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14 Dec 2023, 07:00
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
34% (02:22) correct
66%
(02:03)
wrong
based on 146
sessions
History
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Time
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Not Attempted Yet
12 Days of Christmas 🎅 GMAT Competition with Lots of Questions & Fun
The sequence of non-zero numbers \(a_1\), \(a_2\), \(a_3\), ... is such that \(a_{n} = \frac{a_{n-2}} {a_{n-1}}\) for all \(n ≥ 3\). Is \(a_9 > 0\)?
(1) \(a_3 < 0\)
(2) \(a_1*a_2 < 0\)
The sequence of non-zero numbers \(a_1\), \(a_2\), \(a_3\), ... is such that \(a_{n} = \frac{a_{n-2}} {a_{n-1}}\) for all \(n ≥ 3\). Is \(a_9 > 0\)?
(1) \(a_3 < 0\)
(2) \(a_1*a_2 < 0\)
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17 Dec 2023, 14:28
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GMAT Club Official Explanation:
The sequence of non-zero numbers \(a_1\), \(a_2\), \(a_3\), ... is such that \(a_{n} = \frac{a_{n-2}} {a_{n-1}}\) for all \(n ≥ 3\). Is \(a_9 > 0\)?
(1) \(a_3 < 0\)
This implies that \(a_1\) and \(a_2\) have different signs: either one is positive and the other is negative, or vice versa. Let's examine both scenarios:
If \(a_1\) is positive and \(a_2\) is negative, then we'd have the following pattern:
- + - - + - - + - -
If \(a_1\) is negative and \(a_2\) is positive, then we'd have this pattern:
- - + - - + - - + -
Sufficient.
(2) \(a_1*a_2 < 0\)
This statement essentially provides the same information as the first: \(a_1\) and \(a_2\) have different signs. As we have established, this is sufficient to answer the question.
Answer: D.
General Discussion
14 Dec 2023, 07:38
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(1) If a3 < 0 then a1 is negative and a2 is positive or a1 is positive and a2 is negative
The sequence of signs in the two cases are:
-, +, -, -, +, -, -, +, -
or
+, -, -, +, -, -, +, -, -
There is a pattern that repeats every 3 signs and the signs in positions that are multiples of 3 are the same in both cases (-). The answer is no.
SUFFICIENT
(2) It is the same case as in (1)
SUFFICIENT
IMO D
The sequence of signs in the two cases are:
-, +, -, -, +, -, -, +, -
or
+, -, -, +, -, -, +, -, -
There is a pattern that repeats every 3 signs and the signs in positions that are multiples of 3 are the same in both cases (-). The answer is no.
SUFFICIENT
(2) It is the same case as in (1)
SUFFICIENT
IMO D
