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i dont understand the purpose of the first statement portion of the question. how is that relevant to what the question is asking?

The purpose of the first sentence is two fold; 1) save you time adding consecutive odd integers 2) test quantitative reasoning. That being said, it is not necessary to solve the problem, but it will save you a minute.

Here is how it breaks down: The sum of first N consecutive odd integers is N^2. There are 20 consecutive odd integers from 0-39. Therefore, The sum of the first 20 consecutive odd integers is 20^2 Expressable as, The sum of 1+2...39 = 400 or 20^2 = 400

What is the sum of all odd integers between 13 and 39 inclusive? What is the sum of 13+14+15...39? Since 400 = [1+2...11] + [13+15...39] We can reason that 364 = [6^2] - [20^2]

The sum of first \(N\) consecutive odd integers is \(N^2\) . What is the sum of all odd integers between 13 and 39, inclusive?

A. 351 B. 364 C. 410 D. 424 E. 450

The sum of all odd integers between 13 and 39, inclusive equals to the sum of all integers from 1 to 39, inclusiveminusthe sum of all integers from 1 to 11, inclusive.

Since there are 20 odd integers from 1 to 39, inclusive then the sum of all integers from 1 to 39, inclusive is \(20^2\); Since there are 6 odd integers from 1 to 11, inclusive then the sum of all integers from 1 to 11, inclusive is \(6^2\);

The sum of first \(N\) consecutive odd integers is \(N^2\) . What is the sum of all odd integers between 13 and 39, inclusive?

A. 351 B. 364 C. 410 D. 424 E. 450

The sum of all odd integers between 13 and 39, inclusive equals to the sum of all integers from 1 to 39, inclusiveminusthe sum of all integers from 1 to 11, inclusive.

Since there are 20 odd integers from 1 to 39, inclusive then the sum of all integers from 1 to 39, inclusive is \(20^2\); Since there are 6 odd integers from 1 to 11, inclusive then the sum of all integers from 1 to 11, inclusive is \(6^2\);

So, the required sum is \(20^2-6^2=364\).

Answer: B.

"The sum of all odd integers between 13 and 39, inclusive equals to the sum of all integers from 1 to 39, inclusive minus the sum of all integers from 1 to 11, inclusive."

Should be:

"The sum of all odd integers between 13 and 39, inclusive equals to the sum of all odd integers from 1 to 39, inclusive minus the sum of all odd integers from 1 to 11, inclusive."

The explanation in the problem M20-31 from GMAT Club Tests is most likely copied from Bunuel's explanation and presents the same problem.

Thank you. Typo edited in the tests.
_________________

A=(13+15+...+39) = (1+3+...+39) - (1+3+...+11) Among 2 sums on the right side, the 1st sum has (39-1)/2+1=20 elements -> the 1st sum = 20^2=400 The 2nd has (11-1)/2+1=6 elements -> 6^2=36 => A= 400-36=364