AMC 8 Daily Practice Round 4

Complete problem set with solutions and individual problem pages

Problem 1 Easy

Which of the following fractions is the largest?

  • A.

    \frac13

  • B.

    \frac34

  • C.

    \frac57

  • D.

    \frac79

  • E.

    \frac8{11}

Answer:D

\frac 79 > \frac 34 > \frac 8{11}>\frac 57>\frac 13

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Problem 2 Easy

There is a rule that a\triangle b = 2a + b (for example, 3\triangle 2 = 2\times3 + 2=8). If (x\triangle 3)\triangle 5 =27, the value of x is            .

  • A.

    5

  • B.

    4

  • C.

    3

  • D.

    2

  • E.

    1

Answer:B

(x\triangle 3)\triangle 5 = (2x+3)\triangle 5 = 4x + 6 +5 =4x +11 = 27

Thus, x = 4.

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Problem 3 Easy

There are 4 more apples than bananas in a fruit basket. The total number of fruits in the fruit basket is 60. What is the ratio of the number of bananas to that of apples in the fruit basket?

  • A.

    13:15

  • B.

    15:17

  • C.

    7:8

  • D.

    2:3

  • E.

    13:17

Answer:C

Number of apples: (60+4)\div2=32

Number of bananas: 60-32=28

The ratio is 28:32=7:8

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Problem 4 Easy

Fifty people donate money to an organization. Eddie makes the following bar graph based on their contribution. Find the median of money donated by these fifty people.

  • A.

    50

  • B.

    20

  • C.

    32.4

  • D.

    25

  • E.

    30

Answer:E

The median of fifty datas should be the average of the 50\div2 =25th and 26th datas, which is 30 dollars.

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Problem 5 Easy

In the following figure, the side length of each small square is 1 cm. What is the area of the shaded part?

  • A.

    2.5 cm2

  • B.

    3 cm2

  • C.

    3.5 cm2

  • D.

    4 cm2

  • E.

    4.5 cm2

Answer:C

9-\left( 1\times 2\times \frac 12+2\times 2\times \frac{1}{2}+1\times 3\times \frac{1}{2}+1\times 2\times \frac{1}{2} \right)=3.5 cm2

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