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

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CEO
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Is M < 0? 1. -M = |-M| 2. M^2 =9 [#permalink]  21 Oct 2007, 19:47
Is M < 0?

1. -M = |-M|
2. M^2 =9
Director
Joined: 03 May 2007
Posts: 894
Schools: University of Chicago, Wharton School
Followers: 6

Kudos [?]: 66 [0], given: 7

Re: Challenge - Absolute Values [#permalink]  21 Oct 2007, 19:49
bmwhype2 wrote:
Is M < 0?

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

Should be A. if -m is +ve, m should be -ve.
Director
Joined: 09 Aug 2006
Posts: 765
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Kudos [?]: 72 [0], given: 0

Re: Challenge - Absolute Values [#permalink]  21 Oct 2007, 21:01
bmwhype2 wrote:
Is M < 0?

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

Get A.

Stat 2: Started with stat 2 since it looked simpler. M can be 3 or -3. Insuff.

ACE left.

Stat 1: for -M to be equal to |-M|, M has to be negative; suff.

Plugging in numbers will prove this:

M = 4, -M = -4, |-M| = |-4| = 4; -4 is not equal to 4; M cannot be +ve
M = -4, -M = 4, |-M| = |4| = 4; 4 = 4; M has to be -ve
Senior Manager
Joined: 27 Aug 2007
Posts: 253
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Re: Challenge - Absolute Values [#permalink]  21 Oct 2007, 21:16
Fistail wrote:
bmwhype2 wrote:
Is M < 0?

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

Should be A. if -m is +ve, m should be -ve.

I think the answer is C,

1) INSUFF, Fistal you forgot about 0
2) INSUFF -3 or +3

Together suff since it should be less or equal to zero and -3 or +3, in other words -3

Ans: C
Director
Joined: 03 May 2007
Posts: 894
Schools: University of Chicago, Wharton School
Followers: 6

Kudos [?]: 66 [0], given: 7

Re: Challenge - Absolute Values [#permalink]  21 Oct 2007, 22:05
Ferihere wrote:
Fistail wrote:
bmwhype2 wrote:
Is M < 0?

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

Should be A. if -m is +ve, m should be -ve.

I think the answer is C,

1) INSUFF, Fistal you forgot about 0
2) INSUFF -3 or +3

Together suff since it should be less or equal to zero and -3 or +3, in other words -3

Ans: C

oh yah. thats a good catch on great trap.
you are correct. thanks.
Manager
Joined: 30 Sep 2007
Posts: 144
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Kudos [?]: 5 [0], given: 0

Re: Challenge - Absolute Values [#permalink]  22 Oct 2007, 02:50
Fistail wrote:
Ferihere wrote:
Fistail wrote:
bmwhype2 wrote:
Is M < 0?

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

Should be A. if -m is +ve, m should be -ve.

I think the answer is C,

1) INSUFF, Fistal you forgot about 0
2) INSUFF -3 or +3

Together suff since it should be less or equal to zero and -3 or +3, in other words -3

Ans: C

oh yah. thats a good catch on great trap.
you are correct. thanks.

Fistal, could you please tell me how to test it with value ZERO? please plese sir..
Senior Manager
Joined: 04 Jan 2006
Posts: 280
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Re: Challenge - Absolute Values [#permalink]  22 Oct 2007, 06:25
yash500 wrote:
Fistail wrote:
Ferihere wrote:
Fistail wrote:
bmwhype2 wrote:
Is M < 0?

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

Should be A. if -m is +ve, m should be -ve.

I think the answer is C,

1) INSUFF, Fistal you forgot about 0
2) INSUFF -3 or +3

Together suff since it should be less or equal to zero and -3 or +3, in other words -3

Ans: C

oh yah. thats a good catch on great trap.
you are correct. thanks.

Fistal, could you please tell me how to test it with value ZERO? please plese sir..

Let me try to explain how to get the answer from 1. -M = |-M|

I) |-M| = |M| ; from |a| = |-a|
II) |M| = -M

Case 1: if M > 0, then we get M = -M
2M = 0
M = 0

Case 2: if M < 0, then we get -M = -M
M - M = 0
M = Real Number
But this Real Number is limited by the constraint M < 0. Therefore, the answer for case 2 is M < 0

Case 1 + Case 2 we get M <= 0.

At the end, the answer will be (C)
Director
Joined: 03 May 2007
Posts: 894
Schools: University of Chicago, Wharton School
Followers: 6

Kudos [?]: 66 [0], given: 7

Re: Challenge - Absolute Values [#permalink]  23 Oct 2007, 11:22
bmwhype2 wrote:
Is M < 0?

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

hey bmwhype2,

Can you post the OAs to your questions? most of the questions you submitted do not have OAs.

Senior Manager
Joined: 11 Sep 2005
Posts: 329
Followers: 1

Kudos [?]: 42 [0], given: 0

Re: Challenge - Absolute Values [#permalink]  23 Oct 2007, 12:24
bmwhype2 wrote:
Is M < 0?

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

A..........info 1 gives M<0
info 2 insuff.....
Senior Manager
Joined: 11 Sep 2005
Posts: 329
Followers: 1

Kudos [?]: 42 [0], given: 0

Re: Challenge - Absolute Values [#permalink]  23 Oct 2007, 12:26
Fistail wrote:
Ferihere wrote:
Fistail wrote:
bmwhype2 wrote:
Is M < 0?

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

Should be A. if -m is +ve, m should be -ve.

I think the answer is C,

1) INSUFF, Fistal you forgot about 0
2) INSUFF -3 or +3

Together suff since it should be less or equal to zero and -3 or +3, in other words -3

Ans: C

oh yah. thats a good catch on great trap.
you are correct. thanks.

Oopss missed ZERO.......C is the right answer!
CEO
Joined: 21 Jan 2007
Posts: 2764
Location: New York City
Followers: 9

Kudos [?]: 354 [0], given: 4

Re: Challenge - Absolute Values [#permalink]  04 Nov 2007, 02:27
bmwhype2 wrote:
Is M < 0?

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

This is how i solved it.

Statement (1) tells us the right side is a non negative number. Absolute values are NON NEGATIVE. Therefore, the right side is 0 or a positive #. The left side is negative M. The only way the left side (with its negative M) can equal the right side (with its positive or zero value) is if M is a negative or zero value. We have dont have an exact value for M so we cant answer the stem. INSUFF

Statement (1) tells us m^2 = 9, giving us m=3 and m=-3. Two values. INSUFF

Taken together, M=-3. Stem is answerable. Therefore C.
Re: Challenge - Absolute Values   [#permalink] 04 Nov 2007, 02:27
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# Is M < 0? 1. -M = |-M| 2. M^2 =9

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