufficient.
### Exam Strategy & Shortcut
In Data Sufficiency, you do not need to calculate the exact final value. Just verify if the given parameters in an equation leave only the required variable unknown. Both statements independently provide an equation with only $R$ as the unknown.
### Common Pitfall
A common mistake is unnecessarily calculating the exact value of $R$ for both statements, which wastes time in an exam. Stop once you establish that a unique solution exists.
### Final Answer
Therefore, the correct answer is **if the data either in Statement I or in Statement II alone are sufficient to answer the question;**