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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.

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.

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.

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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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:

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

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):

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

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):