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Is the term odd?

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Is the term odd?

by gmattesttaker2 » Sun Dec 22, 2013 6:04 pm
Hello,

Can you please assist with this:

In a sequence X1, X2, X3,... Xn, ..... ; Xn+3 = Xn+2 + Xn+1 + Xn, is X8 odd?

(1) X1 is odd
(2) Exactly one of the terms X1, X2, and X3 is odd

OA: B

Thanks a lot,
Sri
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by ganeshrkamath » Sun Dec 22, 2013 8:45 pm
gmattesttaker2 wrote:Hello,

Can you please assist with this:

In a sequence X1, X2, X3,... Xn, ..... ; Xn+3 = Xn+2 + Xn+1 + Xn, is X8 odd?

(1) X1 is odd
(2) Exactly one of the terms X1, X2, and X3 is odd

OA: B

Thanks a lot,
Sri

X4 = X1 + X2 + X3
X5 = X2 + X3 + X4 = X2 + X3 + (X1 + X2 + X3) = X1 + 2X2 + 2X3
X6 = X3 + X4 + X5 = X3 + (X1 + X2 + X3) + (X1 + 2X2 + 2X3) = 2X1 + 3X2 + 4X3
X7 = X4 + X5 + X6 = (X1 + X2 + X3) + (X1 + 2X2 + 2X3) + (2X1 + 3X2 + 4X3) = 4X1 + 6X2 + 7X3
X8 = X5 + X6 + X7 = (X1 + 2X2 + 2X3) + (2X1 + 3X2 + 4X3) + (4X1 + 6X2 + 7X3) = 7X1 + 11X2 + 13X3

Statement 1: X1 is odd
Case 1: X2 and X3 are even
X8 = odd
Case 2: X2 is odd and X3 is even
X8 = even
Not sufficient.

Statement 2: Exactly one of the terms X1, X2, and X3 is odd
X8 = odd + even + even
= odd
Sufficient.


Choose B

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by Brent@GMATPrepNow » Mon Dec 23, 2013 6:33 am
ganeshrkamath's solution is great (as usual).

I just wanted to mention that the question needs some additional text that tells test-takers that all of the terms in the sequence are integers. Otherwise, the correct answer here is actually E since we can't conclude that a term is even if that term is not odd.

For example, if X1 = 1, X2 = 1/2 and X3 = 1/3, then X8 is not odd.

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