AMC 8 Daily Practice Round 6

Complete problem set with solutions and individual problem pages

Problem 12 Easy

Consider these two operations: 2 \# 4=2+2.5+3+3.5, 5 \# 3=5+5.5+6. What is the value of  10 \# 5?

  • A.

    10

  • B.

    12

  • C.

    55

  • D.

    50

  • E.

    15

Answer:C

The problem defines a custom operator \# such that:

2 \# 4 = 2 + 2.5 + 3 + 3.5   5 \# 3 = 5 + 5.5 + 6

By observing these examples:

The first number on the left side of = becomes the starting number of the sequence on the right side.

The second number on the left side of = indicates the number of terms in the sequence on the right side.

The sequence forms an arithmetic progression with a common difference of 0.5.

Therefore, for 10 \# 5=10 + 10.5 + 11 + 11.5 + 12 = 55

The value of 10 \# 5 is \boxed{55}

Related Problems
Problem 10 AMC 8 Daily Practice Round 6
Problem 11 AMC 8 Daily Practice Round 6
Problem 13 AMC 8 Daily Practice Round 6
Problem 14 AMC 8 Daily Practice Round 6
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