Multiple choice

For any integer y, HCF (25y + 10, 35y + 30) is equal to

  1. 5

  2. 6

  3. 7

  4. 9

  5. 11
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A Correct answer
AI explanation

Using the Euclidean algorithm, we first find the difference between the multiples: (35y + 30) - (25y + 10) = 10y + 20. We then find the GCD of 25y + 10 and 10y + 20, which equals the GCD of 10y + 20 and 5y - 10. Multiplying 5y - 10 by 2 gives 10y - 20, and the difference between (10y + 20) and (10y - 20) is 40. The HCF must be a factor of 40, and testing y = 0 shows the HCF of 10 and 30 is 5. The result is 5.

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