John ranked 16 th from the bottom and 29 th from the top in his class. How many students are there in his class?

Question

John ranked 16 th from the bottom and 29 th from the top in his class. How many students are there in his class?

1. A. 43
2. B. 41
3. C. 44 (Correct answer)
4. D. 42

Correct Answer

Option C — 44

Detailed Solution & Explanation

The correct answer is 44.

Key Points

• When one person's rank is given from both ends, that person is counted twice, so the total is:
  • $\text{Total} = (\text{rank from top}) + (\text{rank from bottom}) - 1$
• $= 29 + 16 - 1 = \textbf{44}$
• The subtraction of 1 removes the double count of John himself.

Additional Information

• The distractor 43 is what you get by adding without subtracting, and 45 by subtracting from the wrong side — both are placed to catch a misremembered formula.
• The companion formula, for when the total is known and one rank is asked for: $\text{rank from bottom} = \text{Total} - \text{rank from top} + 1$. Here $44 - 29 + 1 = 16$ ✓, which is a quick way to verify.
• A sanity check by counting: 28 students rank above John, 15 below, plus John himself gives $28 + 15 + 1 = 44$.
• Where a question gives ranks for two different people, the arithmetic changes entirely, since neither is double-counted in the same way — read carefully which case applies.