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Intern  Joined: 17 Jan 2010
Posts: 21
If s^4*v^3*x^7 < 0 , is svx < 0? 1) v < 0 2) x >  [#permalink]

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3 00:00

Difficulty:   45% (medium)

Question Stats: 63% (01:27) correct 37% (01:04) wrong based on 238 sessions

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If $$s^4*v^3*x^7 < 0$$, is $$svx < 0?$$

1) $$v < 0$$
2) $$x > 0$$
Intern  Joined: 21 Jan 2010
Posts: 46

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5
Rules to consider:
1. A negative number to the power of an odd number is always negative.
2 .A negative number to the power of an even number is always positive.
3. A negative times a negative is always positive.
4. A negative times a positive is always negative.

You have s^4 which is an even power and will always be positive.
V^3 will be negative if V is negative.
V^3 will be negative if V is negative.
X^7 will be positive if X is positive.
X^7 will be positive if X is positive.

So, solution one, v<0:
We know s^4 is positive.
We know v^3 is negative since v<0 and it is an odd power.
But, x could be either positive or negative, meaning x^7 could be either.
Since we know s^4*v^3*x^7 is negative, we have:
(+)*(-)*(?) = (-)
Therefore we can determine x^7 is positive, and thus x is positive.
HOWEVER, don't get tripped up on 'S' - just because s^4 is positive, s could be positive or negative.
s*v*x = (?)*(-)*(+) is < 0 if s is positive and > 0 if s is negative.
Therefore, one alone is not enough.

Likewise, with solution two, x>0:
We have s^4*v^3*x^7 < 0
So, (+)*(?)*(+) = (-)
Therefore, v^3 must be negative. Thus, v < 0.
HOWEVER, don't get tripped up on 'S' - just because s^4 is positive, s could be positive or negative.
s*v*x = (?)*(-)*(+) is < 0 if s is positive and > 0 if s is negative.
Therefore, two alone is not enough.

Put them together:
V<0
X>0
S^4*V^3*X^7 = (+)*(-)*(+)<0, which they already tell you, so this gives you no new information. S could still be positive or negative (since it is an even power).

So, is s*v*x < 0? We can't determine this, because s could be negative or positive.

So, your answer is e - neither solution alone nor together.

Confusing?
General Discussion
Manager  Joined: 13 Oct 2009
Posts: 92
Location: USA
Schools: IU KSB

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1
rahulms wrote:
If $$s^4*v^3*x^7 < 0$$, is $$svx < 0?$$

1) $$v < 0$$
2) $$x > 0$$

$$s^4*v^3*x^7 < 0$$ says V and X are of different sign and S could be positive or negtive.

to find $$svx < 0?$$

Yes/No question type

V*X= negative and S=positive will give answer Yes

V*X= negative and S=negative will give answer No

Question stem = find whether S is positive or negative

1. V is negative but it doesn't say anything about S; Not SUFF

2. X is positive but it doesn't say anything about S; Not SUFF

1 & 2
Again no clue whether S is positive or negative; Not SUFF

Intern  Joined: 09 Feb 2010
Posts: 1

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If , S^4*v^3*x^7<0, is svx<0?

1) v<0
2) x>0

sol: consider only stmt 1, where v is negative but S is always positive, becoz of its even power, but X can be postive or negative, becoz of its odd power.
so svx can greater or lesser than zero. finally stmt 1 alone is not suffcient to answer
now consider stmt 2, where again S is always positive and V can be positive or negative, becoz of its odd power, and x is always postive.
so, SVX can again greater or lesser than zero. finally stmt 2 alone is not sufficient to answer

but combining both stmt 1 and stmt 2, S is always positive, V is always negative, and X is always positive, now SVX < 0 , can be answered,
both stmts combinely are sufficient to answer.

OA is C
Manager  Joined: 26 May 2005
Posts: 159

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If , S^4*v^3*x^7<0, is svx<0?

1) v<0
2) x>0

sol: consider only stmt 1, where v is negative but S is always positive, becoz of its even power, but X can be postive or negative, becoz of its odd power.
so svx can greater or lesser than zero. finally stmt 1 alone is not suffcient to answer
now consider stmt 2, where again S is always positive and V can be positive or negative, becoz of its odd power, and x is always postive.
so, SVX can again greater or lesser than zero. finally stmt 2 alone is not sufficient to answer

but combining both stmt 1 and stmt 2, S is always positive, V is always negative, and X is always positive, now SVX < 0 , can be answered,
both stmts combinely are sufficient to answer.

OA is C

S is not always positive but S^2 is always positive

E is the answer
Manager  Joined: 16 Apr 2009
Posts: 213

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i do not understand what is the need in solving this

the value of s is not given , so that means s can be 0 and s^2 will also be 0

so, E
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Math Expert V
Joined: 02 Sep 2009
Posts: 58464
If s^4*v^3*x^7 < 0 , is svx < 0? 1) v < 0 2) x >  [#permalink]

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ichha148 wrote:
i do not understand what is the need in solving this

the value of s is not given , so that means s can be 0 and s^2 will also be 0

so, E

Yes, the answer is E. But since $$s^4*v^3*x^7 < 0$$, then s cannot be zero, so we do need some "solving".
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Manager  Joined: 16 Apr 2009
Posts: 213

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oops , yes ,missed that , we do need to solve this _________________
Always tag your question
Current Student B
Status: DONE!
Joined: 05 Sep 2016
Posts: 357
Re: If s^4*v^3*x^7 < 0 , is svx < 0? 1) v < 0 2) x >  [#permalink]

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Definitely agree with E being the answer.

1) v<0 --> means x>0, but we still don't know value of s, thus INSUFFICIENT

2) x>0 --> means v<0, but we still don't know value of s, thus INSUFFICIENT

A,B,D eliminated...

(1) + (2) --> Still INSUFFICIENT as we don't know value of s - it can still be either positive or negative

D eliminated...
Non-Human User Joined: 09 Sep 2013
Posts: 13421
Re: If s^4*v^3*x^7 < 0 , is svx < 0? 1) v < 0 2) x >  [#permalink]

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_________________ Re: If s^4*v^3*x^7 < 0 , is svx < 0? 1) v < 0 2) x >   [#permalink] 03 Feb 2019, 04:59
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