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Set A contains all the even numbers between 2 and 50 inclusive. Set B contains all the even numbers between 102 and 150 inclusive. What is the difference between the sum of elements of set B and that of set A?
- a)2500
- b)5050
- c)11325
- d)6275
- e)2550
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Set A contains all the even numbers between 2 and 50 inclusive. Set B ...
SET A: {2, 4, 6, 8,...., 50}. Set of first 25 consecutive positive even numbers.
SET B: {102, 104, 106,....., 150}. Another set of 25 consecutive even numbers starting from 102.
Difference between 1st term of set A and that of set B is 100. Difference between 2nd term of set A and that of set B is 100.
Each term in set B is 100 more than the corresponding term in set A.
Each term in set B is 100 more than the corresponding term in set A.
So sum of the differences of all the terms is (100 + 100 + 100 + ....) = 25 * 100 = 2500.
Choice A is the correct answer.
Most Upvoted Answer
Set A contains all the even numbers between 2 and 50 inclusive. Set B ...
To find the difference between the sum of elements in Set A and Set B, we need to calculate the sum of each set separately and then subtract the sum of Set A from the sum of Set B.
Set A: Even numbers between 2 and 50 inclusive
Set B: Even numbers between 102 and 150 inclusive
Calculating the sum of Set A:
We know that the set contains all even numbers between 2 and 50 inclusive. To find the sum, we can use the formula for the sum of an arithmetic series:
Sum = (first term + last term) * (number of terms) / 2
The first term in Set A is 2, the last term is 50, and the number of terms is (50-2)/2 + 1 = 25. Plugging these values into the formula:
Sum of Set A = (2 + 50) * (25) / 2 = 52 * 25 / 2 = 1300
Calculating the sum of Set B:
Similarly, we can find the sum of Set B using the same formula. The first term in Set B is 102, the last term is 150, and the number of terms is (150-102)/2 + 1 = 25.
Sum of Set B = (102 + 150) * (25) / 2 = 252 * 25 / 2 = 6300
Subtracting the sum of Set A from the sum of Set B:
Difference = Sum of Set B - Sum of Set A = 6300 - 1300 = 5000
Therefore, the difference between the sum of elements in Set B and Set A is 5000. However, none of the given answer choices match this result. Therefore, there may be an error in the answer choices provided.
Set A: Even numbers between 2 and 50 inclusive
Set B: Even numbers between 102 and 150 inclusive
Calculating the sum of Set A:
We know that the set contains all even numbers between 2 and 50 inclusive. To find the sum, we can use the formula for the sum of an arithmetic series:
Sum = (first term + last term) * (number of terms) / 2
The first term in Set A is 2, the last term is 50, and the number of terms is (50-2)/2 + 1 = 25. Plugging these values into the formula:
Sum of Set A = (2 + 50) * (25) / 2 = 52 * 25 / 2 = 1300
Calculating the sum of Set B:
Similarly, we can find the sum of Set B using the same formula. The first term in Set B is 102, the last term is 150, and the number of terms is (150-102)/2 + 1 = 25.
Sum of Set B = (102 + 150) * (25) / 2 = 252 * 25 / 2 = 6300
Subtracting the sum of Set A from the sum of Set B:
Difference = Sum of Set B - Sum of Set A = 6300 - 1300 = 5000
Therefore, the difference between the sum of elements in Set B and Set A is 5000. However, none of the given answer choices match this result. Therefore, there may be an error in the answer choices provided.
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