A three-digit integer X divides both 34041 and 32506, leaving the same…
2024
A three-digit integer X divides both 34041 and 32506, leaving the same remainder in each case. Find the value of X.
Answer: D. 307 — Concept: If an integer divides two numbers and leaves the same remainder in each case, it must divide their difference exactly — the remainder cancels out…
- A.
125
- B.
128
- C.
523
- D.
307
Attempted by 3 students.
Show answer & explanation
Correct answer: D
Concept: If an integer divides two numbers and leaves the same remainder in each case, it must divide their difference exactly — the remainder cancels out when one number is subtracted from the other.
Difference = 34041 − 32506 = 1535.
Factorize 1535: 1535 = 5 × 307 (307 is prime).
Divisors of 1535 are 1, 5, 307 and 1535.
Since X must be a three-digit integer, the only divisor that fits is 307.
Cross-check: 34041 ÷ 307 = 110 remainder 271, and 32506 ÷ 307 = 105 remainder 271 — the same remainder in both, confirming X = 307.