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 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 Mr. Roy's annual income for the year April 2011 to March 2012? I. Annual income of Mr. Roy is $70\%$ of his boss' annual income. II. Mr. Roy's income for April 2011 was ₹ 12000 and his income increased every month by $10\%$.

### Concept & Formula The goal is to determine if we have enough mathematical constraints to calculate the total annual income. A geometric progression or simple iterative addition of known values over a fixed time period yields a definite, calculable sum. ### Step-by-Step Solution * Target: Find Mr. Roy's total annual income. * Evaluate Statement I: * Mr. Roy's income is $70\%$ of his boss's income. We do not know the boss's income, meaning there is an unknown variable. This statement alone is not sufficient. * Evaluate Statement II: * We have a starting value (April 2011 income = ₹ 12000). * We have a fixed growth rate ($10\%$ increase every month). * We have a fixed time period (April 2011 to March 2012 = 12 months). * The annual income is mathematically the sum of a geometric progression: * $$S = 12000 + 12000(1.1) + 12000(1.1)^2 + ... \text{ up to 12 terms}$$ * Since all parameters are explicitly known, this sum can uniquely be calculated. Statement II alone is sufficient. ### Exam Strategy & Shortcut Recognize the components of a formula rather than computing the result. Statement II provides the principal, the growth rate, and the time. Because all variables in the summation formula are known, the data is inherently sufficient. Do not attempt to calculate the actual summation! ### Common Pitfall A major trap is attempting to compute the full annual income to "prove" the answer. The calculation involves finding $1.1^{11}$, which is highly time-consuming without a calculator. Remember that "calculable" means "sufficient". ### Final Answer **Therefore, the correct answer is 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.**