AMC 8 Daily Practice Round 7

Complete problem set with solutions and individual problem pages

Problem 17 Easy

The following is a plane development diagram of a cube. If the values on the two opposite faces of the cube are equal, what is the value of a - b \times c?

  • A.

    3

  • B.

    4

  • C.

    5

  • D.

    8

  • E.

    10

Answer:C

Through observation, we find three pairs of opposite faces as shown in the figure.

Since the values on opposite faces are equal, we have the following equations:

3a + 2 = 17

7b - 4 = 10

a + 3b - 2c = 11

Solving these equations: -

From 3a + 2 = 17, we get 3a = 15, so a = 5.

From 7b - 4 = 10, we get 7b = 14, so b = 2. -

Substituting a = 5 and b = 2 into a + 3b - 2c = 11, we have 5 + 3 \times 2 - 2c = 11, which simplifies to 11 - 2c = 11, so c = 0.

Finally, we calculate a - b \times c: a - b \times c = 5 - 2 \times 0 = 5

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