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18 Aug 2025, 10:40
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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Question Stats:
100% (00:22) correct
0% (00:00) wrong based on 2 sessions
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The sum of the first 100 positive integers is how much greater than the sum of the first 80 positive integers?
A. 905
B. 1,800
C. 1,805
D. 1,810
E. 1,820
A. 905
B. 1,800
C. 1,805
D. 1,810
E. 1,820
18 Aug 2025, 19:43
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The sum of the first 100 positive integers is how much greater than the sum of the first 80 positive integers?
Sum of First 100 positive integers = 1+2+3+4+5.........+100
Sum of First 80 positive integers = 1+2+3+4+5+6........+80
Difference = (1+2+3+4.....+100)-(1+2+3+4+5+...........+80)
=(81+82+83+84+..........+100)= (n/2)*(first term+last term) = (20/2)*(81+100)=1,810
D
Sum of First 100 positive integers = 1+2+3+4+5.........+100
Sum of First 80 positive integers = 1+2+3+4+5+6........+80
Difference = (1+2+3+4.....+100)-(1+2+3+4+5+...........+80)
=(81+82+83+84+..........+100)= (n/2)*(first term+last term) = (20/2)*(81+100)=1,810
D
Updated on: 30 Aug 2025, 03:48
Originally posted by Sajjad1994 on 30 Aug 2025, 03:47.
Last edited by Sajjad1994 on 30 Aug 2025, 03:48, edited 1 time in total.
Last edited by Sajjad1994 on 30 Aug 2025, 03:48, edited 1 time in total.
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Official Explanation
The sum of the first 80 positive integers means 1 + 2 + 3 ... + 79 + 80. The sum of the first 100 positive integers is 1 + 2 + 3 ... + 79 + 80 + 81 ... 100. There is much duplication on the two lists, and the second exceeds the first exactly by the sum 81 + 82 + 83 ... + 100. One way to complete the problem would be to add those 20 numbers on your calculator to obtain 1,810, (D).
Since this risks a typing error, it is helpful to know how to quickly add numbers in an arithmetic series, one in which all terms are separated by a constant difference, such as 5 + 8 + 11 + 14 + 17, or 81 + 82 + 83 ... + 100. Simply find the typical term by averaging the first and last terms, and multiply this by the number of terms. Here, answer (D).
Answer: D
The sum of the first 80 positive integers means 1 + 2 + 3 ... + 79 + 80. The sum of the first 100 positive integers is 1 + 2 + 3 ... + 79 + 80 + 81 ... 100. There is much duplication on the two lists, and the second exceeds the first exactly by the sum 81 + 82 + 83 ... + 100. One way to complete the problem would be to add those 20 numbers on your calculator to obtain 1,810, (D).
Since this risks a typing error, it is helpful to know how to quickly add numbers in an arithmetic series, one in which all terms are separated by a constant difference, such as 5 + 8 + 11 + 14 + 17, or 81 + 82 + 83 ... + 100. Simply find the typical term by averaging the first and last terms, and multiply this by the number of terms. Here, answer (D).
Answer: D
