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If |5x-5|>x-1, which of the following must be true?

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If |5x-5|>x-1, which of the following must be true?  [#permalink]

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New post 04 Jun 2015, 07:14
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A
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E

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If |5x-5|>x-1, which of the following must be true?

A. x<1
B. x>1
C. x>5
D. x<5
E. None of the above
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Re: If |5x-5|>x-1, which of the following must be true?  [#permalink]

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New post 04 Jun 2015, 07:27
reto wrote:
If |5x-5|>x-1, which of the following must be true?

A. x<1
B. x>1
C. x>5
D. x<5
E. None of the above


\(|5x-5|>x-1\);

Factor out 5: \(5*|x-1|>x-1\). Notice here that LHS must more than or equal to 0.

If x-1 is negative, then (LHS=positive) > (RHS=negative);
If x-1 is positive, then (LHS=5 times some positive value) > (RHS = that positive positive).
If x-1 is 0 (so if x=1), then LHS = RHS.

Therefore, \(|5x-5|>x-1\) holds true for any value of x, but 1.

Answer: E.
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If |5x-5|>x-1, which of the following must be true?  [#permalink]

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New post 04 Jun 2015, 07:31
2
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reto wrote:
If |5x-5|>x-1, which of the following must be true?

A. x<1
B. x>1
C. x>5
D. x<5
E. None of the above


Best way to solve these question is checking options

A. x<1 Take any value of x e.g x=0.5, the primary relation |5x-5|>x-1 is satisfied and but on taking x=2 also the relation holds true which is not considered in option A hence INCORRECT

B. x>1 This option can be ruled out straight away as the values of x less than 1 are also acceptable as checked in option A. Hence, INCORRECT

C. x>5 This option can be ruled out straight away as the values of x less than 1 are also acceptable as checked in option A. Hence, INCORRECT

D. x<5 This option can be ruled out as the values of x Greater than 5 e.g. x=10 are also acceptable and x=1 is not acceptable. Hence, INCORRECT

E. None of the above CORRECT
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Re: If |5x-5|>x-1, which of the following must be true?  [#permalink]

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New post 09 Jun 2016, 21:19
1
reto wrote:
If |5x-5|>x-1, which of the following must be true?

A. x<1
B. x>1
C. x>5
D. x<5
E. None of the above


This equation can be done by using Mod property.

However a simpler way to do it is as follows:

|5x-5|>x-1
take 5 common, left hand side becomes

5 * |x-1|
say |x-1| = y

Question then becomes:

Is 5|y| > y?

|y| --> always positive.

If y is a positive value, then

Is 5|y| > y? --> is always true.

similarly if y is a negative value, even then

Is 5|y| > y? --> is always true.

Only when y = 0, does this not hold good.


Both A and B can be true, we are not sure. so we cant say that always A will be true or always B will be true.

E is the answer.
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Re: If |5x-5|>x-1, which of the following must be true?  [#permalink]

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New post 09 Jun 2016, 21:26
1
mup05ro wrote:
Bunuel wrote:
reto wrote:
If |5x-5|>x-1, which of the following must be true?

A. x<1
B. x>1
C. x>5
D. x<5
E. None of the above


\(|5x-5|>x-1\);

Factor out 5: \(5*|x-1|>x-1\). Notice here that LHS must more than or equal to 0.

If x-1 is negative, then (LHS=positive) > (RHS=negative);
If x-1 is positive, then (LHS=5 times some positive value) > (RHS = that positive positive).
If x-1 is 0 (so if x=1), then LHS = RHS.

Therefore, \(|5x-5|>x-1\) holds true for any value of x, but 1.

Answer: E.




Bunuel,

I did it in the following way

when x>0
5x-5>x-1
4x-4>0
4(x-1)>0
x>1


when x<0
-5x+5>x-1
-6x+6>0
x<1

Now how do i approach the problem?
Since I have two different ranges for x, I can say neither must be true??


x > 0 and x < 0 have no role to play in this question. The ranges you must consider are (x - 1) >= 0 and (x - 1) < 0.

I have explained why here: http://www.veritasprep.com/blog/2014/06 ... -the-gmat/
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Re: If |5x-5|>x-1, which of the following must be true?  [#permalink]

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New post 04 Nov 2017, 11:10
1
reto wrote:
If |5x-5|>x-1, which of the following must be true?

A. x<1
B. x>1
C. x>5
D. x<5
E. None of the above


I think the main nuance here is "which of the following must be true". Not "can, could".
It is pretty obvious but since nobody mentioned it...

Maybe this is the reson why many people choose B or even A.
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If |5x-5|>x-1, which of the following must be true?  [#permalink]

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New post 02 Jan 2019, 04:32
1
applebear wrote:
Bunuel wrote:
reto wrote:
If |5x-5|>x-1, which of the following must be true?

A. x<1
B. x>1
C. x>5
D. x<5
E. None of the above


\(|5x-5|>x-1\);

Factor out 5: \(5*|x-1|>x-1\). Notice here that LHS must more than or equal to 0.

If x-1 is negative, then (LHS=positive) > (RHS=negative);
If x-1 is positive, then (LHS=5 times some positive value) > (RHS = that positive positive).
If x-1 is 0 (so if x=1), then LHS = RHS.

Therefore, \(|5x-5|>x-1\) holds true for any value of x, but 1.

Answer: E.

in this case, shouldn't both the answers A and B be correct? because both of them must be true for the inequality to exist? can anyone please help me out? :sad:


Look.
If you choose option A. x > 1 must be true, you will be wrong because x can be equal to zero for example -----> so x need not be more than 1
If you choose option B. x < 1 must be true, the same
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Re: If |5x-5|>x-1, which of the following must be true?  [#permalink]

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New post 09 Jun 2016, 19:49
Bunuel wrote:
reto wrote:
If |5x-5|>x-1, which of the following must be true?

A. x<1
B. x>1
C. x>5
D. x<5
E. None of the above


\(|5x-5|>x-1\);

Factor out 5: \(5*|x-1|>x-1\). Notice here that LHS must more than or equal to 0.

If x-1 is negative, then (LHS=positive) > (RHS=negative);
If x-1 is positive, then (LHS=5 times some positive value) > (RHS = that positive positive).
If x-1 is 0 (so if x=1), then LHS = RHS.

Therefore, \(|5x-5|>x-1\) holds true for any value of x, but 1.

Answer: E.




Bunuel,

I did it in the following way

when x>0
5x-5>x-1
4x-4>0
4(x-1)>0
x>1


when x<0
-5x+5>x-1
-6x+6>0
x<1

Now how do i approach the problem?
Since I have two different ranges for x, I can say neither must be true??
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Re: If |5x-5|>x-1, which of the following must be true?  [#permalink]

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New post 10 Jun 2016, 03:23
1
VeritasPrepKarishma wrote:
mup05ro wrote:
reto wrote:
If |5x-5|>x-1, which of the following must be true?

A. x<1
B. x>1
C. x>5
D. x<5
E. None of the above






Bunuel,

I did it in the following way

when x>0
5x-5>x-1
4x-4>0
4(x-1)>0
x>1


when x<0
-5x+5>x-1
-6x+6>0
x<1

Now how do i approach the problem?
Since I have two different ranges for x, I can say neither must be true??


x > 0 and x < 0 have no role to play in this question. The ranges you must consider are (x - 1) >= 0 and (x - 1) < 0.



thank you karishma
now that from (x - 1) >= 0 and (x - 1) < 0 we know x>=1 and x<1 , what do we understand?

should I think that since x cannot be both greater than and less than 1, neither is correct?
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If |5x-5|>x-1, which of the following must be true?  [#permalink]

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New post Updated on: 07 Nov 2017, 08:11
mup05ro wrote:
Bunuel wrote:
reto wrote:
If |5x-5|>x-1, which of the following must be true?

A. x<1
B. x>1
C. x>5
D. x<5
E. None of the above


\(|5x-5|>x-1\);

Factor out 5: \(5*|x-1|>x-1\). Notice here that LHS must more than or equal to 0.

If x-1 is negative, then (LHS=positive) > (RHS=negative);
If x-1 is positive, then (LHS=5 times some positive value) > (RHS = that positive positive).
If x-1 is 0 (so if x=1), then LHS = RHS.

Therefore, \(|5x-5|>x-1\) holds true for any value of x, but 1.

Answer: E.




Bunuel,

I did it in the following way

when x>0
5x-5>x-1
4x-4>0
4(x-1)>0
x>1


when x<0
-5x+5>x-1
-6x+6>0
x<1

Now how do i approach the problem?
Since I have two different ranges for x, I can say neither must be true??

Originally posted by testcracker on 09 Aug 2017, 07:34.
Last edited by testcracker on 07 Nov 2017, 08:11, edited 1 time in total.
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Re: If |5x-5|>x-1, which of the following must be true?  [#permalink]

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New post 01 Jan 2019, 23:52
Bunuel wrote:
reto wrote:
If |5x-5|>x-1, which of the following must be true?

A. x<1
B. x>1
C. x>5
D. x<5
E. None of the above


\(|5x-5|>x-1\);

Factor out 5: \(5*|x-1|>x-1\). Notice here that LHS must more than or equal to 0.

If x-1 is negative, then (LHS=positive) > (RHS=negative);
If x-1 is positive, then (LHS=5 times some positive value) > (RHS = that positive positive).
If x-1 is 0 (so if x=1), then LHS = RHS.

Therefore, \(|5x-5|>x-1\) holds true for any value of x, but 1.

Answer: E.

in this case, shouldn't both the answers A and B be correct? because both of them must be true for the inequality to exist? can anyone please help me out? :sad:
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Re: If |5x-5|>x-1, which of the following must be true?  [#permalink]

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New post 02 Aug 2019, 15:51
how can x+1>=0? that would mean x=1 is an acceptable solution, which it is not.
That said, don't most absolute value problems exist on a range? Unless the answer offers both ranges as a single selection, we are simply supposed to ignore the fact that the "right" answers are both up there? Definitely feels more like a logic trap if so.
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Re: If |5x-5|>x-1, which of the following must be true?   [#permalink] 02 Aug 2019, 15:51
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