Multiple choice

If r is the remainder when each of 4749, 5601 and 7092 is divided by the greatest possible number d (> 1), then the value of (d + r) will be:

  1. 276

  2. 271

  3. 298

  4. 282

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A Correct answer
AI explanation

To find the greatest possible number that leaves the same remainder, we use the Euclidean algorithm method of finding the highest common factor of the differences between the numbers. The differences are 5601 minus 4749 equals 852, 7092 minus 5601 equals 1491, and 7092 minus 4749 equals 2343. The highest common factor of 852, 1491, and 2343 is 213, which means d equals 213. Dividing 4749 by 213 gives a quotient of 22 and a remainder of 63, meaning r is 63, and adding d plus r gives 213 plus 63 equals 276.