AMC 8 Daily Practice Round 9

Complete problem set with solutions and individual problem pages

Problem 11 Easy

A sequence of 6 lights (either on or off) is used to represent numbers. The diagram provided shows the representations for the numbers 1 to 5. Based on this pattern, what number does the sequence ●○○●●○ represent?

  • A.

    23

  • B.

    24

  • C.

    25

  • D.

    26

  • E.

    27

Answer:C

The given sequence can be converted into a binary number, where a lit light is represented as 1 and an unlit light as 0.

Thus, the sequence ●○○●●○ corresponds to the binary number: 011001_2

Converting this to decimal:

0 \times 2^5 + 1 \times 2^4 + 1 \times 2^3 + 0 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 = 16 + 8 + 1 = 25

Thus, the number represented by the sequence is 25.

The answer is \text{C}.

Related Problems
Problem 9 AMC 8 Daily Practice Round 9
Problem 10 AMC 8 Daily Practice Round 9
Problem 12 AMC 8 Daily Practice Round 9
Problem 13 AMC 8 Daily Practice Round 9
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