GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
QOTD#25 |1 – 5| = |5 – m|
[#permalink]
28 Sep 2016, 14:45
28 Sep 2016, 14:45
3
Expert Reply
2
Bookmarks
00:00
Question Stats:
72% (00:38) correct
27% (00:45) wrong based on 165 sessions
Hide Show timer Statistics
\(|1 - 5| = |5 - m|\)
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.
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
Question: 3
Page: 282
Re: QOTD#25 |1 – 5| = |5 – m|
[#permalink]
28 Sep 2016, 14:47
28 Sep 2016, 14:47
2
Expert Reply
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.
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.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: QOTD#25 |1 – 5| = |5 – m|
[#permalink]
12 Nov 2016, 06:50
12 Nov 2016, 06:50
1
1
Bookmarks
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
Answer:
Show: ::
D
