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PS: Absolute values [#permalink]
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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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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: \(\frac{X}{X} < X\) \(\frac{X}{X}  X < 0\) \(X  XX < 0\) \(X(1X) < 0\) ==> X<0 or 1X<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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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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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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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.
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Re: PS: Absolute values [#permalink]
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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.



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Re: PS: Absolute values [#permalink]
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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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09 Jan 2009, 23:26
Yeh, the answer should be (B).
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Re: PS: Absolute values [#permalink]
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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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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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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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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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15 Jan 2009, 09:46
xALIx 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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15 Jan 2009, 11:18
Vemuri wrote: xALIx 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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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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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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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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Re: PS: Absolute values [#permalink]
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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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15 Jan 2009, 16:50
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/xsgoodonet27185.html
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Re: PS: Absolute values [#permalink]
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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/xsgoodonet27185.html Enough said Ian.
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