AMC 8 Daily Practice Round 6

Complete problem set with solutions and individual problem pages

Problem 15 Easy

For two natural numbers a and b, their least common multiple (LCM) minus their greatest common divisor (GCD) is defined as a \pm b,  a \pm b = [a, b] - (a, b). What is the value of  125 \pm 25?

  • A.

    0

  • B.

    25

  • C.

    50

  • D.

    100

  • E.

    125

Answer:D

1. Compute the GCD of 125 and 25:      (125, 25) = 25

2. Compute the LCM of 125 and 25:      [125, 25] = 125

3. Subtract the GCD from the LCM:      125 \pm 25 = [125, 25] - (125, 25) = 125 - 25 = 100

Final Answer:  \boxed{100}

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