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if x(x-5)(x+2)=0, is x negative? 1)x^2 - 7x >= 0 2) x^2 - [#permalink]
 09 Oct 2006, 08:42
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if x(x-5)(x+2)=0, is x negative?
1)x^2 - 7x >= 0
2) x^2 - 2x - 15>=0
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B it is
(1) is insuff
Because x^2-7x>=0 means that x>=7 or x<=0
x(x-5)(x+2)=0 so x could be 0;5;-2
(1) only we get x= 0 (not negative) or -2 (negative)
So B is correct (x can get only one value 5 )
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if x(x-5)(x+2)=0, is x negative?
1)x^2 - 7x >= 0
2) x^2 - 2x - 15>=0
from stem
x is either = 0 or 5 or -2 question asks is x = -2
substitute in one
f(0) = could be , f(5) = wrong f(-2) = right.........insuff
from two
f(0) = wrong , f(5) = could be f(-2) = wrong....insuff
my answer is E
BUT as far as i know GMAT doesnt give the two statment with coontradiction ( case of f(-2))............. i doubt this is a gmat question.
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(B) as well,
Stat1:
x^2 - 7x >= 0
<=> x*(x-7) >=0
<=> x <= 0 or x >= 7
Since x(x-5)(x+2)=0, hence x = 0 or x = -2
INSUFF
Stat2:
x^2 - 2x - 15>=0
<=> (x-5)(x+3) >=0
<=> x >= 5 or x <= -3
Since x(x-5)(x+2)=0, hence x is forced to be equal to 5.
SUFF
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Fig can you elaborate on the logic of your answer ( Z level students teaching style plz?
thanks in advance
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yezz wrote: Fig can you elaborate on the logic of your answer ( Z level students teaching style plz?
thanks in advance
At least, I can try 
Since x(x-5)(x+2)=0, then x could be -2, 0 or 5.
If we have a close look on these possible solutions, we can observe that 1 is negative, 1 is without sign and 1 is positive.
To answer the problem quesion :'is x negative?', we could have these groups of solutions:
> groupe 1 : x = 5 (Not neg)
> groupe 2 : x = 5 or x = 0 (Not neg)
> groupe 3 : x = 0 (Not neg)
> groupe 4 : x = -2 (Neg)
Now, we could look at the statments. These statments have normally to give us 1 of the above group in order to respond all answers except (E).
Stat1: x^2 - 7x >= 0
Thus, x*(x-7) >=0
<=> x <= 0 or x >= 7
The bold inequality shows us that x is negative or 0. It's not match to 1 of the 4 groups definied to answer the question. -2 is negative but 0 is neither negative nor positive.
INSUFF
Stat2: x^2 - 2x - 15>=0
Thus, (x-5)(x+3) >=0
<=> x >= 5 or x <= -3
Bingo, -2 and 0 are out the possible values of x while x=5 (groupe 1) is contained in the bold inequality.
SUFF
Hope this help
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man i need to have some more rest........you rock my mate. thanks a million
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Hey ,
Getting bk to the inequality basics,...i'm awfully weak in inequalities...
thus, (x-5)(x+3) >=0
<=> x >= 5 or x <= -3
does x+3 >=0, not mean tht x>= -3( when u subtract 3 on both sides...)
please clear this doubt for me.....it wud help me a lot..coz inequality probs always pull me down..
_________________
ARISE AWAKE AND REST NOT UNTIL THE GOAL IS ACHIEVED
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Raghavender wrote: Hey ,
Getting bk to the inequality basics,...i'm awfully weak in inequalities...
thus, (x-5)(x+3) >=0
<=> x >= 5 or x <= -3
does x+3 >=0, not mean tht x>= -3( when u subtract 3 on both sides...)
please clear this doubt for me.....it wud help me a lot..coz inequality probs always pull me down..
Actually, the equation (x-5)(x+3) = x^2 - 2x - 15 = a*x^2 + b*x + c has the sign of :
o a (1 here) when x is not between the 2 roots, thus > 0
o -a (-1) when x is between the 2 roots, thus < 0
By the way, we have so:
(x-5)(x+3) >=0
<=> x >= 5 or x <= -3
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Manager
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the OA is C...very weird...
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imaru wrote: the OA is C...very weird...
What is the source of the question? 
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Fig wrote: Raghavender wrote: Hey ,
Getting bk to the inequality basics,...i'm awfully weak in inequalities...
thus, (x-5)(x+3) >=0
<=> x >= 5 or x <= -3
does x+3 >=0, not mean tht x>= -3( when u subtract 3 on both sides...)
please clear this doubt for me.....it wud help me a lot..coz inequality probs always pull me down.. Actually, the equation (x-5)(x+3) = x^2 - 2x - 15 = a*x^2 + b*x + c has the sign of : o a (1 here) when x is not between the 2 roots, thus > 0 o -a (-1) when x is between the 2 roots, thus < 0 By the way, we have so: (x-5)(x+3) >=0 <=> x >= 5 or x <= -3 Fig - Thanks for the explanation. I kinda get it but am still a bit confused. How do you get x<=-3 ...when I subtarct three from x+3>=0 I get x>=-3. Thanks very much in advance.
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Matrix02 wrote: Fig wrote: Raghavender wrote: Hey ,
Getting bk to the inequality basics,...i'm awfully weak in inequalities...
thus, (x-5)(x+3) >=0
<=> x >= 5 or x <= -3
does x+3 >=0, not mean tht x>= -3( when u subtract 3 on both sides...)
please clear this doubt for me.....it wud help me a lot..coz inequality probs always pull me down.. Actually, the equation (x-5)(x+3) = x^2 - 2x - 15 = a*x^2 + b*x + c has the sign of : o a (1 here) when x is not between the 2 roots, thus > 0 o -a (-1) when x is between the 2 roots, thus < 0 By the way, we have so: (x-5)(x+3) >=0 <=> x >= 5 or x <= -3 Fig - Thanks for the explanation. I kinda get it but am still a bit confused. How do you get x<=-3 ...when I subtarct three from x+3>=0 I get x>=-3. Thanks very much in advance. Well, I can try
To seach (x-5)(x+3) >=0 is similar to study the sign of the function f(x) = (x-5)(x+3).
A great tool that Maths gives us is the table of signs. Once a fonction is factorized in "famous" forms of basic functions, such as a*x+b, we decompose the function and use the properties of the multiplication to determine what values of x give a positive sign and what values of x give a negative sign to the studied function f(x).
This table of signs is fast to draw and brings to the solution
I attached u the resulting table. To find the result signs for f(x), we multiply vertically + and - as they are +1 and -1.
So, when x <= -3 : sign(f(x)) = sign( (x-5)(x+3) ) = (-1)*(-1) = +1
I also join u the draw of the function f(x). U will visually remark that f(x) is positive on values of x not between the 2 roots.
This result is linked to my former post. The sign of a*x^2 + b*x + c
Attachments
Graph.jpg [ 31.16 KiB | Viewed 330 times ]
Signs-Table.jpg [ 14.17 KiB | Viewed 327 times ]
Last edited by Fig on 12 Oct 2006, 00:49, edited 2 times in total.
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Hell no...........Fig am no engneering expert like you are ....and obviously most of the people on this forum. 
Man if this is Gmat I d rather kill myself ...
Cant we have a premetive down to earth explanation for prople like me ............I know u can Plzzzzzzzz.
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yezz wrote: Hell no...........Fig am no engneering expert like you are ....and obviously most of the people on this forum. Man if this is Gmat I d rather kill myself ... Cant we have a premetive down to earth explanation for prople like me ............I know u can Plzzzzzzzz. Well Sorry ... the table of signs is my best way to explain (x+3)(x-5) without possible confusions .
The famous result to remember is :
sign(a*x^2+b*x+c) = sign(-a) between the roots.
In this DS, we apply it 2 times
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Thanks so much FIG for the great explanation. I need to take some time to let it sink in and try some more problems. Great graphs..I really appreciate it.
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Ok Fig then ........on Gday I will guess
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U are welcome Matrix02
yezz... I believe that u will not guess but rather get it right
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This is the spirit..........man you are the man
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