For any sequence of $n$ consecutive positive integers,

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AAPL: Moderator; Posts: 2672; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

by AAPL » Tue May 07, 2019 3:36 am

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For any sequence of $n$ consecutive positive integers, $S_e$ denotes the sum of all even integers and $S_o$ denotes the sum of all odd integers. Which of the following must be true?

1. There is at least one such sequence for which $S_e > S_o$
2. There is at least one such sequence for which $S_e = S_o$
3. There is at least one such sequence for which $S_e < S_o$

A. 1 only
B. 2 only
C. 3 only
D. 1 & 2 only
E. 1 & 3 only

OA E

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Source: Beat The GMAT — Problem Solving | Tue May 07, 2019 3:36 am

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Tue May 07, 2019 5:44 am

If you take the sequence 1, 2, the sum of the even integers is 2 and the sum of the odd integers is 1, so $S_e > S_o$ and item 1 can be true.

If you take the sequence 2, 3, the sum of the even integers is 2 and the sum of the odd integers is 3, so $S_e < S_o$, and item 3 can be true.

That leaves only answer E, so we don't need to check item 2.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8178; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Thu May 09, 2019 5:08 pm

AAPL wrote:GMAT Paper Tests

For any sequence of $n$ consecutive positive integers, $S_e$ denotes the sum of all even integers and $S_o$ denotes the sum of all odd integers. Which of the following must be true?

1. There is at least one such sequence for which $S_e > S_o$
2. There is at least one such sequence for which $S_e = S_o$
3. There is at least one such sequence for which $S_e < S_o$

A. 1 only
B. 2 only
C. 3 only
D. 1 & 2 only
E. 1 & 3 only

OA E

If the sequence is {1, 2, 3, 4}, we see that Se = 6 and So = 4, so Se > So.

If the sequence is {2, 3, 4, 5}, we see that Se = 6 and So = 8, so Se < So.

(Note: Since the answer choices don't have a choice that is 1, 2 & 3, we don't have to analyze whether Se = So can be true or not.)

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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