Product 48, difference 2 — Aptitude Question
Product 48, difference 2: The product of two sisters' ages is 48 and their difference is 2. Answer and worked solution on CodeKairo.
- Topic: Problems on Ages
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 50 seconds
Question
The product of two sisters' ages is 48 and their difference is 2. What is the sum of their ages?
Options
- 12
- 14
- 16
- 20
Show the answer and the worked solution
Correct answer: B. 14
Worked solution
- Factor pairs of 48: (1, 48), (2, 24), (3, 16), (4, 12), (6, 8).
- The pair differing by 2 is 6 and 8.
- Sum = 14.
Answer: 14.
The idea
For small products, list factor pairs instead of solving a quadratic. Algebraically, (a + b)² = (a − b)² + 4ab = 4 + 192 = 196, so a + b = 14.
Shortcut. Two numbers 2 apart multiply to one less than the square of their mean: 48 + 1 = 49 = 7², so the ages are 6 and 8 and the sum is 2 × 7 = 14.
Common trap. 16 comes from grabbing the familiar factor pair 4 × 12 without checking the difference, which is 8, not 2.