Sum and product — Mathematical Reasoning Aptitude Question
Sum and product: Two numbers have a sum of 15 and a product of 56. What is the difference between them? Answer and worked solution on CodeKairo.
- Topic: Mathematical Reasoning
- Section: Logical Reasoning
- Difficulty: Medium
- Time target: 75 seconds
Question
Two numbers have a sum of 15 and a product of 56. What is the difference between them?
Options
- 1
- 3
- 5
- 7
Show the answer and the worked solution
Correct answer: A. 1
Worked solution
- Factor pairs of 56: (1, 56), (2, 28), (4, 14), (7, 8).
- Only 7 and 8 add to 15.
- Their difference is 1.
Answer: 1.
The idea
List factor pairs rather than solving a quadratic. Algebraically, (a − b)² = (a + b)² − 4ab = 225 − 224 = 1, giving the same answer.
Shortcut. Back-substitute: a difference of 1 with a sum of 15 means 7 and 8, and 7 × 8 = 56 checks at once.
Common trap. "7" — finding the pair 7 and 8 and reporting the smaller number instead of their difference.