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Intern
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21 Nov 2009, 04:31
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Is M < 0 ?

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

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Senior Manager
Joined: 31 Aug 2009
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21 Nov 2009, 04:40
I'm not so good with modulus questions wrongs but here goes:

1) Need to consider the following cases.
If M > 0 then |-M|= M so this is not the case.
If M < 0 then
Left side: |-M| = |-(-M)| = M
Right side: -(-M) = M
So it is true for this case.
Not so sure about this one but if M = 0 then |-M| = -M = 0 so it is true for this case.
So because of M <= 0 then this is not suff. (Unless my last case is not true)

2) M^2 = 9 means M = |3| which is neg or pos. not suff.

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Manager
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21 Nov 2009, 05:28
gmat620 wrote:
Is M < 0 ?

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

Question Stem : Is M < 0 ?

St. (1) : (-M) = |(-M)|
Now, |-M| basically means this :
(a) When (-M) > 0, |(-M)| = (-M)
(b) When (-M) < 0, |(-M)| = -(-M)
Thus, for statement 1 to be valid, it would seem that (-M) must be greater than 0 which means M must be less than 0.
However, the value of M = 0 also satisfies this statement. Thus M <= 0.
Hence Statement is Insufficient.

St. (2) : M^2 = 9
This means that M = ±3
Therefore M can be positive or negative.
Statement Insufficient.

St. (1) and (2) together : M <= 0 , M = ± 3
The only value that satisfies both statements is - 3.
Thus we can conclude that M < 0.
Hence Sufficient.

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Click below to check out some great tips and tricks to help you deal with problems on Remainders!
http://gmatclub.com/forum/compilation-of-tips-and-tricks-to-deal-with-remainders-86714.html#p651942

1) Translating the English to Math : http://gmatclub.com/forum/word-problems-made-easy-87346.html

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21 Nov 2009, 05:34
gmat620 wrote:
Is M < 0 ?

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

First of all: absolute value NEVER NEGATIVE. Meaning that it can be zero or positive.

(1) -M=|-M|, as RHS (Right Hand Side) is never negative, LHS also must be >=0. So we get -M>=0 --> M<=0.

If M<=0 --> RHS=|-M|=|M|=-M --> -M=-M --> 0=0. Which means that equation - M = | - M | is always true for the values of M which satisfy M<=0.

But the question asks whether M is negative and we got that M is not positive. Hence not sufficient.

(2) M^2=9 --> M=3 or M=-3, two possible values of M, positive or negative. Not sufficient.

(1)+(2) M is not positive (M<=0), hence M can not me 3 --> so M=-3. Sufficient.

I guess confusing part was -M=|-M|.
First: |-x|=|x|.

Second: when you see: -x=|some expression|, you can say that x either negative or zero. When x is negative -x becomes positive, so LHS and RHS are both positive.
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Intern
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21 Nov 2009, 07:09
Thanks a lot friends....I am lucku to have you ppl around....Ok please confirm what I get from your explanation is correct or not

if -M > 0,
RHS : |-M| can be written as -M

Now we have LHS which is -M, so we have both side equal, this case is correct.

if -M < 0,
RHS : |-M | can be written as - (-M) = M
LHS: -M

so this cannot be correct because RHS != LHS

so first one i.e -M > 0 is correct

THanks one again for your precious time.

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21 Nov 2009, 07:27
gmat620 wrote:
Thanks a lot friends....I am lucku to have you ppl around....Ok please confirm what I get from your explanation is correct or not

if -M > 0,
RHS : |-M| can be written as -M

Now we have LHS which is -M, so we have both side equal, this case is correct.

if -M < 0,
RHS : |-M | can be written as - (-M) = M
LHS: -M

so this cannot be correct because RHS != LHS

so first one i.e -M > 0 is correct

THanks one again for your precious time.

First: |-M|=|M| ALWAYS. So when you see |-some expression|, you can just write |some expression|. It would be easier to proceed in most of the cases.

If M<0 --> |M|=-M
If M>0 --> |M|=M
If M=0 --> |M|=0
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21 Nov 2009, 07:40
gmat620 wrote:
Thanks a lot friends....I am lucku to have you ppl around....Ok please confirm what I get from your explanation is correct or not

if -M > 0, This means that M < 0
RHS : |-M| can be written as -M. Since M is less than 0, -M is a positive value.

Now we have LHS which is -M (also a positive value since M is negative), so we have both side equal (both sides are positive), this case is correct. (Not correct because the question stem asks if M is less than 0. However, in this case, M can be equal to 0 and still satisfy the statement).

if -M < 0, This means that M > 0
RHS : |-M | can be written as - (-M) = M This again means that RHS will be positive.
LHS: -M Sine M is greater than 0, -M will be less than 0.

so this cannot be correct because RHS != LHS . Yes. Because LHS is negative and RHS is positive.

so first one i.e -M > 0 is correct Again, it would be correct if we were asked Is M <=0. But we are asked specifically if M < 0. Since M can be less than 0 as well as 0, the question stem cannot be answered. Remember to always check the inequality with the value 0.

THanks one again for your precious time. Most Welcome.

I have just added details to your flow of thinking. It might be easier than trying to enforce my own. I do hope it helps.
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Click below to check out some great tips and tricks to help you deal with problems on Remainders!
http://gmatclub.com/forum/compilation-of-tips-and-tricks-to-deal-with-remainders-86714.html#p651942

1) Translating the English to Math : http://gmatclub.com/forum/word-problems-made-easy-87346.html

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Intern
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Posts: 45

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21 Nov 2009, 08:24
Thanks a lot friends......!!

I love to be here.

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