Sum of even numbers

Concept: Sum of an arithmetic progression.

The GMAT Math practice question given below is a sequences and series question. Concept: computing sums of two series of even numbers.

Question: 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?

  1. 2500
  2. 5050
  3. 11325
  4. 6275
  5. 2550

Explanatory Answer

Video explanation coming soon.

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.

So sum of the differences of all the terms is (100 + 100 + 100 + ....) = 25 * 100 = 2500.

Choice A is the correct answer.

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