Difficulty: Easy
Correct Answer: 75
Explanation:
Introduction:
This question examines your understanding of the basic division algorithm and how quotient, remainder, dividend, and divisor are related. It is a direct application of a simple formula that is fundamental in arithmetic and number theory.
Given Data / Assumptions:
Concept / Approach:
The division algorithm states that: Dividend = Divisor × Quotient + Remainder. Using this formula and the given values, we can set up an equation in D and solve for the divisor directly. Because the numbers are small, this is straightforward and does not require trial and error.
Step-by-Step Solution:
Use the division algorithm: 4150 = D × 55 + 25. Subtract the remainder from both sides: 4150 − 25 = D × 55. Compute 4150 − 25: 4125 = D × 55. Now solve for D: D = 4125 / 55. Compute 55 × 75 to check: 55 × 70 = 3850 and 55 × 5 = 275, total 3850 + 275 = 4125. Therefore, 4125 / 55 = 75. So the divisor D is 75.
Verification / Alternative check:
Verify by performing the division directly: 4150 ÷ 75 = 55 remainder 25. 75 × 55 = 4125, and 4150 − 4125 = 25. This matches the given quotient and remainder exactly, confirming D = 75.
Why Other Options Are Wrong:
If D = 68, 65, or 70, then D × 55 + 25 would not equal 4150. For example, 70 × 55 + 25 = 3850 + 25 = 3875, which is less than 4150. Similarly, using 65 or 68 leads to incorrect dividends that do not match 4150, so they cannot be the correct divisor.
Common Pitfalls:
Some students attempt to divide 4150 by each option and then check the remainder manually, which is slower and more error prone than using the division formula directly. Others forget to subtract the remainder before dividing, or mistakenly divide by the quotient. Always start from the standard equation: Dividend = Divisor × Quotient + Remainder.
Final Answer:
The required divisor in this division problem is 75.
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