Multiple choice

When 1062, 1134 and 1182 are divided by the greatest number x, the remainder in each case is y. What is the value of (x - y)?

  1. 17

  2. 18

  3. 16

  4. 19

  5. 20
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B Correct answer
Explanation

x = HCF(1134-1062, 1182-1134, 1182-1062) = HCF(72, 48, 120) = 24. Remainder y = 1062 mod 24 = 6. x - y = 24 - 6 = 18.

AI explanation

To find the greatest number that leaves the same remainder, we calculate the highest common factor of the differences between the numbers. The differences are 1134 minus 1062 equals 72, and 1182 minus 1134 equals 48. The highest common factor of 72 and 48 is 24, so the greatest number x is 24. Dividing 1062 by 24 gives a quotient of 44 with a remainder of 6, making y equal to 6. Subtracting y from x gives 24 minus 6 equals 18, so the result is 18.

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