When a number is divided by 38, the quotient is 70 and the remainder is 12. What is the original number?

Introduction / Context:
This arithmetic question checks your understanding of the division algorithm, which relates dividend, divisor, quotient, and remainder. When a number is divided by a given divisor, you can reconstruct the original number using a simple formula involving the quotient and remainder. This type of question is common in basic number operations and aptitude exams.

Given Data / Assumptions:

• Divisor = 38.
• Quotient = 70.
• Remainder = 12.
• We are asked to find the original number (dividend).

Concept / Approach:
The division algorithm states that for any integers dividend, divisor, quotient and remainder, the relationship is: dividend = divisor * quotient + remainder. We simply substitute the given values into this formula. This gives a direct computation for the original number without trial and error or checking each option individually.

Step-by-Step Solution:

Verification / Alternative check:
To verify, divide 2672 by 38. First, 38 * 70 = 2660, and 2672 - 2660 = 12. So when 2672 is divided by 38, the quotient is indeed 70 and the remainder is 12. This confirms that 2672 is the correct original number and matches the given quotient and remainder exactly.

Why Other Options Are Wrong:

Common Pitfalls:
Common errors include multiplying the divisor by a wrong quotient or miscalculating the product 38 * 70. Some students also mistakenly subtract remainder instead of adding it. Always remember the correct formula: dividend = divisor * quotient + remainder, and perform multiplication carefully to avoid arithmetic slips.

Final Answer:
2672