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Find the pairs of consecutive even positive integers both of which are smaller than 10 and their sum of more than 11
- a)(4, 8)
- b)(6, 8)
- c)(6, 8) and (4, 8)
- d)(6, 4)(4, 2)
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Find the pairs of consecutive even positive integers both of which are...
Let x be the smaller of the two consecutive even positive integers .
Then the other integer is x+2.
Since both the integers are smaller than 10,x<10 ....(1)
Also the sum of the two integers is more than 11.
x+(x+2)>11
⇒ 2x+2>11
⇒ 2x>11−2
⇒ 2x>9
⇒ x>9/2
⇒ x>4.5....(2)
From (1) and (2) we obtain 4.5>x>11
Since x is an even number, x can take the values 6,8 and 10.
Thus the required possible pairs are (6,8).
Then the other integer is x+2.
Since both the integers are smaller than 10,x<10 ....(1)
Also the sum of the two integers is more than 11.
x+(x+2)>11
⇒ 2x+2>11
⇒ 2x>11−2
⇒ 2x>9
⇒ x>9/2
⇒ x>4.5....(2)
From (1) and (2) we obtain 4.5>x>11
Since x is an even number, x can take the values 6,8 and 10.
Thus the required possible pairs are (6,8).
Most Upvoted Answer
Find the pairs of consecutive even positive integers both of which are...
Understanding Consecutive Even Positive Integers
To find pairs of consecutive even positive integers that are both smaller than 10 and have a sum greater than 11, we first identify the even positive integers less than 10.
Even Positive Integers Less Than 10
- The even positive integers are: 2, 4, 6, 8.
Identifying Consecutive Pairs
- The possible pairs of consecutive even integers from the list are:
- (2, 4)
- (4, 6)
- (6, 8)
Calculating Sums
- Now, we will calculate the sum of each pair:
- (2, 4): 2 + 4 = 6 (not greater than 11)
- (4, 6): 4 + 6 = 10 (not greater than 11)
- (6, 8): 6 + 8 = 14 (greater than 11)
Conclusion
Among the pairs we examined, only (6, 8) meets the criteria of being both smaller than 10 and having a sum greater than 11.
Thus, the correct answer is option 'B', which consists of the pair (6, 8). This pair is the only consecutive even positive integers under 10 that add up to more than 11.
Final Summary
- Valid pairs:
- (2, 4): Sum = 6
- (4, 6): Sum = 10
- (6, 8): Sum = 14 (Valid Pair)
Only option 'B' is correct as it meets all the specified conditions.
To find pairs of consecutive even positive integers that are both smaller than 10 and have a sum greater than 11, we first identify the even positive integers less than 10.
Even Positive Integers Less Than 10
- The even positive integers are: 2, 4, 6, 8.
Identifying Consecutive Pairs
- The possible pairs of consecutive even integers from the list are:
- (2, 4)
- (4, 6)
- (6, 8)
Calculating Sums
- Now, we will calculate the sum of each pair:
- (2, 4): 2 + 4 = 6 (not greater than 11)
- (4, 6): 4 + 6 = 10 (not greater than 11)
- (6, 8): 6 + 8 = 14 (greater than 11)
Conclusion
Among the pairs we examined, only (6, 8) meets the criteria of being both smaller than 10 and having a sum greater than 11.
Thus, the correct answer is option 'B', which consists of the pair (6, 8). This pair is the only consecutive even positive integers under 10 that add up to more than 11.
Final Summary
- Valid pairs:
- (2, 4): Sum = 6
- (4, 6): Sum = 10
- (6, 8): Sum = 14 (Valid Pair)
Only option 'B' is correct as it meets all the specified conditions.
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Find the pairs of consecutive even positive integers both of which are smaller than 10 and their sum of more than 11a)(4, 8)b)(6, 8)c)(6, 8) and (4, 8)d)(6, 4)(4, 2)Correct answer is option 'B'. Can you explain this answer?
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