From the given statements, determine from which statement(s) the exact value of $(x - y)$ can be found, where $x\%$ and $y\%$ represent the percentage of questions attempted by students B and D respectively.

Statements:

I. Student B attempted the highest number of questions and student D attempted the lowest number of questions.

II. If student B attempted more than 200 questions, then student D attempted less than 190 questions.

Choose the correct option:

Question

From the given statements, determine from which statement(s) the exact value of $(x - y)$ can be found, where $x\%$ and $y\%$ represent the percentage of questions attempted by students B and D respectively.

Statements:

I. Student B attempted the highest number of questions and student D attempted the lowest number of questions.

II. If student B attempted more than 200 questions, then student D attempted less than 190 questions.

Choose the correct option:

Accepted Answer

**Solution:**

1. Total questions attempted by all students = 800.

2. Given:
   - A attempted 25% of 800 = $200$ questions.
   - C attempted 24% of 800 = $192$ questions.

3. From statement (I):
   - B attempted the highest number of questions, so B attempted $240$ questions (maximum).
   - Therefore, $x\% = \frac{240}{800} 	imes 100 = 30\%$.
   - Since total percentage must be 100%, $x + y + 25 + 24 = 100$.
   - So, $x + y = 100 - 25 - 24 = 51$.
   - Substituting $x = 30$, we get $y = 51 - 30 = 21$.
   - Hence, $(x - y) = 30 - 21 = 9$.

4. From statement (II):
   - B attempted more than 200 questions, so $x > \frac{200}{800} 	imes 100 = 25\%$.
   - D attempted less than 190 questions, so $y < \frac{190}{800} 	imes 100 = 23.75\%$.
   - Since $x$ and $y$ can take multiple values within these ranges, the exact value of $(x - y)$ cannot be determined.

**Conclusion:** Only statement (I) alone is sufficient to find the exact value of $(x - y)$.

**Answer:** Only (I)

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