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How many pairs of consecutive odd positive integers, smaller than 18 and having their sum as more than 20, are possible?
- a)3
- b)5
- c)1
- d)2
Correct answer is option 'A'. Can you explain this answer?
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How many pairs of consecutive odd positive integers, smaller than 18 a...
To find the number of pairs of consecutive odd positive integers that are smaller than 18 and have a sum greater than 20, we can follow the steps below:
1. Identify the consecutive odd positive integers: The consecutive odd positive integers start from 1 and increment by 2. So, the consecutive odd positive integers smaller than 18 are: 1, 3, 5, 7, 9, 11, 13, 15, 17.
2. Find the pairs with a sum greater than 20: We need to find pairs of these consecutive odd positive integers whose sum is greater than 20. We can check all possible pairs and count the ones that satisfy this condition.
- Pair 1: 1 + 3 = 4 (sum is not greater than 20)
- Pair 2: 3 + 5 = 8 (sum is not greater than 20)
- Pair 3: 5 + 7 = 12 (sum is not greater than 20)
- Pair 4: 7 + 9 = 16 (sum is not greater than 20)
- Pair 5: 9 + 11 = 20 (sum is not greater than 20)
- Pair 6: 11 + 13 = 24 (sum is greater than 20)
- Pair 7: 13 + 15 = 28 (sum is greater than 20)
- Pair 8: 15 + 17 = 32 (sum is greater than 20)
3. Count the number of pairs: From the above calculations, we can see that there are 3 pairs of consecutive odd positive integers smaller than 18 whose sum is greater than 20.
Therefore, the correct answer is option A) 3.
1. Identify the consecutive odd positive integers: The consecutive odd positive integers start from 1 and increment by 2. So, the consecutive odd positive integers smaller than 18 are: 1, 3, 5, 7, 9, 11, 13, 15, 17.
2. Find the pairs with a sum greater than 20: We need to find pairs of these consecutive odd positive integers whose sum is greater than 20. We can check all possible pairs and count the ones that satisfy this condition.
- Pair 1: 1 + 3 = 4 (sum is not greater than 20)
- Pair 2: 3 + 5 = 8 (sum is not greater than 20)
- Pair 3: 5 + 7 = 12 (sum is not greater than 20)
- Pair 4: 7 + 9 = 16 (sum is not greater than 20)
- Pair 5: 9 + 11 = 20 (sum is not greater than 20)
- Pair 6: 11 + 13 = 24 (sum is greater than 20)
- Pair 7: 13 + 15 = 28 (sum is greater than 20)
- Pair 8: 15 + 17 = 32 (sum is greater than 20)
3. Count the number of pairs: From the above calculations, we can see that there are 3 pairs of consecutive odd positive integers smaller than 18 whose sum is greater than 20.
Therefore, the correct answer is option A) 3.
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How many pairs of consecutive odd positive integers, smaller than 18 and having their sum as more than 20, are possible?a)3b)5c)1d)2Correct answer is option 'A'. Can you explain this answer?
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