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Is M < 0? 1) -M = |-M| 2) M^2 = 9

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Is M < 0? 1) -M = |-M| 2) M^2 = 9 [#permalink] New post 25 Feb 2010, 19:49
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A
B
C
D
E

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  5% (low)

Question Stats:

80% (01:26) correct 20% (00:40) wrong based on 10 sessions
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?
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Re: M01, Question 17 on the GClub tests [#permalink] New post 25 Feb 2010, 21:32
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.
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Re: M01, Question 17 on the GClub tests [#permalink] New post 12 Mar 2010, 01:53
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?
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Re: M01, Question 17 on the GClub tests [#permalink] New post 12 Mar 2010, 15:46
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.
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Re: M01, Question 17 on the GClub tests [#permalink] New post 13 Mar 2010, 17:45
Is M < 0?

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

1) M is either 0 or negative, insufficient

2) M can be either positive or negative, insufficient

1 and 2, taken together, M is negative, sufficient

Thus, C.
Re: M01, Question 17 on the GClub tests   [#permalink] 13 Mar 2010, 17:45
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