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Sequences - DS

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Sequences - DS

by neeg » Thu Feb 28, 2013 6:57 am
In the infinite sequence S, each term Sn after S2 is equal to the sum of the two terms Sn-1 and Sn-2. If S1 is 4, what is the value uf S2?

(1) S3 = 7
(2) S4 = 10[/quote][/list]
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by GMATGuruNY » Thu Feb 28, 2013 8:04 am
neeg wrote:In the infinite sequence S, each term Sn after S2 is equal to the sum of the two terms Sn-1 and Sn-2. If S1 is 4, what is the value uf S2?

(1) S3 = 7
(2) S4 = 10
Each term after Sâ‚‚ is equal to the sum of the preceding two terms.

Statement 1: S₃ = 7
Since S₃ = S� + S₂ and S� = 4, we get:
7 = 4 + Sâ‚‚
Sâ‚‚ = 3.
SUFFICIENT.

Statement 2: Sâ‚„ = 10
S₄ = S₃ + S₂
S₃ = S₂ + S�.
Adding the two equations, we get:
S₄ + S₃ = (S₃ + S₂) + (S₂ + S�)
S₄ = 2(S₂) + S�.
Substituting S₄ = 10 and S� = 4, we get:
10 = 2(Sâ‚‚) + 4
6 = 2(Sâ‚‚)
Sâ‚‚ = 3.
SUFFICIENT.

The correct answer is D.

In many cases, knowing ANY TWO VALUES in a sequence will be sufficient information to calculate EVERY OTHER VALUE in the sequence.
Here, if one of the two statements gave the value of S�₀₀₀, we would still have sufficient information to determine the value of S₂.
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by Anurag@Gurome » Thu Feb 28, 2013 9:57 am
neeg wrote:In the infinite sequence S, each term Sn after S2 is equal to the sum of the two terms Sn-1 and Sn-2. If S1 is 4, what is the value of S2?

(1) S3 = 7
(2) S4 = 10
No mathematics is needed here if you understand that "any term after S₂ is sum of the two terms Sn-1 and Sn-2" means any terms after S₂ is the sum of the previous two consecutive terms. Hence, if we know the values of S� and S₂, we can determine the value of any term after S₂. This means, if we know the values of any two terms among S�, S₂, and Sn (Sn is some term after S₂), we can determine the value of the third one.

Hence, both statements are individually sufficient.

The correct answer is D.

Word of Caution: In this case we can conclude the underlined fact because the relation among the terms is linear and we can found any term from S� and S₂ and we can trace back either S� or S₂ from any later term and any one of them.
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