Multiple choice

Suppose x is the largest number by which 152, 277 and 427 are divided, then in each case the remainder y is obtained. Find the value of (x - y)?

  1. 21

  2. 23

  3. 27

  4. 29

  5. None of these
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B Correct answer
Explanation

If x gives the same remainder y for all three numbers, then x must divide the differences. 277 - 152 = 125, 427 - 277 = 150. GCD(125, 150) = 25. Testing: 152 = 25×6 + 2, 277 = 25×11 + 2, 427 = 25×17 + 2. So x = 25, y = 2. Therefore x - y = 23.

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