If three times the greater of two numbers is divided by the smaller number, the quotient will be 6 and the remainder will be 6. If five times the smaller number is divided by the greater number, the quotient will be 2 and the remainder will be 3. What is the difference between the numbers?
- A. 8
- B. 9 ✓
- C. 10
- D. 12
Correct Answer: B. 9
Explanation
Let the greater be x and smaller be y. We get 3x = 6y + 6 \implies x - 2y = 2 and 5y = 2x + 3. Substituting x = 2y + 2 into the second gives 5y = 2(2y+2) + 3 \implies 5y = 4y + 7 \implies y = 7. Then x = 16. The difference is 16 - 7 = 9.
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