Problem 6 · 1990 AJHSME
Medium
Fractions, Decimals & Percents
compare-operations
Which of these five numbers is the largest?
Show answer
Answer: D — 13579 ÷ (1/2468).
Show hints
Hint 1 of 2
Every choice starts from the same 13579. So don't compute any of them — just ask which *operation* changes that number the most.
Still stuck? Show hint 2 →
Hint 2 of 2
The trap is dividing by a fraction. Dividing by 1/2468 isn't 'making it smaller' — remember dividing by a fraction less than 1 *flips it over* and multiplies.
Show solution
Approach: compare the effect of each operation, don't compute
- All five choices begin with 13579, so compare what each operation *does*. Adding or subtracting 1/2468 (a tiny bit less than half) barely nudges it; multiplying by 1/2468 shrinks it; '13579.2468' is just a hair over 13579.
- The standout is ÷ (1/2468). Dividing by a fraction means multiplying by its flip: 13579 ÷ (1/2468) = 13579 × 2468 ≈ 33,000,000. That dwarfs everything else.
- So the largest is 13579 ÷ (1/2468).
- *Worth keeping:* dividing by a number smaller than 1 makes things *bigger*. That counterintuitive flip is exactly the trap this problem tests.
Mark:
· log in to save