Directions: Each of the questions given below consists of a statement and/or a question followed by two statements labelled I and II. 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. A and B together can complete a task in 7 days. B alone can do it in 20 days. What part of the work was carried out by A ? I. A completed the job alone after A and B worked together for 5 days. II. Part of the work done by A could have been done by B and C together in 6 days.

### Concept & Logic To find "what part of the work was carried out by A," we need to know the specific scenario of how the work was done (who worked for how many days). $$ \text{Work Done} = \text{Rate} \times \text{Time} $$ The total work done by A and B combined equals 1 (the whole task). ### Step-by-Step Solution From the main statement: * A and B together take 7 days: Rate of $(A+B) = \frac{1}{7}$. * B alone takes 20 days: Rate of $B = \frac{1}{20}$. * Rate of $A = \frac{1}{7} - \frac{1}{20} = \frac{20-7}{140} = \frac{13}{140}$. From Statement I: * A and B worked together for 5 days. Then A completed it alone. * We need to find the fraction of total work A performed in this scenario. * The easiest way is to find how much work B did, and subtract that from 1. * B only worked during the first 5 days. * Work done by B = Rate of B $\times$ Time B worked = $\frac{1}{20} \times 5 = \frac{5}{20} = \frac{1}{4}$. * Since B did $\frac{1}{4}$ of the work, A must have done the rest: $1 - \frac{1}{4} = \frac{3}{4}$. * Statement I gives us the exact answer. From Statement II: * This statement only provides a hypothetical equivalence relating A's work to B and C's work. It does not describe the actual scenario of how the task was completed in reality. It is insufficient. ### Exam Strategy & Shortcut When a question asks "What part of the work was carried out by X" in a specific event, track the *other* worker. If you know exactly how many days worker Y worked, you calculate Y's fraction of the work. X simply did whatever was left ($1 - Y$). Statement I provides exactly how long B worked. ### Common Pitfall Do not spend time calculating A's exact number of days working alone unless asked. Calculating B's work and subtracting from the total (1) is much faster and less prone to arithmetic errors. ### Final Answer Therefore, the correct answer is **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;**