If x= +-|x|,then which of following could be true?
I x=0
II x>0
III x<0
Answer is I and III ,Can anyone explain me the reasoning behind it?
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Akashdeep13
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Hi Akashdeep13,
When posting GMAT questions, you should make sure to post the ENTIRE prompt (including the 5 answer choices). In many cases, the answers themselves provide a clue as to how to go about solving the problem.
Here, I think that there's a typo in your post. I assume that the equation is supposed to be...
X = -|X|
You can approach this prompt with logic and Number Properties or by TESTing VALUES.
Since the absolute value of a number will either be 0 or positive, when you put a "-" in front of that math, you could end up with either a 0 OR a negative result. As such, the given equation means that X could either be 0 OR X could be negative. So Roman Numerals I and III could be true.
GMAT assassins aren't born, they're made,
Rich
When posting GMAT questions, you should make sure to post the ENTIRE prompt (including the 5 answer choices). In many cases, the answers themselves provide a clue as to how to go about solving the problem.
Here, I think that there's a typo in your post. I assume that the equation is supposed to be...
X = -|X|
You can approach this prompt with logic and Number Properties or by TESTing VALUES.
Since the absolute value of a number will either be 0 or positive, when you put a "-" in front of that math, you could end up with either a 0 OR a negative result. As such, the given equation means that X could either be 0 OR X could be negative. So Roman Numerals I and III could be true.
GMAT assassins aren't born, they're made,
Rich
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OptimusPrep
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x= -|x|Akashdeep13 wrote:If x= +-|x|,then which of following could be true?
I x=0
II x>0
III x<0
Answer is I and III ,Can anyone explain me the reasoning behind it?
Modulus of a number means the distance of a number from the origin.
Hence |x| will always be positive or 0
and - |x| will always be negative or 0
Statements I and III are correct.
Does this help?
What problems were you facing with the reasoning?
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Akashdeep13
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Hi ankur,
I am not unable to understand how you derived that. Can you please a little more on how we arrive at that conclusion?
I am not unable to understand how you derived that. Can you please a little more on how we arrive at that conclusion?
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800_or_bust
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The absolute value of any value x must be greater than or equal zero (0, only in the case where x = 0). Multiplying a positive number by -1 as implied by the negative sign in front of the absolute value function will always yield a negative number. Therefore, x must be less than or equal to zero.Akashdeep13 wrote:Hi ankur,
I am not unable to understand how you derived that. Can you please a little more on how we arrive at that conclusion?
800 or bust!
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Akashdeep13
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800_or_bust wrote:The absolute value of any value x must be greater than or equal zero (0, only in the case where x = 0). Multiplying a positive number by -1 as implied by the negative sign in front of the absolute value function will always yield a negative number. Therefore, x must be less than or equal to zero.Akashdeep13 wrote:Hi ankur,
I am not unable to understand how you derived that. Can you please a little more on how we arrive at that conclusion?
Hi
800_or_bust wrote:,
I got the answer if there was a negative sign in the question .But positive sign in the given question. Doesn't it mean to say we have to check for x= +|x| also, in that case x<0 will fail. Correct me if i am wrong. Or there is a typo in the question.
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OptimusPrep
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|x| is nothing but the magnitude of the value.Akashdeep13 wrote:Hi ankur,
I am not unable to understand how you derived that. Can you please a little more on how we arrive at that conclusion?
For Ex: |-3| = 3 = |3|
Although I am not quite sure of what you are trying to say here,Akashdeep13 wrote: I got the answer if there was a negative sign in the question .But positive sign in the given question. Doesn't it mean to say we have to check for x= +|x| also, in that case x<0 will fail. Correct me if i am wrong. Or there is a typo in the question
But yes, there is a typo in the question.
It should read "If x= -|x|,then which of following could be true?"
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Matt@VeritasPrep
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|x| is never negative, so -|x| is never positive.
Since x = -|x|, x is never positive.
Hence x ≤ 0, and i and iii are both possible.
Since x = -|x|, x is never positive.
Hence x ≤ 0, and i and iii are both possible.
