The following line graph gives the percentage of the number of candidates who…

Concept: When a combined total is split between two groups in an unspecified proportion, and each group's rate (percentage) is different, the resulting weighted value depends on the actual, unknown split. Unless the individual group sizes (or their ratio) are given, only a range of possible combined values can be found — not one exact number.

Application:

1. From the graph, the percentage of candidates qualified is 60% in 1996 and 50% in 1997.

2. Let the number of candidates who appeared in 1996 be x and in 1997 be y, so x + y = 47400.

3. Total qualified = 0.6x + 0.5y = 0.5(x + y) + 0.1x = 0.5(47400) + 0.1x = 23700 + 0.1x.

4. Since only the sum x + y = 47400 is given (not x itself), the value 23700 + 0.1x cannot be pinned down to one number.

5. Feasible range: at x = 0 (all 47400 appeared in 1997), qualified = 23700. At x = 47400 (all 47400 appeared in 1996), qualified = 28440. So the true total qualified lies somewhere between 23700 and 28440.

Cross-check:

Test each numeric option against this feasible range of 23700 to 28440: 34700, 32100, and 31500 are all greater than 28440, the highest value the total qualified can possibly take. So none of these three numbers can ever be the qualified total, no matter how the 47400 candidates are split between the two years.

Result: Because the exact split between 1996 and 1997 is not given, and every numeric option offered lies outside the range that is actually achievable, the total qualified in the two years together cannot be determined from the data given — the data is inadequate.