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# If x is a positive integer, is y^2 (x^3 - x + 1)

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VP
Joined: 30 Jun 2008
Posts: 1028

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If x is a positive integer, is y^2 (x^3 - x + 1) [#permalink]

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02 Oct 2008, 00:00
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If $$x$$ is a positive integer, is $$y^2 (x^3 - x + 1) > 75?$$

1. $$y > 1$$
2. $$(x-1)^2=16$$
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Kudos [?]: 736 [0], given: 1

Manager
Joined: 30 Sep 2008
Posts: 111

Kudos [?]: 20 [0], given: 0

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02 Oct 2008, 00:13
(1). y > 1

y = 2, x = 0 -> not satisfy
y = 10, x = 0 -> satisfy

(1) insufficient

(2) (x-1)^2=16, x positive negative => x = 5

x = 5, y = 0 - > not satify
x = 5, y = 1 -> satisfy

=> (2) insufficient

(1) & (2), x = 5, y > 1

y^2 (x^3 - x + 1 ) > = x^3 - x + 1 > = 121 > 75

sufficient

Kudos [?]: 20 [0], given: 0

VP
Joined: 17 Jun 2008
Posts: 1373

Kudos [?]: 430 [0], given: 0

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02 Oct 2008, 01:37
lylya4 wrote:
(1). y > 1

y = 2, x = 0 -> not satisfy
y = 10, x = 0 -> satisfy

(1) insufficient

(2) (x-1)^2=16, x positive negative => x = 5

x = 5, y = 0 - > not satify
x = 5, y = 1 -> satisfy

=> (2) insufficient

(1) & (2), x = 5, y > 1

y^2 (x^3 - x + 1 ) > = x^3 - x + 1 > = 121 > 75

sufficient

IMO E
x=-3 or 5 with x=-3 we get the opposite answer hence INSUFFI
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Kudos [?]: 430 [0], given: 0

Intern
Joined: 07 Sep 2008
Posts: 25

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

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02 Oct 2008, 02:24
Manager,

My take is that is E cos
1- doesn't give you a value for x
2- x=5 or x = -3 , doesn't give a value for y

Both together, the statement is correct only if x = 5, but for x=-3, it's not valid. so it's E

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Intern
Joined: 07 Sep 2008
Posts: 25

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02 Oct 2008, 02:26
let me correct myself. i didn't see that is says that x is a positive integer, so it's C

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Re: DS - Inequality   [#permalink] 02 Oct 2008, 02:26
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