Mathematics > Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer.

The sum of the positive odd integers less than 50 is subtracted from the sum of the positive even integers less than or equal to 50. What is the resulting difference?

(A) 0

(B) 25

(C) 50

(D) 100

(E) 200 

正确答案>>>

The correct answer is B

Explanation

The sum of the positive odd integers less than 50 is 1 + 3 + 5 + ... + 45 + 47 + 49, and the sum of the positive even integers less than or equal to 50 is 2 + 4 + 6 + ... + 46 + 48 + 50. When the first sum is subtracted from the second, the terms can be regrouped to form (2 minus 1) plus (4 minus 3) + ... + (48 minus 47) + (50 minus 49), which is just 1 + 1 + 1 + ... + 1, where there are 25 ones. Therefore, the correct answer is 25.