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A sequence An is there such that An=(An-1)-(An-2) where n are integers

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A sequence An is there such that An=(An-1)-(An-2) where n are integers  [#permalink]

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New post 18 Feb 2017, 00:57
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A sequence \(A_n\) is there such that \(A_{n}=A_{n-1}-A_{n-2}\) where \(n\) are integers greater than \(2\). What is the value of \(A_5\)?

(1) \(A_{4} - A_{3}=3\)
(2) \(A_{14}=1\)

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Re: A sequence An is there such that An=(An-1)-(An-2) where n are integers  [#permalink]

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New post 18 Feb 2017, 02:31
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ziyuenlau wrote:
A sequence \(A_n\) is there such that \(A_{n}=A_{n-1}-A_{n-2}\) where \(n\) are integers greater than \(2\). What is the value of \(A_5\)?

(1) \(A_{4} - A_{3}=3\)
(2) \(A_{14}=1\)


Hi

Nice question.

(1) This is fairy straightforward. \(A_5 = A_4 - A_3 = 3\) Sufficient

(2) This one is tricky.

In fact we have only two variables to operate - \(A_1\) and \(A_2\).

\(A_3 = A_2 - A_1\)

\(A_4 = A_3 - A_2 = - A_1\)

\(A_5 = A_4 - A_3 = - A_2\)

\(A_6 = A_5 - A_4 = - A_3\)

\(A_7 = A_6 - A_5 = A_1\)

\(A_8 = A_7 - A_6 = A_2\)

\(A_9 = A_8 - A_7 = A_3\)

We could have stopped at \(A_7\) but \(A_9\) gives better picture of the full cycle. As we can see, we have a cycle of 6, after \(A_6\) which the pattern repeats.

\(A_1, A_2, A_3, - A_1, - A_2, - A_3, A_1 ...\)

\(A_{14}\) give remainder \(2\) upon division by \(6\), that is \(A_{14} = A_2 = 1\)

\(A_5 = - A_2 = - 1\) Sufficient

Answer D
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Re: A sequence An is there such that An=(An-1)-(An-2) where n are integers  [#permalink]

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New post 04 May 2017, 13:27
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ziyuen wrote:
A sequence \(A_n\) is there such that \(A_{n}=A_{n-1}-A_{n-2}\) where \(n\) are integers greater than \(2\). What is the value of \(A_5\)?

(1) \(A_{4} - A_{3}=3\)
(2) \(A_{14}=1\)

Hmm.. Even tough we can get an answer from each statement, I would say that this is not a good quality question. In GMAT DS, Statement 1 and Statement 2 give the exact same answer rather than 2 different ones like in this question.

Anyways,

From Statement 1, \(A_5\) = 3

From Statement 2, \(A_5\) = -1

Answer D
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Re: A sequence An is there such that An=(An-1)-(An-2) where n are integers  [#permalink]

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New post 12 Nov 2017, 11:08
Answer (D)

But two statements contradicting giving two diff values for A5
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Re: A sequence An is there such that An=(An-1)-(An-2) where n are integers &nbs [#permalink] 12 Nov 2017, 11:08
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