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# For each positive integer k, the quantity

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Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129034 [1], given: 12187

For each positive integer k, the quantity [#permalink]

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07 May 2013, 02:13
1
KUDOS
Expert's post
1. For each positive integer k, the quantity $$x_k$$ is defined such that $$x_k = x_{k+1} * ( x_{k+2})^3$$

In addition, $$x_3 = 1$$. In the table, select values for $$x_1$$ and $$x_4$$ that are jointly compatible with these conditions. Select only two values, one in each column.

$$x_1$$ -- $$x_4$$
------------------------------- 0
------------------------------- 2
------------------------------- 5
------------------------------- 8
------------------------------- 16
------------------------------- 64
_________________

Kudos [?]: 129034 [1], given: 12187

Manager
Status: *Lost and found*
Joined: 25 Feb 2013
Posts: 123

Kudos [?]: 124 [1], given: 14

Location: India
Concentration: General Management, Technology
GMAT 1: 640 Q42 V37
GPA: 3.5
WE: Web Development (Computer Software)
Re: For each positive integer k, the quantity [#permalink]

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07 May 2013, 11:07
1
KUDOS
Bunuel wrote:
1. For each positive integer k, the quantity $$x_k$$ is defined such that $$x_k = x_{k+1} * ( x_{k+2})^3$$

In addition, $$x_3 = 1$$. In the table, select values for $$x_1$$ and $$x_4$$ that are jointly compatible with these conditions. Select only two values, one in each column.

$$x_1$$ -- $$x_4$$
------------------------------- 0
------------------------------- 2
------------------------------- 5
------------------------------- 8
------------------------------- 16
------------------------------- 64

From the above it can be deduced, that x1 = x2 = (x4)^3. Hence, for values of x1, x4 only 2,8 satisfy the same. If the above values apply, I believe the expression x-k cannot be said always an integer. since x-5 = (1/2)^(1/3). But since the question mentions it a 'quantity', it seems that fits the question as well.

Please correct me if I am wrong

Regards,
Arpan
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Kudos [?]: 124 [1], given: 14

Manager
Joined: 11 Jun 2010
Posts: 83

Kudos [?]: 18 [0], given: 17

Re: For each positive integer k, the quantity [#permalink]

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16 May 2013, 20:18
X3 = 1
therefore x1=x2*1 or x1=x2 and
x2 = 1*(x4)^3
X1 = (x4)^3
only combinations for x1 and x4 where x1 can be cube of x4 is 8 for x1 and 2 for x4

And X1 = 8 / X4 = 2

Kudos [?]: 18 [0], given: 17

Re: For each positive integer k, the quantity   [#permalink] 16 May 2013, 20:18
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# For each positive integer k, the quantity

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