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01 Oct 2024, 10:33
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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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
Indicate all such integers.
A. 8
B. 9
C. 10
D. 12
E. 14
F. 15
G. 16
H. 18
10 Feb 2025, 11:21
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OE
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.
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.
