2. 外语
  3. Two different positive integers x and y are selected from the odd integers that are less than 10. If z = x + y and z is less tha

Two different positive integers x and y are selected from the odd integers that are less than 10. If z = x + y and z is less tha

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问题 Two different positive integers x and y are selected from the odd integers that are less than 10. If z = x + y and z is less than 10, which of the following integers could be the sum of x, y, and z ?
Indicate all such integers.
A 8
B 9
C 10
D 12
E 14
F 15
G 16
H 18
选项
答案A，D，G
解析 The only pairs of positive odd integers x and y that are less than 10 and satisfy the condition x + y < 10 are the pair 1 and 3, the pair 1 and 5, the pair 1 and 7, and the pair 3 and 5. Since z = x + y, it follows that the sum of x, y> and z is equal to 2z. The sum for each of the four possible pairs is found as follows.
    1 and 3: z = 4, and the sum of x, y, and z is 2z, or 8.
    1 and 5: z = 6, and the sum of x, y, and z is 12.
    1 and 7: z - 8, and the sum of x, y, and z is 16.
    3 and 5: z = 8, and the sum of x, y, and z is 16.
Thus the only possible values of the sum of x, y, and z are 8, 12, and 16. The correct answer consists of Choices A, D, and G.
This explanation uses the following strategies.
Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation
Strategy 8: Search for a Mathematical Relationship
Strategy 11: Divide into Cases
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