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PS: Absolute values

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PS: Absolute values [#permalink]

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New post 08 Jan 2009, 17:57
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X/|X| < X.

Which of the following must be true about X? (X does not equal 0)

X>1
X>-1
|X|<1
|X|=1
|X|^2>1

I tried plugging in numbers, and got the answer incorrectly.

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Re: PS: Absolute values [#permalink]

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New post 08 Jan 2009, 20:47
bigfernhead wrote:
X/|X| < X.

Which of the following must be true about X? (X does not equal 0)

X>1
X>-1
|X|<1
|X|=1
|X|^2>1

I tried plugging in numbers, and got the answer incorrectly.



I think A.

When X > 1, left side always becomes 1, which is less than X

Another way is:

\(\frac{X}{|X|} < X\)
\(\frac{X}{|X|} - X < 0\)
\(X - |X|X < 0\)
\(X(1-|X|) < 0\)

==> X<0 or 1-|X|<0
Solving further, we have three possible values: X<0, X>1, X<-1

But, the given condition satisfied only for X>1

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Re: PS: Absolute values [#permalink]

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New post 08 Jan 2009, 21:20
It should be A.

If X is +ve , X/|X| = 1 and if X is -ve then X/|X| = -1

So, X/|X| < X is true for all +ve X > 1 and for all -ve X so that -1 <X<0

A is true

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Re: PS: Absolute values [#permalink]

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New post 08 Jan 2009, 21:59
square both sides

(X^2/X^2)< X^2 OR (X^2)>1

If you remove inequality, X would be +/-1. So, X>1 to satisfy the condition

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Re: PS: Absolute values [#permalink]

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New post 08 Jan 2009, 22:07
bigfernhead wrote:
X/|X| < X.

Which of the following must be true about X? (X does not equal 0)

X>1
X>-1
|X|<1
|X|=1
|X|^2>1

I tried plugging in numbers, and got the answer incorrectly.


bigfernhead wont be happy until he/she gets explanation for B. :lol:
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Re: PS: Absolute values [#permalink]

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New post 09 Jan 2009, 08:18
Lol. Bingo :-)

Sorry, but the OA is not A.

GMAT TIGER wrote:
bigfernhead wrote:
X/|X| < X.

Which of the following must be true about X? (X does not equal 0)

X>1
X>-1
|X|<1
|X|=1
|X|^2>1

I tried plugging in numbers, and got the answer incorrectly.


bigfernhead wont be happy until he/she gets explanation for B. :lol:

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Re: PS: Absolute values [#permalink]

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New post 09 Jan 2009, 20:05
defenitely B

x/x = 1 or x/-x=-1, so 1<x or -1<x, so it is always true that x>-1

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Re: PS: Absolute values [#permalink]

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New post 09 Jan 2009, 23:26
Yeh, the answer should be (B).
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Re: PS: Absolute values [#permalink]

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New post 12 Jan 2009, 23:49
How can (B) be correct? Try substituting x = 0.5

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Re: PS: Absolute values [#permalink]

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New post 13 Jan 2009, 00:55
linau1982 wrote:
defenitely B

x/x = 1 or x/-x=-1, so 1<x or -1<x, so it is always true that x>-1


IMO, if x>1 or x> -1, it will be always true that x>1

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Re: PS: Absolute values [#permalink]

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New post 15 Jan 2009, 05:54
i think it should be E

X/ |X| < X
i.e 1/|X| < 1 (Since X is not equal to 0, we can cancel at both end)
i.e 1 < |X|
i.e |X| > 1
squaring both sides we get
|X|^2 > 1

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Re: PS: Absolute values [#permalink]

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New post 15 Jan 2009, 09:07
lionell84 wrote:
How can (B) be correct? Try substituting x = 0.5


This is not a well worded question. Because X can also = -0.5
So it doesn't always have to be >1. Nevertheless >1 is the option that always holds true, compared to other choices.
Answer is A.

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Re: PS: Absolute values [#permalink]

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New post 15 Jan 2009, 09:46
x-ALI-x wrote:
lionell84 wrote:
How can (B) be correct? Try substituting x = 0.5


This is not a well worded question. Because X can also = -0.5
So it doesn't always have to be >1. Nevertheless >1 is the option that always holds true, compared to other choices.
Answer is A.


I agree. I am unable to make B the right answer with Substitution. Only A seems to be the right answer. Please explain if the answer is different.

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Re: PS: Absolute values [#permalink]

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New post 15 Jan 2009, 11:18
Vemuri wrote:
x-ALI-x wrote:
lionell84 wrote:
How can (B) be correct? Try substituting x = 0.5


This is not a well worded question. Because X can also = -0.5
So it doesn't always have to be >1. Nevertheless >1 is the option that always holds true, compared to other choices.
Answer is A.


I agree. I am unable to make B the right answer with Substitution. Only A seems to be the right answer. Please explain if the answer is different.


If you plug in 1, it proves that B is not necessarily true.

It must be A

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Re: PS: Absolute values [#permalink]

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New post 15 Jan 2009, 14:47
lionell84 wrote:
How can (B) be correct? Try substituting x = 0.5


Why does it matter that x can't be 0.5? No matter what value x can have, x certainly must be greater than -1. The question asks *what must be true*; it does not ask 'which of the following gives every possible value of x and no other values'. There's quite a big difference. Even if we had been able to conclude that x was equal to 2 billion, it certainly then must be true that x is greater than -1. It doesn't make any difference whether x is allowed to be 0.5 or not.

alpha_plus_gamma wrote:
linau1982 wrote:
defenitely B

x/x = 1 or x/-x=-1, so 1<x or -1<x, so it is always true that x>-1


IMO, if x>1 or x> -1, it will be always true that x>1


If x > -1, it is not always true that x > 1. x might be -0.3, for example.

B is certainly the correct answer to this question.
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Re: PS: Absolute values [#permalink]

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New post 15 Jan 2009, 15:54
EDIT: I was an idiot for not noticing it the first time, if x>1 then x > -1, thus

x>1 is the answer

You have to assume abs(x) can be either positive or negative. abs(x) = x if x>=0, also abs(x) = -x if x < 0. Since both conditions have to be met, we have the following:

Assuming x = positive:

x/x < x; or 1<x

Assuming x = negative

x/-x <x; or -1<x

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Re: PS: Absolute values [#permalink]

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New post 15 Jan 2009, 16:03
IanStewart wrote:
lionell84 wrote:
How can (B) be correct? Try substituting x = 0.5


Why does it matter that x can't be 0.5? No matter what value x can have, x certainly must be greater than -1. The question asks *what must be true*; it does not ask 'which of the following gives every possible value of x'. There's quite a big difference. Even if we had been able to conclude that x was equal to 2 billion, it certainly then must be true that x is greater than -1. It doesn't make any difference whether x is allowed to be 0.5 or not.

alpha_plus_gamma wrote:
linau1982 wrote:
defenitely B

x/x = 1 or x/-x=-1, so 1<x or -1<x, so it is always true that x>-1


IMO, if x>1 or x> -1, it will be always true that x>1


If x > -1, it is not always true that x > 1. x might be -0.3, for example.

B is certainly the correct answer to this question.


B is not the answer...

0.5 > -1

yet the equation would read 0.5>0.5/abs(0.5) or 0.5 > 1, which is false. Answer is A. Both inequalities x>-1 and x>1 has to be satisfied, thus it must be x>1

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New post 15 Jan 2009, 16:21
so can we all agree that the correct answer is A?

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Re: PS: Absolute values [#permalink]

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New post 15 Jan 2009, 16:50
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chicagocubsrule wrote:
so can we all agree that the correct answer is A?


kevin0118 wrote:
B is not the answer...


The answer is B. Those who think the answer is A are misunderstanding the question. The question is *not* asking for the solution set for x. It is simply asking what must be true of x. I think we can agree that if x/|x| < x, then either -1 < x < 0, or 1 < x. If that's true, then no matter what x is, x is certainly greater than -1; that must be true. B.

It is of no importance that x cannot equal 0.5. If you think that's relevant to the question, you're not answering the question that's being asked -- you're answering the question "under what conditions will x/|x| always be true?" Notice that's the precise opposite question to the one being asked.

It should be clear, in any case, that A is incorrect; it does not need to be true that x > 1, because x could be -0.5, for example.

I explained, with a different example, here for anyone who remains unconvinced (scroll way down):

http://www.beatthegmat.com/xs-good-one-t27185.html
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Re: PS: Absolute values [#permalink]

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New post 15 Jan 2009, 19:51
bigfernhead wrote:
X/|X| < X.

Which of the following must be true about X? (X does not equal 0)

X>1
X>-1
|X|<1
|X|=1
|X|^2>1

I tried plugging in numbers, and got the answer incorrectly.


If x = 0.5, statement X/|X| < X does not hold true. So 0.5 is out of the scope. Any values 0 or > 0 but 1 or smaller than 1 are out of scope. But x can be >-1 but smaller than 0. Similarly any value > 1 is possible for x.

So that bring x > -1.

IanStewart wrote:
chicagocubsrule wrote:
so can we all agree that the correct answer is A?


kevin0118 wrote:
B is not the answer...


The answer is B. Those who think the answer is A are misunderstanding the question. The question is *not* asking for the solution set for x. It is simply asking what must be true of x. I think we can agree that if x/|x| < x, then either -1 < x < 0, or 1 < x. If that's true, then no matter what x is, x is certainly greater than -1; that must be true. B.

It is of no importance that x cannot equal 0.5. If you think that's relevant to the question, you're not answering the question that's being asked -- you're answering the question "under what conditions will x/|x| always be true?" Notice that's the precise opposite question to the one being asked.

It should be clear, in any case, that A is incorrect; it does not need to be true that x > 1, because x could be -0.5, for example.

I explained, with a different example, here for anyone who remains unconvinced (scroll way down):

http://www.beatthegmat.com/xs-good-one-t27185.html

:cool

Enough said Ian. 8-)
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Re: PS: Absolute values   [#permalink] 15 Jan 2009, 19:51

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