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# QOTD#25 |1 – 5| = |5 – m|

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Joined: 07 Jun 2014
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GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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QOTD#25 |1 – 5| = |5 – m| [#permalink]  28 Sep 2016, 14:45
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Expert's post
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Question Stats:

69% (00:31) correct 30% (00:58) wrong based on 36 sessions
$$|1 - 5| = |5 - m|$$

 Quantity A Quantity B m 4

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Drill 1
Question: 3
Page: 282
[Reveal] Spoiler: OA

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Sandy
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GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4711
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1615 [1] , given: 376

Re: QOTD#25 |1 – 5| = |5 – m| [#permalink]  28 Sep 2016, 14:47
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Expert's post
Explanation

We solve for m.

If $$|1 - 5| = |5 - m|$$, then $$|- 4| = |5 - m|$$, or $$4 = |5 - m|$$.

When you see absolute values, remember to consider both positive and negative solutions: $$5 - m = 4$$ or $$5 - m = -4$$, so m can equal 1 or 9, leaving you with choice D for the answer.
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Re: QOTD#25 |1 – 5| = |5 – m| [#permalink]  12 Nov 2016, 06:50
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Expert's post
sandy wrote:
$$|1 - 5| = |5 - m|$$

 Quantity A Quantity B m 4

When solving equations involving ABSOLUTE VALUE, there are 3 steps:
1. Apply the rule that says: If |x| = k, then x = k and/or x = -k
2. Solve the resulting equations
3. Plug solutions into original equation to check for extraneous roots

So, if |1 - 5| = |5 - m|, then we must consider two cases:

1 - 5 = 5 - m and 1 - 5 = -(5 - m)

1 - 5 = 5 - m
-4 = 5 - m
-9 = -m
m = 9

[b]1 - 5 = -(5 - m)

-4 = -5 + m
1 = m

So, we have two solutions: m = 9 and m = 1
Now plug them into the original equation to ensure they work.

m = 9
|1 - 5| = |5 - 9|
|-4| = |-4|
4 = 4
WORkS!

m = 1
|1 - 5| = |5 - 1|
|-4| = |4|
4 = 4
WORKS!

If m = 9, then Quantity A is greater
If m = 1, then Quantity B is greater

[Reveal] Spoiler:
D

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Re: QOTD#25 |1 – 5| = |5 – m|   [#permalink] 12 Nov 2016, 06:50
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