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punzo
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Post subject: If x is not equal to 0, is |x| less than 1?  Posted: Thu Feb 25, 2010 5:49 am |
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If x is not equal to 0, is |x| less than 1?
(1) x/|x| < x
(2) |x| > x
My explaination for Statement 1 is
x / lxl < x
x< x. lxl
If x is +ve
x < x.x
x > 1
IF x is -ve
-x < -x.lxl
Div both sides by-1
x > x. lxl
x < 1
Therefore, insufficient
Is there something wrong with my explaination??
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sandeepgupta176
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Post subject: Re: If x is not equal to 0, is |x| less than 1? Posted: Thu Feb 25, 2010 6:32 am |
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May be we can go through in this way
in statement 1
x / [x] < x
now reciprocating
[x]/x > 1/x
cancelling x in denominator
[x] > 1
which shows its not less than 1.
Tell me if i am incorrect
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htchanit
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Post subject: Re: If x is not equal to 0, is |x| less than 1? Posted: Thu Feb 25, 2010 10:13 pm |
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Hello, In my opinion, reciprocating is somehow dangerous and eliminating 1/x without knowing 1/x negative or positive is not right. since x < x.[x] and x not equal 0 : 1. if x >0 then 1 < [x] (eliminate x both sides) 2. if x <0 then 1 > [x] (eliminate x both sides) => cant give final result of [x] => (insufficient) On the other hand, if "[x] > x" => "x < 0" => (insufficient) So I will pick "C" (both together makes anything) :D ! sandeepgupta176 wrote: May be we can go through in this way
in statement 1
x / [x] < x
now reciprocating
[x]/x > 1/x
cancelling x in denominator
[x] > 1
which shows its not less than 1.
Tell me if i am incorrect
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shailesh244
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Post subject: Re: If x is not equal to 0, is |x| less than 1? Posted: Fri Feb 26, 2010 5:47 am |
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statement : 1
x/[x]< x
x=2 ,so 2/[2]< 2
we cannot take any -ve value as doing so will result as below
x= -3 ,so -3/[-3] = -3/3 = -1 < -3 (which is not true)
so we conclude that x should be positive and greater equal to 2
if x=1, 1/[1]=1 < 1 (which is also not true)
so x >=2
So statement 1 is Sufficient as answer to [x]< 1 is NO.
Statement 2 :
[x]> x
if x= -1 , [-1]>1 1>1 (which cannot be possible) NO
x=-2, [-2]> -2 --->2>-2 Yes
1 Yes and 1 No so insufficient.
My Answer would be A. Please suggest flaws if any. Thanks.
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shailesh244
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Post subject: Re: If x is not equal to 0, is |x| less than 1? Posted: Fri Feb 26, 2010 5:48 am |
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Also we should abstain from dividing / multiplying as we do not know the signs of the variable.
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htchanit
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Post subject: Re: If x is not equal to 0, is |x| less than 1? Posted: Fri Feb 26, 2010 10:59 pm |
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Hello, I suggest you to plug-in with x = -1/2 to see let's try: x/[x] < x <=> (-1/2)/(1/2) < -1/2 clearly : [-1/2] < 1 , in this case [x] < 1 shailesh244 wrote: statement : 1
x/[x]< x
x=2 ,so 2/[2]< 2
we cannot take any -ve value as doing so will result as below
x= -3 ,so -3/[-3] = -3/3 = -1 < -3 (which is not true)
so we conclude that x should be positive and greater equal to 2
if x=1, 1/[1]=1 < 1 (which is also not true)
so x >=2
So statement 1 is Sufficient as answer to [x]< 1 is NO.
Statement 2 :
[x]> x
if x= -1 , [-1]>1 1>1 (which cannot be possible) NO
x=-2, [-2]> -2 --->2>-2 Yes
1 Yes and 1 No so insufficient.
My Answer would be A. Please suggest flaws if any. Thanks.
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Ben Ku
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Post subject: Re: If x is not equal to 0, is |x| less than 1? Posted: Tue Mar 30, 2010 7:27 pm |
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Posts: 824
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punzo wrote: If x is not equal to 0, is |x| less than 1?
(1) x/|x| < x
(2) |x| > x
My explaination for Statement 1 is
x / lxl < x
x< x. lxl
If x is +ve
x < x.x
x > 1
IF x is -ve
-x < -x.lxl
Div both sides by-1
x > x. lxl
x < 1
Therefore, insufficient
Is there something wrong with my explaination?? This response is fine. The key for this response is if x < x^2 and x > 0, then x > 1. If x < x^2, then 0 < x < 1.
_________________
Ben Ku
Instructor
ManhattanGMAT
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Ben Ku
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Post subject: Re: If x is not equal to 0, is |x| less than 1? Posted: Tue Mar 30, 2010 7:28 pm |
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Posts: 824
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sandeepgupta176 wrote: May be we can go through in this way
in statement 1
x / [x] < x
now reciprocating
[x]/x > 1/x
cancelling x in denominator
[x] > 1
which shows its not less than 1.
Tell me if i am incorrect The process of "cancelling x in denominator" is the same as multiplying both sides by x. Since we don't know whether x is positive or negative, we cannot do this.
_________________
Ben Ku
Instructor
ManhattanGMAT
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Ben Ku
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Post subject: Re: If x is not equal to 0, is |x| less than 1? Posted: Tue Mar 30, 2010 7:30 pm |
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Posts: 824
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htchanit wrote: Hello, In my opinion, reciprocating is somehow dangerous and eliminating 1/x without knowing 1/x negative or positive is not right. since x < x.[x] and x not equal 0 : 1. if x >0 then 1 < [x] (eliminate x both sides) 2. if x <0 then 1 > [x] (eliminate x both sides) => cant give final result of [x] => (insufficient) On the other hand, if "[x] > x" => "x < 0" => (insufficient) So I will pick "C" (both together makes anything) :D ! sandeepgupta176 wrote: May be we can go through in this way
in statement 1
x / [x] < x
now reciprocating
[x]/x > 1/x
cancelling x in denominator
[x] > 1
which shows its not less than 1.
Tell me if i am incorrect This solution is good!
_________________
Ben Ku
Instructor
ManhattanGMAT
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Ben Ku
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Post subject: Re: If x is not equal to 0, is |x| less than 1? Posted: Tue Mar 30, 2010 7:32 pm |
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Posts: 824
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shailesh244 wrote: statement : 1
x/[x]< x
x=2 ,so 2/[2]< 2
we cannot take any -ve value as doing so will result as below
x= -3 ,so -3/[-3] = -3/3 = -1 < -3 (which is not true)
so we conclude that x should be positive and greater equal to 2
if x=1, 1/[1]=1 < 1 (which is also not true)
so x >=2
So statement 1 is Sufficient as answer to [x]< 1 is NO.
Statement 2 :
[x]> x
if x= -1 , [-1]>1 1>1 (which cannot be possible) NO
x=-2, [-2]> -2 --->2>-2 Yes
1 Yes and 1 No so insufficient.
My Answer would be A. Please suggest flaws if any. Thanks. The problem with trying different numbers is choosing the number to choose. We tried x = 2, 1, and -3. However, this doesn't represent all possible values for x. Working out the algebra and using theory will help getting to the answer. We cannot conclude that x >= 2.
_________________
Ben Ku
Instructor
ManhattanGMAT
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sprparvathy
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Post subject: Re: If x is not equal to 0, is |x| less than 1? Posted: Sat Jun 05, 2010 11:36 am |
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May be I am asking this too late? Is the answer C?
Combining st 1 and 2 we know that X<1 and X<0. However [X] need not be less than 1 right? Then how can C be the answer?
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vijaykumar.kondepudi
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Post subject: Re: If x is not equal to 0, is |x| less than 1? Posted: Mon Jun 07, 2010 12:22 am |
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Yes the Answer is C.
Check out htchanit solution.
Combiniing St1 and St2, we know that,
If x< 0, then |x| < 1. (NOT x < 1).
That gives you the required result.
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RonPurewal
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Post subject: Re: If x is not equal to 0, is |x| less than 1? Posted: Wed Jun 23, 2010 9:35 am |
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statement (2) means that x is negative.
this is not enough information to tell whether |x| is less than 1.
insufficient.
--
to interpret statement (1), note that the fraction x/|x| is equal to 1 for any positive value of x, and equal to -1 for any negative value of x.
therefore, to solve this equation, and just consider the positive and negative cases separately.
if x is a positive number, then this inequality can be rewritten as 1 < x.
if x is a negative number, then this inequality can be rewritten as -1 < x. since this only applies to negative values, we can amend this to give -1 < x < 0.
therefore, statement (1) means that EITHER x > 1 OR -1 < x < 0.
for the first possibility, |x| is greater than 1; for the second, |x| is less than 1. insufficient.
--
together:
the only interval that satisfies both statements is -1 < x < 0, in which all numbers satisfy |x| < 1.
sufficient.
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monira.linda
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Post subject: Re: If x is not equal to 0, is |x| less than 1? Posted: Sat May 14, 2011 4:09 pm |
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Hi,
After reading all explanations, I am still confused :-(
For statement 1, when X<0
We derived x/-x < x but if we are trying for x<0, then are not we suppose to change all Xs to -X like below:
-x/-x < -x => X<- 1
Pls help!!!
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jnelson0612
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Post subject: Re: If x is not equal to 0, is |x| less than 1? Posted: Sat May 14, 2011 10:10 pm |
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monira.linda wrote: Hi,
After reading all explanations, I am still confused :-(
For statement 1, when X<0
We derived x/-x < x but if we are trying for x<0, then are not we suppose to change all Xs to -X like below:
-x/-x < -x => X<- 1
Pls help!!! Okay, here's statement 1: (1) x/|x| < x Rather than do all the manipulation you suggest, which is scary considering that we have both an inequality and an absolute value sign, let's think about what is means when x is negative by plugging in a real number. Let's use x=-2. Thus: -2/|-2| < -2 which is: -2/2 < -2, or -1<-2. This is NOT true, so x cannot be a negative integer. You can test it out with other negative integers such as -1 and -5, for example, and see that this statement, which we have to regard as true, does not allow us to use negative integers, since they do not work out in the statement. Now test a fraction between -1 and 0 such as -1/2. Does -1/2 work in this statement? You will see that it does, so thus x cannot be a negative integer but CAN be between -1 and 0. This illustrates how testing numbers is often very valuable on data sufficiency.
_________________
Jamie Nelson
ManhattanGMAT Instructor
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