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 | What is the average number of candidates appearing for the entrance exam from State D in the years 2007, 2008 and 2009 together ?

### Concept & Logic To find the average number of appearing candidates, sum the actual numerical values for State D in the specified years and divide by the total number of years (3). ### Step-by-Step Solution 1. **Extract the N Values for State D:** - 2007: $1.88$ lakhs - 2008: $1.83$ lakhs - 2009: $2.01$ lakhs 2. **Sum the Values:** - Total appearing = $1.88 + 1.83 + 2.01 = 5.72$ lakhs. 3. **Convert to Actual Integers:** - $5.72 \text{ lakhs} = 5.72 \times 100,000 = 572,000$. 4. **Calculate the Average:** - Average = $\frac{572,000}{3}$. - Performing the division: $572,000 \div 3 = 190,666$ with a remainder of $2$. - Expressed as a mixed fraction: $190666 \frac{2}{3}$. ### Exam Strategy & Shortcut Once you have the total $5.72$ lakhs, recognize that $5.72$ divided by $3$ is slightly less than $2$ ($1.9$ something). $5.72 / 3 = 1.9066...$ in lakhs. Therefore, the answer must be in the range of $190,000$. Looking at the options, $190666 \frac{2}{3}$ is the only sensible choice. You don't need to carry out the division to the very last decimal point if you check the magnitude. ### Common Pitfall A standard trap here is failing to convert the decimal value in lakhs ($5.72/3 = 1.9066$) into the full numerical value. This oversight leads to choosing distractor options like (a) $1907 \frac{2}{3}$ due to missing the zeroes multiplier. ### Final Answer Therefore, the correct answer is **$190666 \frac{2}{3}$**.