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is uv^5 < 0

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is uv^5 < 0  [#permalink]

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New post 08 Oct 2016, 06:40
3
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00:00
A
B
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Difficulty:

  75% (hard)

Question Stats:

43% (01:25) correct 57% (01:29) wrong based on 167 sessions

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Is \(uv^{5}\) < 0

1. uv < 0

2. u + \(v^{5}\) = 0

Keep the Kudos coming in and let the Questions come out :-D :-D :-D :-D

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Re: is uv^5 < 0  [#permalink]

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New post 08 Oct 2016, 08:02
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idontknowwhy94 wrote:
Is \(uv^{5}\) < 0

1. uv < 0

2. u + \(v^{5}\) = 0



Target question: Is uv⁵ < 0?

Statement 1: uv < 0
First of all, this tells us that u ≠ 0 and v ≠ 0
Since we can be certain that v⁴ > 0 (since 4 is an even exponent), we can take uv < 0 and multiply both sides by v⁴ and the inequality symbol will remain in the same direction.
When we do this, we get: uv⁵ < 0 Perfect!
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: u + v⁵ = 0
There are several values of u and v that satisfy statement 2. Here are two:
Case a: u = 1 and v = -1, in which case uv⁵ = (1)(-1)⁵ = -1. Here, uv⁵ is less than 0
Case b: u = 0 and v = 0, in which case uv⁵ = (0)(0)⁵ = 0. Here, uv⁵ is NOT less than 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer:

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Re: is uv^5 < 0  [#permalink]

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New post 08 Oct 2016, 08:47
St 1: uv < 0
This implies two things :

i) u ≠ 0 and v ≠ 0
ii) Either u is negative ; v is positive OR u is positive; v is negative

Also, numbers with even powers cannot have negative values so v^4 will always have positive value.
uv <0
u.v.v^4 < 0.v^4
u.v^5 < 0 SUF

St 2: u + v⁵ = 0
Plug in key values for this case
u = 1 ; v=-1
1+ (-1)^5 = 1-1 = 0

Try another
u = 0.5 ; v=0
0.5 + 0 = 0.5

So we can see, there are no consistent values for this scenario. INSUF

So, answer is option A
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Re: is uv^5 < 0  [#permalink]

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New post 08 Oct 2016, 09:14
idontknowwhy94 wrote:
Is \(uv^{5}\) < 0

1. uv < 0

2. u + \(v^{5}\) = 0

Keep the Kudos coming in and let the Questions come out :-D :-D :-D :-D

1) U & V have opp. signs..
thus UV<0 always............suff.....

2) if U=V=0 ...........NO
if U=32 & V=-2...........YES...........insufff

Ans A
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Re: is uv^5 < 0  [#permalink]

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New post 08 Oct 2018, 00:00
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Re: is uv^5 < 0   [#permalink] 08 Oct 2018, 00:00
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