For any sequence of \(n\) consecutive positive integers,

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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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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.
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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

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