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I kind of don't agree to the OE to this question. When 0 is neither positive nor negative such as +0 or -0 don't even exist then, what will be value of |0|? If so, can M ever be 0 at all, based on the equation given in stmt 1?

Let's then consider squaring on both sides, that leaves us with (M - M)(2M) = 0. So M essentially has to be 0, or absolutely anything, is the final output of the statement. Then M being +3 or -3 from stmt 2 does not solve our situation. M is anything from stmt 1, can be positive or negative and unsure of it's value even from stmt 2.

As per both my explanations above, E should have been the answer?

Re: Is M < 0? 1) -M = |-M| 2) M^2 = 9 [#permalink]

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25 Feb 2010, 22:32

Is M < 0?

1) -M = |-M| M<=0 -> any negative value of M, the equation holds good M=-3, RHS = 3 and LHS is 3. 0 coz if M=0, both sides are 0. Not sufficient 2) M^2 = 9. M=+3 or -3 Not sufficient

Combining M=-3

C

Barney - yes 0 is neither positive nor negative and you wont get a question asking what is |-0| .. but if a variable is given and the variable is of the kind y=-x, for all x, then for x=0, we say y = 0 --- do you say for x=0, there is no such value as -0 so this is INVALID? No right -- we can substitute 0 in a variable and it the value by chance comes up as -0, the value would be taken as 0.

Re: Is M < 0? 1) -M = |-M| 2) M^2 = 9 [#permalink]

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12 Mar 2010, 02:53

BarneyStinson wrote:

Is M < 0?

1) -M = |-M| 2) M^2 = 9.

I kind of don't agree to the OE to this question. When 0 is neither positive nor negative such as +0 or -0 don't even exist then, what will be value of |0|? If so, can M ever be 0 at all, based on the equation given in stmt 1?

Let's then consider squaring on both sides, that leaves us with (M - M)(2M) = 0. So M essentially has to be 0, or absolutely anything, is the final output of the statement. Then M being +3 or -3 from stmt 2 does not solve our situation. M is anything from stmt 1, can be positive or negative and unsure of it's value even from stmt 2.

As per both my explanations above, E should have been the answer?

stmt1: -M = |-M| there can be two cases -M = -M or -M = M => 2M = 0 => M= 0 So, M < 0 is not true

stmt2: M^2 = 9 => M = 3, -3 it is not suff not answering the question. Should not A be the answer of this question? |x| is actually the amount of x irrespective of its sign. Usually it is used to calculate distances on the coordinates. So, |0| means something with no value right? _________________

Re: Is M < 0? 1) -M = |-M| 2) M^2 = 9 [#permalink]

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12 Mar 2010, 16:46

sidhu4u wrote:

BarneyStinson wrote:

Is M < 0?

1) -M = |-M| 2) M^2 = 9.

I kind of don't agree to the OE to this question. When 0 is neither positive nor negative such as +0 or -0 don't even exist then, what will be value of |0|? If so, can M ever be 0 at all, based on the equation given in stmt 1?

Let's then consider squaring on both sides, that leaves us with (M - M)(2M) = 0. So M essentially has to be 0, or absolutely anything, is the final output of the statement. Then M being +3 or -3 from stmt 2 does not solve our situation. M is anything from stmt 1, can be positive or negative and unsure of it's value even from stmt 2.

As per both my explanations above, E should have been the answer?

stmt1: -M = |-M| there can be two cases -M = -M or -M = M => 2M = 0 => M= 0 So, M < 0 is not true

stmt2: M^2 = 9 => M = 3, -3 it is not suff not answering the question. Should not A be the answer of this question? |x| is actually the amount of x irrespective of its sign. Usually it is used to calculate distances on the coordinates. So, |0| means something with no value right?

value of |0| is 0. inequality questions hinges on the 0 values a lot. so dont ignore those.

Re: Is M < 0? 1) -M = |-M| 2) M^2 = 9 [#permalink]

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09 Sep 2015, 21:08

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I kind of don't agree to the OE to this question. When 0 is neither positive nor negative such as +0 or -0 don't even exist then, what will be value of |0|? If so, can M ever be 0 at all, based on the equation given in stmt 1?

Let's then consider squaring on both sides, that leaves us with (M - M)(2M) = 0. So M essentially has to be 0, or absolutely anything, is the final output of the statement. Then M being +3 or -3 from stmt 2 does not solve our situation. M is anything from stmt 1, can be positive or negative and unsure of it's value even from stmt 2.

As per both my explanations above, E should have been the answer?

Is \(m<0\)?

(1) \(-m=|-m|\) --> first of all \(|-m|=|m|\), (for example: \(|-3|=|3|=3\)), so we have \(-m=|m|\), as RHS is absolute value which is always non-negative, then LHS, \({-m}\) must also be non-negative --> \(-m\geq{0}\) --> \(m\leq{0}\), so \(m\) could be either negative or zero. Not sufficient.

(2) \(m^2=9\) --> \(m=3=positive\) or \(m=-3=negative\). Not sufficient.

(1)+(2) Intersection of the values from (1) and (2) is \(m=-3=negative\), hence answer to the question "is \(m<\)0" is YES. Sufficient.

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