Question

When Rafael entered the class, there were already 10 students in the class. 5 students entered the class between Roger and Rafael. Total 10 students entered after Roger. Exactly how many students are in the class finally?

• A. 15
• B. 25
• C. 27
• D. Cannot be decided

Hint:

Try both orders, Roger before Rafael and Rafael before Roger, and check if they give the same final count.

Answer 1

The Correct Option is D

Step 1: Notice that the order of Roger and Rafael's entry is not given.
The passage never states whether Roger entered the class before Rafael or after Rafael. This missing detail changes the entire calculation, so both possibilities must be tested separately.
Step 2: Case 1, assume Roger entered before Rafael.
Here the 5 students who entered between Roger and Rafael all entered after Roger and before Rafael. When Rafael entered, 10 students were already present, and this count does not include Rafael himself. So the students before Roger, plus Roger, plus the 5 in between, must total 10, which gives 4 students before Roger since 4 plus 1 plus 5 equals 10. We are also told 10 students entered after Roger in total. The 5 in between plus Rafael already make 6 of those 10, so 4 more students enter after Rafael. Adding everyone up gives 4 before Roger, plus 1 Roger, plus 5 in between, plus 1 Rafael, plus 4 after Rafael, which totals 15 students.
Step 3: Case 2, assume Rafael entered before Roger.
Here, when Rafael entered, 10 students were already present, all of them before Rafael. After Rafael, the 5 students who entered between Roger and Rafael enter next, followed by Roger. So up to and including Roger, the room has 10 plus 1 Rafael plus 5 in between plus 1 Roger, which is 17 students. Since 10 students enter after Roger in total, the final count becomes 17 plus 10, which is 27 students.
Step 4: Compare the two cases.
Case 1 gives a final total of 15 students, while Case 2 gives a final total of 27 students. Both scenarios satisfy every clue in the passage exactly, yet they produce two different totals.
Step 5: Conclude that the answer cannot be pinned down.
Because the passage never says whether Roger or Rafael entered first, both 15 and 27 remain valid outcomes. Since the given data supports more than one final answer, the correct choice is Cannot be decided, not any single fixed number.