Directions: The question below consists of a question and two statements numbered I and II given below it. You have to decide whether the data given in the statements are sufficient to answer the questions. Read both the statements and given answer. What is the number of trees planted in the field in row and column? I. Number of columns is more than the number of rows by 4. II. Number of columns is 20.

## Concept & Logic This is a **Data Sufficiency** problem. The core objective is NOT to calculate the final numerical answer, but purely to determine if you have enough mathematical constraints (equations) to solve for the unknown variables. To find the total number of trees planted in a grid, we need both the number of rows ($R$) and the number of columns ($C$). Total Trees = $R \times C$. ## Step-by-Step Solution * **Target:** Find $R \times C$. We need unique values for both $R$ and $C$. * **Evaluate Statement I alone:** "Number of columns is more than the number of rows by 4." Equation: $C = R + 4$ This is a linear equation with two variables. It has infinite possible solutions (e.g., $R=1, C=5$; $R=10, C=14$). Therefore, Statement I alone is **Not Sufficient**. * **Evaluate Statement II alone:** "Number of columns is 20." Equation: $C = 20$ We have $C$, but no information about $R$. Therefore, Statement II alone is **Not Sufficient**. * **Evaluate Statements I and II combined:** From II, we know $C = 20$. Substitute this into the equation from I ($C = R + 4$): $$20 = R + 4$$ $$R = 16$$ Now we have both $C = 20$ and $R = 16$. We can successfully calculate the total trees ($20 \times 16 = 320$). Since combining both statements yields a unique answer, both are necessary. ## Exam Strategy & Shortcut In Data Sufficiency, your goal is to count variables and independent equations. We need $R$ and $C$ (2 variables). Statement I gives 1 equation relating the two. (Not enough). Statement II gives 1 distinct value. (Not enough). Combined, you have a system of 2 distinct linear equations for 2 variables. This guarantees a single solution. Stop evaluating and immediately mark that both are required. **Do not waste time actually multiplying 20 by 16.** ## Common Pitfall The most frequent mistake in Data Sufficiency is doing unnecessary arithmetic to find the final numerical answer (like calculating 320). Every second spent doing math after proving sufficiency is wasted exam time. ## Final Answer Therefore, the correct answer is If the data in both Statement I and II together are necessary to answer the question.