AMC 8 Daily Practice Round 5

Complete problem set with solutions and individual problem pages

Problem 1 Easy

A computer can do 7\times {{10}^{9}} operations per second. Then, it can do            operations in 5\times {{10}^{2}} seconds.

  • A.

    35\times {{10}^{10}}

  • B.

    3.5\times {{10}^{11}}

  • C.

    3.5\times {{10}^{12}}

  • D.

    3.5\times {{10}^{19}}

  • E.

    3.5\times {{10}^{18}}

Answer:C

7\times {{10}^{9}}\times 5\times {{10}^{2}}=3.5\times {{10}^{12}}

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Problem 2 Easy

A total of 46 bicycles and tricycles are in the garage. If there are 100 wheels in total, there should be            tricycles in the garage.

  • A.

    8

  • B.

    12

  • C.

    24

  • D.

    38

  • E.

    6

Answer:A

(100-2\times46)\div(3-2)=8

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Problem 3 Easy

There are some odd numbers: 1, 3, 5, 7, \cdots and 39. If you choose one randomly, the probability that you get a prime number is            .

  • A.

    \frac{1}{10}

  • B.

    \frac{3}{5}

  • C.

    \frac{13}{20}

  • D.

    \frac{11}{20}

  • E.

    \frac{7}{20}

Answer:D

There are 11 odd prime numbers among 1 to 39 which are 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, and 37. Thus, the probability is \frac {11}{20}.

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Problem 4 Easy

After removing two adjacent odd numbers from 60 natural numbers 41-100, the average of the remaining numbers is 71. The product of the two numbers removed is            .

  • A.

    3137

  • B.

    3143

  • C.

    3153

  • D.

    3135

  • E.

    3145

Answer:D

(41+100)\times60\div2-58\times71=112

112\div2=56, so the two odd numbers are 55 and 57, which have a product of 3135.

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Problem 5 Easy

Fill the seven odd numbers 1-13 in each circle so that the sum of each three numbers in a line can be 25. Which number should be filled in the central circle?

  • A.

    1

  • B.

    3

  • C.

    7

  • D.

    11

  • E.

    13

Answer:E

(25\times3-1-3-5-7-9-11-13)\div2=13

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