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Solve for x: 0<|x|-4x<5 = ? [#permalink]
 16 Aug 2009, 00:44
Question Stats:
51% (02:30) correct
48% (01:16) wrong based on 31 sessions
Solve for x: 0<|x|-4x<5 = ? A. x<0 B. 0<x<1 C. -3/5<x<1 D. -3/5<x<0 E. -1<x<0
Last edited by Bunuel on 04 Dec 2012, 03:22, edited 2 times in total.
Renamed the topic and edited the question.
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I am getting E as an answer if x is -ve. If x is -ve, we get 0 < -5x < 5 Dividing both sides by -5, we flip both the sides and we land up on 0 > x > -1 ie -1 < x < 0. Is that the correct method to solve this problem? Please explain.
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Senior Manager
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IMO E:
5 + 4x > |x|
5 + 4x > x first cndtn
5 > - 3x
x>-5/3
or
5 + 4x > -x
x > -1
using
4x < |x|
or 4x < x
x<0
or 4x < -x
x<0
thus range lies between -1 to 0
correct me if i m wrong!!
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0<|x|-4x<5 = ?
A. x<0
B. 0<x<1
C. -3/5<x<1
D. -3/5<x<0
E. -1<x<0
i did it this way
split the inquality into 2
a) /x/-4x<5 ie: -5<x-4x<5 ie: -5<-3x<5 ie: 5/3>x>-5/3....1
b) /x/-4x>0 thus /x/>4x thus eithe x>4x ie: -3x>0 ie: x <0 or -x<4x ie: x>-4x ie: x>0
and i get lost here??
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Director
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0<-5x<5
=> -1<x<0
Answer E.
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I'm also getting E. 2 cases x > 0 or x < 0 0< -x - 4x < 5 => 0< -5x < 5 => x > -1 and x < 0 x - 4x < 5 => -3x < 5 => x > -5/3 so x > 0 as x is +ve So -1 < x < 0 Answer E
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hi,
apply definition absolute value obtain two possibilites:
A. if x≥0 then 0<|x|-4x<5 go 0<x-4x<5 go 0<-3x<5, go 0>x>-5/3. The intersection is empty
B. if x<0 then 0<|x|-4x<5 go 0<-x-4x<5 go 0<-5x<5 go 0>x>-1. the intersection is -1<x<0
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puneetj wrote: Got to the correct answer but took too much time...E If you get messed up in mods, such a question can be done in under a minute by trying out some values. Now, I am no fan of plugging in numbers, especially not in DS questions, but such questions are perfect for plugging in if you are not comfortable with algebra. Why? Because they have asked for the range of x. If there is even one value in the given range that doesn't satisfy the inequality, it is not the answer and if there is even one value outside the given range that does satisfy the inequality, it is not the answer. 0<|x|-4x<5 = ? A. x<0 B. 0<x<1 C. -3/5<x<1 D. -3/5<x<0 E. -1<x<0 Say, consider option A. If x = -1, |x|-4x = 5 which doesn't satisfy the inequality so A is out. If x = 1/2, |x|-4x is negative so B and C are out. If x = -4/5, |x|-4x = 4 so D is out and E is the answer.
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0<|x|-4x<5
A. x<0
Test: x=-5
|-5|-4(-5) = 5 + 20 is not less than 5
FALSE!
B. 0<x<1
Test: x=\frac{1}{4}
\frac{1}{4}-4(\frac{1}{4})=-\frac{3}{4} is not greater than 0
FALSE!
C. -3/5<x<1
x<1 as tested with B
FALSE!
D. -3/5<x<0
E. -1<x<0
We see that D and E are almost the same except for E. covers -3/5 unlike D.
Let x=-3/5
|-\frac{3}{5}|-4(-\frac{3}{5})=\frac{15}{5}=3
Answer: E
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VeritasPrepKarishma wrote: puneetj wrote: Got to the correct answer but took too much time...E If you get messed up in mods, such a question can be done in under a minute by trying out some values. Now, I am no fan of plugging in numbers, especially not in DS questions, but such questions are perfect for plugging in if you are not comfortable with algebra. Why? Because they have asked for the range of x. If there is even one value in the given range that doesn't satisfy the inequality, it is not the answer and if there is even one value outside the given range that does satisfy the inequality, it is not the answer. 0<|x|-4x<5 = ? A. x<0 B. 0<x<1 C. -3/5<x<1 D. -3/5<x<0 E. -1<x<0 Say, consider option A. If x = -1, |x|-4x = 5 which doesn't satisfy the inequality so A is out. If x = 1/2, |x|-4x is negative so B and C are out. If x = -4/5, |x|-4x = 4 so D is out and E is the answer. I believe the choice of -4/5 to execlude D is wrong -4/5 is not in the range of -3/5<x<0 ????? accordingly i think both D and E could solve as the right range in my opinion is -5/3 < x < 0??? am i right or wrong plz advise!
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Re: Solve for x: 0<|x|-4x<5 = ? [#permalink]
10 May 2013, 23:46
yezz wrote: Solve for x: 0<|x|-4x<5 = ?
A. x<0
B. 0<x<1
C. -3/5<x<1
D. -3/5<x<0
E. -1<x<0 |x|-4x>0 = |x|>4x = \frac{x}{|x|}<1 --> x<0. Again, |x|-4x<5 = -x-4x<5 = -5x<5-->x>-1. E.
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yezz wrote: VeritasPrepKarishma wrote: puneetj wrote: Got to the correct answer but took too much time...E If you get messed up in mods, such a question can be done in under a minute by trying out some values. Now, I am no fan of plugging in numbers, especially not in DS questions, but such questions are perfect for plugging in if you are not comfortable with algebra. Why? Because they have asked for the range of x. If there is even one value in the given range that doesn't satisfy the inequality, it is not the answer and if there is even one value outside the given range that does satisfy the inequality, it is not the answer. 0<|x|-4x<5 = ? A. x<0 B. 0<x<1 C. -3/5<x<1 D. -3/5<x<0 E. -1<x<0 Say, consider option A. If x = -1, |x|-4x = 5 which doesn't satisfy the inequality so A is out. If x = 1/2, |x|-4x is negative so B and C are out. If x = -4/5, |x|-4x = 4 so D is out and E is the answer. I believe the choice of -4/5 to execlude D is wrong -4/5 is not in the range of -3/5<x<0 ????? accordingly i think both D and E could solve as the right range in my opinion is -5/3 < x < 0??? am i right or wrong plz advise!
Focus on "and if there is even one value outside the given range that does satisfy the inequality, it is not the answer." given above. -4/5 is a value which satisfies 0 < |x|-4x < 5 since |-4/5|-4(-4/5) = 4. Since -4/5 does not lie in the range -3/5<x<0 so (D) cannot be the answer. The correct range needs to cover all possible values of x.
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Re: Solve for x: 0<|x|-4x<5 = ? [#permalink]
11 May 2013, 06:31
@Karishma ... U r absolutely right , been away for years from GMAT ... E is the perfect answer
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Re: Solve for x: 0<|x|-4x<5 = ? [#permalink]
12 May 2013, 07:44
we ve got 3 critical values that are ( 0 from modulus , -5/3& -1 from /x/ = 5+4x) , draw on the number line and test values
.....-5/3........-1...........0....................
only -1<x<0 is the range where all values of x satisfy the compound inequality 0</x/-4x<5
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Re: Solve for x: 0<|x|-4x<5 = ?
[#permalink]
12 May 2013, 07:44
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