Directions: Study the following table carefully and answer the questions given below: Number (N) of Candidates (In lakhs) Appearing For An Entrance Examination From Six Different States And The Percentage (P) of Candidates Clearing the Same Over the Years | YEAR | A (N) | A (P) | B (N) | B (P) | C (N) | C (P) | D (N) | D (P) | E (N) | E (P) | F (N) | F (P) | | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | | **2004** | 1.23 | 42 | 1.04 | 51 | 1.11 | 32 | 1.32 | 24 | 1.23 | 36 | 1.33 | 31 | | **2005** | 1.05 | 43 | 1.12 | 62 | 1.07 | 47 | 1.15 | 49 | 1.18 | 55 | 1.24 | 24 | | **2006** | 2.04 | 38 | 1.48 | 32 | 1.08 | 28 | 1.96 | 35 | 1.42 | 49 | 1.58 | 26 | | **2007** | 1.98 | 41 | 2.07 | 43 | 1.19 | 30 | 1.88 | 46 | 1.36 | 47 | 1.79 | 29 | | **2008** | 1.66 | 53 | 1.81 | 50 | 1.56 | 42 | 1.83 | 60 | 1.73 | 57 | 1.86 | 34 | | **2009** | 1.57 | 39 | 1.73 | 36 | 1.64 | 52 | 2.01 | 56 | 1.69 | 55 | 1.95 | 37 | In which year did the highest number of candidates clear the entrance exam from State D ?

### Concept & Strategy To determine the highest absolute number of successful candidates for a given state over several years, we must calculate the product of the appearing candidates (N) and the passing percentage (P) for State D for the years listed in the options. ### Step-by-Step Solution We need to evaluate the number of candidates clearing for State D in the given options (2006, 2007, 2008, 2009). The actual number is $N \times P\%$. We can just compare $N \times P$ directly without dividing by 100. 1. **2006:** $1.96 \times 35 \approx 2 \times 35 = 70$ (Exact: $68.6$) 2. **2007:** $1.88 \times 46 \approx 1.9 \times 46 \approx 87$ (Exact: $86.48$) 3. **2008:** $1.83 \times 60 = 109.8$ 4. **2009:** $2.01 \times 56 \approx 2 \times 56 = 112$ (Exact: $112.56$) Comparing the values: $112.56 > 109.8 > 86.48 > 68.6$. The highest value occurs in the year 2009. ### Exam Strategy & Shortcut Do not perform precise decimal multiplications for every year unless two values are exceptionally close. Use rounding to quickly estimate. For instance, in 2008, $1.8 \times 60 \approx 108$. In 2009, $2 \times 56 \approx 112$. Since 112 is clearly larger than 108, and the exact values confirm this trend, 2009 is definitively the answer without wasting time on perfect arithmetic. ### Common Pitfall A frequent mistake is simply looking at the highest "N" value or the highest "P" value independently and guessing the answer. The highest "N" or "P" does not guarantee the highest product. Both variables must be evaluated together. ### Final Answer Therefore, the correct answer is **2009**.