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Retired Moderator Joined: 29 Apr 2015
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If |5x-5|>x-1, which of the following must be true?  [#permalink]

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27 00:00

Difficulty:   75% (hard)

Question Stats: 52% (01:46) correct 48% (01:44) wrong based on 566 sessions

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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
Math Expert V
Joined: 02 Sep 2009
Posts: 60555
Re: If |5x-5|>x-1, which of the following must be true?  [#permalink]

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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

$$|5x-5|>x-1$$;

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.

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

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2
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

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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Posts: 9
Re: If |5x-5|>x-1, which of the following must be true?  [#permalink]

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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.

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??
Manager  Joined: 18 Jan 2010
Posts: 238
Re: If |5x-5|>x-1, which of the following must be true?  [#permalink]

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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.

Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9998
Location: Pune, India
Re: If |5x-5|>x-1, which of the following must be true?  [#permalink]

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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.

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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Veritas Prep GMAT Instructor

Intern  Joined: 01 Feb 2015
Posts: 9
Re: If |5x-5|>x-1, which of the following must be true?  [#permalink]

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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?
Senior Manager  G
Status: love the club...
Joined: 24 Mar 2015
Posts: 260
If |5x-5|>x-1, which of the following must be true?  [#permalink]

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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.

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.
Senior Manager  P
Joined: 26 Jun 2017
Posts: 390
Location: Russian Federation
Concentration: General Management, Strategy
WE: Information Technology (Other)
Re: If |5x-5|>x-1, which of the following must be true?  [#permalink]

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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.
Manager  B
Joined: 16 Oct 2017
Posts: 52
Location: India
GPA: 4
Re: If |5x-5|>x-1, which of the following must be true?  [#permalink]

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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.

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? Senior Manager  P
Joined: 26 Jun 2017
Posts: 390
Location: Russian Federation
Concentration: General Management, Strategy
WE: Information Technology (Other)
If |5x-5|>x-1, which of the following must be true?  [#permalink]

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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.

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? 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
Intern  B
Joined: 30 Jun 2019
Posts: 9
Re: If |5x-5|>x-1, which of the following must be true?  [#permalink]

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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. Re: If |5x-5|>x-1, which of the following must be true?   [#permalink] 02 Aug 2019, 15:51
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