The sum of the first 100 positive integers is how much greater than th

Question

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

VerbalKnight · Answer

Sum of first n consecutive numbers =  \frac{n*(n+1)}{2}

Sum of first 100 consecutive numbers  = 50*101 = 5050

Sum of first 80 consecutive numbers  = 40*81 = 3240

Difference  = 5040 - 3240 = 1810  ----  Option D

SHoylandBPrep · Answer

You basically need to find the sum of the integers from 81 to 100. Since these are consecutive integers, the average of the first and last numbers is equal to the mean of the numbers.

→ Average =  \frac{81+100}{2}  =  \frac{181}{2}  = 90.5

Calculate the number of numbers.

→ Number of numbers = (100 – 81) + 1 = 20

Finally, multiply these to find the sum.

→ Sum = Average × Number of numbers

→ Sum = 90.5 × 20 = 1810

ScottTargetTestPrep · Answer

Solution:
 
The difference between the the sum of the first 100 positive integers and the sum of the first 80 positive integers is the sum of the integers from 81 to 100, inclusive, i.e., 81 + 82 + … + 99 + 100. We can use the following formula to calculate the sum:

Sum = Average x quantity

Sum = (81 + 100)/2 x 20 = 181 x 10 = 1,810

Answer: D

vigneshvrk · Answer

Sum of consecutive integers is n(a1+an)/2
1 to 100 = 100(101)/2 = 5050
1 to 80 = 80(81)/2 = 3240

5050 - 3240 = 1,810

Answer is   D

EgmatQuantExpert · Answer

Approach 1

Given

To Find

• The sum of the first 100 positive integers is how much greater than the sum of the first 80 positive integers

Approach and Working Out

• Sum of 100 integers = 100 × 101/2 = 5050

• Sum of 80 integers = 80 × 81/2 = 3240

• Answer = 5050 – 3240 = 1810

Correct Answer: Option D

EgmatQuantExpert · Answer

Approach 2

Given

To Find

• The sum of the first 100 positive integers is how much greater than the sum of the first 80 positive integers

Approach and Working Out

• We need to find the sum from 81 to 100
• First term is 81 and the last term is 100. The sum is 181.
• 2nd term is 82 and the 2nd last term is 99. The sum is 181.
• We can form 10 such pairs and hence the sum = 181 * 10 = 1810

Correct Answer: Option D

The sum of the first 100 positive integers is how much greater than th

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The sum of the first 100 positive integers is how much greater than th

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