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1. What topics are being tested here? (A) Evenly spaced sets and (B) Statistics

2. What do I know about evenly spaced sets?

(A) average = ( first term + last term ) / 2 = (39+13)/2 = 26 (B) # of terms in the set = [last term - first term)/multiple (which is 2) + 1 = (39-13)/2 + 1 = 14 terms

As such

Sum = 14 * 26 = 364

Answer (B)
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Far better is it to dare mighty things, to win glorious triumphs, even though checkered by failure... than to rank with those poor spirits who neither enjoy nor suffer much, because they live in a gray twilight that knows not victory nor defeat. - T. Roosevelt

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.

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