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# All the terms of a certain sequence x1,x2,........xn are positive...

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Joined: 22 Nov 2016
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All the terms of a certain sequence x1,x2,........xn are positive... [#permalink]

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28 Oct 2017, 11:58
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Difficulty:

75% (hard)

Question Stats:

36% (01:11) correct 64% (01:58) wrong based on 11 sessions

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All the terms of a certain sequence $$x_1,x_2,........x_n$$ are positive integers. The $$n^t^h$$ term (n>1) of the sequence is given by the formula:
$$x_n =x_(n-1) + 1$$ (If $$x_(n-1)$$ is even)
$$x_n =x_(n-1) + 3$$ (If $$x_(n-1)$$ is odd)

What is the value of $$x_1 + x_6$$?

(1) The second term of the sequence is 3
(2) Two of the first three terms of the sequence are even and add up to 8
[Reveal] Spoiler: OA

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All the terms of a certain sequence x1,x2,........xn are positive... [#permalink]

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28 Oct 2017, 12:09
sasyaharry wrote:
All the terms of a certain sequence x1,x2,........xn are positive integers. The nth term (n>1) of the sequence is given by the formula:
xn =xn-1 + 1 (If xn-1 is even)
xn =xn-1 + 3 (If xn-1 is odd)

What is the value of x1 + x6?

(1) The second term of the sequence is 3
(2) Two of the first three terms of the sequence are even and add up to 8

Odd numbers are being added to $$x_{n-1}$$, so if $$x_{n-1}$$ is even then $$x_n$$ is odd and if $$x_{n-1}$$ is odd then $$x_n$$ is even

to know the value of $$x_1+x_6$$ we only need value of $$x_1$$ remaining can be found out through the formula given in the question stem

Statement 1: implies $$x_2=x_n=3=odd$$, so $$x_{n-1}=x_1=even$$. we can substitute the value of $$x_2$$ in the equation $$x_n=x_{n-1}+1$$ to get $$x_1$$. Sufficient

Statement 2: the sequence will have alternate odd and even numbers, so if out of 1st three two are even, this implies $$x_1$$ is even, $$x_2$$ is odd and $$x_3$$ is even

given $$x_1+x_3=8 =>x_1+x_2+3=8$$

or $$x_1+x_1+1+3=8$$, so $$x_1$$ can be calculated. Sufficient

Option D

Kudos [?]: 257 [0], given: 35

All the terms of a certain sequence x1,x2,........xn are positive...   [#permalink] 28 Oct 2017, 12:09
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# All the terms of a certain sequence x1,x2,........xn are positive...

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