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The average of x and y is 4 and both x and y are positive integers. How many pairs of (x, y) satisfy this condition?
- a)3
- b)4
- c)5
- d)7
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
The average of x and y is 4 and both x and y are positive integers. Ho...
Here, total sum of x + y should be equal to 8 and for that, the pairs of x and y are (1, 7), (2, 6), (3, 5), (4, 4), (7, 1), (6, 2) and (5, 3).
Hence, there are total 7 pairs.
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The average of x and y is 4 and both x and y are positive integers. Ho...
To find the number of pairs of positive integers (x, y) that satisfy the given condition, we can start by listing out all the possible pairs of positive integers and checking which ones have an average of 4.
Let's consider all possible values for x and y from 1 to 10.
1. For x = 1, the possible values for y are 3, 4, 5, 6, 7, 8, 9, and 10. None of these pairs have an average of 4.
2. For x = 2, the possible values for y are 2, 3, 4, 5, 6, 7, 8, 9, and 10. The pairs (2, 6), (2, 8), and (2, 10) have an average of 4.
3. For x = 3, the possible values for y are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. The pairs (3, 5) and (3, 7) have an average of 4.
4. For x = 4, the possible values for y are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. The pairs (4, 4) and (4, 6) have an average of 4.
5. For x = 5, the possible values for y are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. The pairs (5, 3) and (5, 5) have an average of 4.
6. For x = 6, the possible values for y are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. The pairs (6, 2) and (6, 4) have an average of 4.
7. For x = 7, the possible values for y are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. The pair (7, 1) has an average of 4.
8. For x = 8, the possible values for y are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. None of these pairs have an average of 4.
9. For x = 9, the possible values for y are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. None of these pairs have an average of 4.
10. For x = 10, the possible values for y are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. None of these pairs have an average of 4.
From the above analysis, we can see that there are a total of 7 pairs of positive integers (x,
Let's consider all possible values for x and y from 1 to 10.
1. For x = 1, the possible values for y are 3, 4, 5, 6, 7, 8, 9, and 10. None of these pairs have an average of 4.
2. For x = 2, the possible values for y are 2, 3, 4, 5, 6, 7, 8, 9, and 10. The pairs (2, 6), (2, 8), and (2, 10) have an average of 4.
3. For x = 3, the possible values for y are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. The pairs (3, 5) and (3, 7) have an average of 4.
4. For x = 4, the possible values for y are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. The pairs (4, 4) and (4, 6) have an average of 4.
5. For x = 5, the possible values for y are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. The pairs (5, 3) and (5, 5) have an average of 4.
6. For x = 6, the possible values for y are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. The pairs (6, 2) and (6, 4) have an average of 4.
7. For x = 7, the possible values for y are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. The pair (7, 1) has an average of 4.
8. For x = 8, the possible values for y are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. None of these pairs have an average of 4.
9. For x = 9, the possible values for y are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. None of these pairs have an average of 4.
10. For x = 10, the possible values for y are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. None of these pairs have an average of 4.
From the above analysis, we can see that there are a total of 7 pairs of positive integers (x,
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