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How many numbers must be selected from the set {1, 2, 3, 4} to guarantee that at least one pair of these numbers add up to 7?
- a)14
- b)5
- c)9
- d)24
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
How many numbers must be selected from the set {1, 2, 3, 4} to guarant...
With 2 elements pairs which give sum as 7 = {(1,6), (2,5), (3,4), (4,3)}. So choosing 1 element from each group = 4 elements (in worst case 4 elements will be either {1,2,3,4} or {6,5,4,3}). Now using pigeonhole principle = we need to choose 1 more element so that sum will definitely be 7. So Number of elements must be 4 + 1 = 5.
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How many numbers must be selected from the set {1, 2, 3, 4} to guarant...
Problem: How many numbers must be selected from the set {1, 2, 3, 4} to guarantee that at least one pair of these numbers add up to 7?
Solution:
To find the minimum number of selections required to guarantee that at least one pair adds up to 7, we need to consider all possible combinations of numbers from the given set.
Step 1: Consider all possible pairs of numbers from the set {1, 2, 3, 4}.
The possible pairs are:
1 + 6
2 + 5
3 + 4
4 + 3
5 + 2
6 + 1
Step 2: Determine the maximum number of selections needed to guarantee that at least one pair adds up to 7.
From the given set, the highest possible sum of two numbers is 6 + 1 = 7. Therefore, to guarantee that at least one pair adds up to 7, we need to select both numbers 6 and 1.
Step 3: Calculate the number of selections required.
Since we need to select both 6 and 1, the minimum number of selections required is 2.
Step 4: Verify the minimum number of selections.
We can verify this by selecting any two numbers from the set. Let's consider the selection of 2 and 3. The sum of these two numbers is 2 + 3 = 5, which is less than 7. Therefore, we need to select at least one more number to guarantee that at least one pair adds up to 7.
Conclusion: The minimum number of selections required from the set {1, 2, 3, 4} to guarantee that at least one pair adds up to 7 is 2. Thus, the correct answer is option 'B' (5).
Solution:
To find the minimum number of selections required to guarantee that at least one pair adds up to 7, we need to consider all possible combinations of numbers from the given set.
Step 1: Consider all possible pairs of numbers from the set {1, 2, 3, 4}.
The possible pairs are:
1 + 6
2 + 5
3 + 4
4 + 3
5 + 2
6 + 1
Step 2: Determine the maximum number of selections needed to guarantee that at least one pair adds up to 7.
From the given set, the highest possible sum of two numbers is 6 + 1 = 7. Therefore, to guarantee that at least one pair adds up to 7, we need to select both numbers 6 and 1.
Step 3: Calculate the number of selections required.
Since we need to select both 6 and 1, the minimum number of selections required is 2.
Step 4: Verify the minimum number of selections.
We can verify this by selecting any two numbers from the set. Let's consider the selection of 2 and 3. The sum of these two numbers is 2 + 3 = 5, which is less than 7. Therefore, we need to select at least one more number to guarantee that at least one pair adds up to 7.
Conclusion: The minimum number of selections required from the set {1, 2, 3, 4} to guarantee that at least one pair adds up to 7 is 2. Thus, the correct answer is option 'B' (5).
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How many numbers must be selected from the set {1, 2, 3, 4} to guarantee that at least one pair of these numbers add up to 7?a)14b)5c)9d)24Correct answer is option 'B'. Can you explain this answer?
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