Product 48, difference 2 — Aptitude Question
Product 48, difference 2: The product of the ages of two sisters is 48 and the difference is 2. Answer and worked solution on CodeKairo.
- Topic: Problems on Ages
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 40 seconds
Question
The product of the ages of two sisters is 48 and the difference is 2. What is the sum of their ages?
Options
- 12
- 14
- 16
- 18
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
With small products, list factor pairs instead of solving a quadratic. If you must: (a + b)² = (a − b)² + 4ab = 4 + 192 = 196, so a + b = 14.
Shortcut. With a gap of 2, the mean age m satisfies (m − 1)(m + 1) = m² − 1 = 48, so m = 7 and the sum is 14.
Common trap. 16 — the sum of 4 and 12, another factor pair of 48 grabbed without checking that their difference is 8, not 2.