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Find all pairs of consecutive even positive integers, both of which are larger than 5, such that their sum is less than 23.
- a)(4,6),(6,8),(8,10)
- b)(6,8) ,(8,10) ,(10,12)
- c)(3,5), (5,7),(7,9)
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Find all pairs of consecutive even positive integers, both of which ar...
Explanation:
To find the pairs of consecutive even positive integers whose sum is less than 23, we can start by listing the consecutive even positive integers greater than 5.
Consecutive even positive integers greater than 5:
6, 8, 10, 12, 14, 16, 18, 20, 22, ...
Now, we need to find the pairs whose sum is less than 23.
Pairs:
- (6, 8): 6 + 8 = 14
- (8, 10): 8 + 10 = 18
- (10, 12): 10 + 12 = 22
- (12, 14): 12 + 14 = 26
- (14, 16): 14 + 16 = 30
- (16, 18): 16 + 18 = 34
- (18, 20): 18 + 20 = 38
- (20, 22): 20 + 22 = 42
Explanation of options:
a) (4, 6), (6, 8), (8, 10): The sum of the pair (4, 6) is 10, which is less than 23. However, the pair (8, 10) has a sum of 18, which is also less than 23. Therefore, option a) is incorrect.
b) (6, 8), (8, 10), (10, 12): The sum of all pairs in option b) is less than 23. Therefore, option b) is correct.
c) (3, 5), (5, 7), (7, 9): The pair (3, 5) has a sum of 8, which is less than 23. However, the pair (7, 9) has a sum of 16, which is also less than 23. Therefore, option c) is incorrect.
d) None of these: This option is incorrect since option b) is correct.
Conclusion:
The correct answer is option b) (6, 8), (8, 10), (10, 12).
To find the pairs of consecutive even positive integers whose sum is less than 23, we can start by listing the consecutive even positive integers greater than 5.
Consecutive even positive integers greater than 5:
6, 8, 10, 12, 14, 16, 18, 20, 22, ...
Now, we need to find the pairs whose sum is less than 23.
Pairs:
- (6, 8): 6 + 8 = 14
- (8, 10): 8 + 10 = 18
- (10, 12): 10 + 12 = 22
- (12, 14): 12 + 14 = 26
- (14, 16): 14 + 16 = 30
- (16, 18): 16 + 18 = 34
- (18, 20): 18 + 20 = 38
- (20, 22): 20 + 22 = 42
Explanation of options:
a) (4, 6), (6, 8), (8, 10): The sum of the pair (4, 6) is 10, which is less than 23. However, the pair (8, 10) has a sum of 18, which is also less than 23. Therefore, option a) is incorrect.
b) (6, 8), (8, 10), (10, 12): The sum of all pairs in option b) is less than 23. Therefore, option b) is correct.
c) (3, 5), (5, 7), (7, 9): The pair (3, 5) has a sum of 8, which is less than 23. However, the pair (7, 9) has a sum of 16, which is also less than 23. Therefore, option c) is incorrect.
d) None of these: This option is incorrect since option b) is correct.
Conclusion:
The correct answer is option b) (6, 8), (8, 10), (10, 12).
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Find all pairs of consecutive even positive integers, both of which are larger than 5, such that their sum is less than 23.a)(4,6),(6,8),(8,10)b)(6,8) ,(8,10) ,(10,12)c)(3,5), (5,7),(7,9)d)none of theseCorrect answer is option 'B'. Can you explain this answer?
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