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# If |m+5|−5 = m, which of the following must be true?

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Senior Manager
Joined: 21 Oct 2013
Posts: 419
If |m+5|−5 = m, which of the following must be true?  [#permalink]

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02 Aug 2014, 06:28
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55% (hard)

Question Stats:

59% (01:35) correct 41% (01:37) wrong based on 472 sessions

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If |m+5|−5 = m, which of the following must be true?

A. m = 0
B. m = −10
C. m is a multiple of 5.
D. m ≥ −5
E. |m+5| > 0
Math Expert
Joined: 02 Sep 2009
Posts: 51071
Re: If |m+5|−5 = m, which of the following must be true?  [#permalink]

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02 Aug 2014, 07:46
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goodyear2013 wrote:
If |m+5|−5 = m, which of the following must be true?

A. m = 0
B. m = −10
C. m is a multiple of 5.
D. m ≥ −5
E. |m+5| > 0

|m + 5| - 5 = m --> |m + 5| = m + 5.

We know that |x| = x, when $$x\geq{0}$$. Therefore, from |m + 5| = m + 5 it follows that $$m+5\geq{0}$$ --> $$m\geq{-5}$$.

P.S. |x| = -x, when $$x\leq{0}$$.
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Posts: 172
Re: If |m+5|−5 = m, which of the following must be true?  [#permalink]

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02 Aug 2014, 23:26
1
goodyear2013 wrote:
If |m+5|−5 = m, which of the following must be true?

A. m = 0
B. m = −10
C. m is a multiple of 5.
D. m ≥ −5
E. |m+5| > 0

Case 1 : |m+5| = 0, then m= -5
|-5+5|−5 = -5 --> true

Case 2; |m+5| < 0, then m< -5
|m+5|−5 = -m - 5 -5 = m , then m = -5 --> false

Case 3: Case 2; |m+5| > 0, then m> -5
|m+5|−5 = m+5 -5 = m , then m = m --> always true

Only case 1 and 3 satisfy the equation, so D is the answer.
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Re: If |m+5|−5 = m, which of the following must be true?  [#permalink]

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03 Aug 2014, 22:46
Make a positive and a negative case

|m + 5| - 5 = m --> |m + 5| = m + 5

Positive:
m + 5 = m + 5 --> m = 0

Negative
m + 5 = -m - 5
2m = -10 --> m = -5

As you can see only answer D satisfy both conditions.
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Re: If |m+5|−5 = m, which of the following must be true?  [#permalink]

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23 Aug 2015, 04:31
My answer is D.only multiple number picking works on the answer choice D
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Re: If |m+5|−5 = m, which of the following must be true?  [#permalink]

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23 Aug 2015, 05:25
goodyear2013 wrote:
If |m+5|−5 = m, which of the following must be true?

A. m = 0
B. m = −10
C. m is a multiple of 5.
D. m ≥ −5
E. |m+5| > 0

|m+5| = m+5
Either m+5 = m+5 or -m-5 = m+5
In the second case, m=-5
When m<-5, the equation does not hold true. LHS is always positive and RHS is negative.
Therefore, m> or = -5
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Re: If |m+5|−5 = m, which of the following must be true?  [#permalink]

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30 Jul 2018, 12:53
Michellegeorge777 wrote:
Why is answer choice (A) wrong?

You're looking for a statement that must be true. In other words, the right answer will be something that definitely has to be true no matter what.

Does m have to equal 0? No, because m could also equal a lot of other different numbers: m could be 1, 10, or 100. Since (A) doesn't necessarily have to be the case - it could be true, it could be false, depending on what m is - it isn't the right answer.

You can think about this like a Data Sufficiency problem. The information you know is what the question says: you know that |m + 5| - 5 = m. You don't know anything else about m. Can you conclude that m must equal 0? No, you don't have enough info to conclude that.

In contrast, you can conclude that m definitely must be greater than or equal to -5.
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Re: If |m+5|−5 = m, which of the following must be true?  [#permalink]

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30 Jul 2018, 23:12
I agree with D. But why E is wrong? |m+5| should be always positive.
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Re: If |m+5|−5 = m, which of the following must be true?  [#permalink]

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30 Jul 2018, 23:22
sghoshgt wrote:
I agree with D. But why E is wrong? |m+5| should be always positive.

Absolute value is always non-negative, not positive. So, it could be 0 as well. |m + 5| = 0 for m = -5.
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Re: If |m+5|−5 = m, which of the following must be true?  [#permalink]

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01 Aug 2018, 15:29
goodyear2013 wrote:
If |m+5|−5 = m, which of the following must be true?

A. m = 0
B. m = −10
C. m is a multiple of 5.
D. m ≥ −5
E. |m+5| > 0

Isolating the absolute value, we have:

|m + 5| = m + 5

We see that the absolute value of an expression is equal to the expression itself. That could only be true if the expression is nonnegative. That is,

m + 5 ≥ 0

m ≥ -5

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Re: If |m+5|−5 = m, which of the following must be true? &nbs [#permalink] 01 Aug 2018, 15:29
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