BTGmoderatorDC wrote:The sum of the first 100 positive integers is 5,050. What is the sum of the first 200 positive integers?
A. 10,000
B. 10,200
C. 15,050
D. 20,050
E. 20,100
OA E
Source: Official Guide
We can use the formula: average x number = sum. To find the average, we add the first and last numbers and divide by 2. Thus, the sum of the first 200 integers is:
(1 + 200)/2 x 200 = 201 x 100 = 20,100
Alternate solution:
SInce the sum of the first 100 positive integers (i.e., 1 to 100) is 5,050 and each of the next 100 positive integers (i.e., 101 to 200) is 100 more than its counterpart in the first 100 integers (101 is 100 more than 1, 102 is 100 more than 2, etc.), then the sum of the integers from 101 to 200 (inclusive) is 100 x 100 = 10,000 more than 5,050, i.e., 15,050. Therefore, the sum of the first 200 positive integers (i.e., 1 to 200) is 5,050 + 15,050 = 20,100.
Answer: E
