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All the terms of a certain sequence x1,x2,........xnx1,x2,........xn a

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All the terms of a certain sequence x1,x2,........xnx1,x2,........xn a [#permalink]

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New post 26 Jan 2018, 13:06
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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

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[Reveal] Spoiler: OA

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Re: All the terms of a certain sequence x1,x2,........xnx1,x2,........xn a [#permalink]

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New post 26 Jan 2018, 14:11
X2 = x1 + 3, x3 = x2+2 = x1+5, x4 = x3+3 = x2 + 4, x5 = x4+1 = x2+5, x6 = x5+3 = x2+8.
(1) x2 = 3...x1 = 0, x6 = 11. Works.
(2) x1&x2 = even.. Not possible as x2 = x1+odd = odd
x2&x3 = even, X2 = 3,x3 = 5..not possible as both not even
x3 and x1 not possible as both can't be even at the same time. thus not (2)


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Re: All the terms of a certain sequence x1,x2,........xnx1,x2,........xn a [#permalink]

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New post 27 Jan 2018, 10:57
DTUguy wrote:
X2 = x1 + 3, x3 = x2+2 = x1+5, x4 = x3+3 = x2 + 4, x5 = x4+1 = x2+5, x6 = x5+3 = x2+8.
(1) x2 = 3...x1 = 0, x6 = 11. Works.
(2) x1&x2 = even.. Not possible as x2 = x1+odd = odd
x2&x3 = even, X2 = 3,x3 = 5..not possible as both not even
x3 and x1 not possible as both can't be even at the same time. thus not (2)


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Re: All the terms of a certain sequence x1,x2,........xnx1,x2,........xn a [#permalink]

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New post 27 Jan 2018, 11:10
SandhyAvinash 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

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Re: All the terms of a certain sequence x1,x2,........xnx1,x2,........xn a   [#permalink] 27 Jan 2018, 11:10
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