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Is M \lt 0? 1. -M = |-M| 2. M^2 = 9Source: GMAT Club Tests - hardest GMAT questions Answer explaination: From statement (1) we have that should be negative or zero. Not enough for the strict condition. From statement (2) can be 3 or -3. Not enough again. If we combine two statements then .Could somebody please explain how can we ever have modulus of any number as negative ? I beleive modulus of a positive number , negative number or zero is positive.... So isnt statement one completely false ? From statement 2 we can infer that M can be either negative or positive .... but cannot answer the question... What should be the answer ?
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Re: m01 - Q17 - Wrong answer [#permalink]
 18 Sep 2008, 06:35
Hi. First, modulus of zero is neither positive nor negative. Second, try plugging a negative number in S1. You're right, the |-M| part is always positive, but the left-hand part isn't. That is why we need both S1 and S2 to answer the question. From S2 we know that M is either -3 or 3. From S1 we know that M is either negative or zero. combining the two Statements we get M=-3. Answer C. Hope this helps.
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Re: m01 - Q17 - Wrong answer [#permalink]
25 Sep 2008, 13:10
dzyubam wrote: Hi.
First, modulus of zero is neither positive nor negative.
Second, try plugging a negative number in S1. You're right, the |-M| part is always positive, but the left-hand part isn't. That is why we need both S1 and S2 to answer the question. From S2 we know that M is either -3 or 3. From S1 we know that M is either negative or zero. combining the two Statements we get M=-3. Answer C.
Hope this helps. how is S1 possible to be negative. i understand that modulus of zero will always be zero, but the first statement doesn't allow for negative result. for example lets plug -3 in S1. -3=|-3| , thus -3=3 but this is not true! so S1 tells me that M=0, what am i missing here?
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Re: m01 - Q17 - Wrong answer [#permalink]
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elmagnifico wrote: dzyubam wrote: Hi.
First, modulus of zero is neither positive nor negative.
Second, try plugging a negative number in S1. You're right, the |-M| part is always positive, but the left-hand part isn't. That is why we need both S1 and S2 to answer the question. From S2 we know that M is either -3 or 3. From S1 we know that M is either negative or zero. combining the two Statements we get M=-3. Answer C.
Hope this helps. how is S1 possible to be negative. i understand that modulus of zero will always be zero, but the first statement doesn't allow for negative result. for example lets plug -3 in S1. -3=|-3| , thus -3=3 but this is not true! so S1 tells me that M=0, what am i missing here? you took M=3 (+VE) thats not possible M must be -ve here.. M=-3 -(-3) = |-(-3) --> 3=3
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Re: m01 - Q17 - Wrong answer [#permalink]
25 Sep 2008, 13:19
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Wait. Let's see. S1 states -M = |-M| Now we plug in -3 as you suggested: -(-3) = |-(-3)| --> 3 = 3. Now we plug in a positive number 3: -(3) = |-(3)| --> -3 = 3. This is why we know that S1 tells us the M \le 0. Do you agree? Saw the post made but still decided to proceed with mine.
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Re: m01 - Q17 - Wrong answer [#permalink]
25 Sep 2008, 14:28
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dzyubam wrote: Wait. Let's see. S1 states
-M = |-M|
Now we plug in -3 as you suggested:
-(-3) = |-(-3)| -->
3 = 3.
Now we plug in a positive number 3:
-(3) = |-(3)| -->
-3 = 3.
This is why we know that S1 tells us the M \le 0. Do you agree?
Saw the post made but still decided to proceed with mine. thanks for your post. both, you and x2suresh deserve a tap on the shoulder. (and kudos:)
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Re: m01 - Q17 - Wrong answer [#permalink]
06 Nov 2008, 14:45
I still didn't get this.
Isn't -3 = 3 invalid ?? we cannot even apply the values as such to arrive at the answer.
For me only answer that fits value of M is -ve values from S1.
-M = |-M| this can be true only if M is -ve right ?? hence sufficient ?
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Re: m01 - Q17 - Wrong answer [#permalink]
06 Nov 2008, 15:47
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S1 is insufficient by itself. Consider M = -3 and M = 0. We have a strict inequality in the question, so we'll need S2. mbaobsessed wrote: I still didn't get this.
Isn't -3 = 3 invalid ?? we cannot even apply the values as such to arrive at the answer.
For me only answer that fits value of M is -ve values from S1.
-M = |-M| this can be true only if M is -ve right ?? hence sufficient ?
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Re: m01 - Q17 - Wrong answer [#permalink]
06 Nov 2008, 22:16
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Also look at stmt1 this way.
|-M| is an absolute value and hence >=0.
Left side of the equation is -M.
Thus, we are comparing -M to some value that is >=0.
This is possible only in two cases
Case1: when M = 0
Case2, when m<0.
Hence, statement 1 gives M <=0 and is not sufficient to answer the question.
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Initially i thought answer to be A but,looking at the explanation by both dzyubam and x2suresh, C seems to be correct answer. Kudos to both of you.
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nice explanations thanks. I also thought A at first but you need the information from B
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From S1 we can say -M>=0 From S2 we can say M=+3,-3 so Ans:M=-3
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The correct answer is C.
(1) is not sufficient because -M = |-M| means M = 0 or M < 0.
For example:
-0 = |-0| : correct
-(-1) = |-(-1)| : correct
M > 0 is impossible because if M > 0, then -M < 0 but |-M| is non-negative.
(2) is not sufficient because M = -3 or M = 3.
(1) & (2) together: sufficient because M = -3, so the answer to the question is YES.
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itiskavikatha wrote: Is M \lt 0?
1. -M = |-M|
2. M^2 = 9 This question was also posted in DS subforum. Below is my solution from there: 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. Answer: C. Hope it's clear.
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I initially considered S1 as enough. Apparently not. I didn't consider the case when M = 0. I always make this mistake!
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Was in trap - forgot to check for zero. Rest Bunnel explains as it
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man...silly mistake! chose A as i overlooked M=0 scenario. C is correct.
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