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24 Sep 2010, 11:53
Kudos
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
59% (02:02) correct
41%
(02:10)
wrong
based on 370
sessions
History
Date
Time
Result
Not Attempted Yet
|x + 1| < |x^2 + 2x + 2|
A: (-infinity, +infinity)
B: (-1, +infinity)
C: (-infinity, -1)
D: no solutions
E: (-1, 1)
A: (-infinity, +infinity)
B: (-1, +infinity)
C: (-infinity, -1)
D: no solutions
E: (-1, 1)
gurpreetsingh
Joined: 12 Oct 2009
Last visit: 15 Jun 2019
Posts: 2,273
Given Kudos: 235
Status:<strong>Nothing comes easy: neither do I want.</strong>
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Products:
24 Sep 2010, 11:59
Kudos
Bookmarks
gmatbull
please how do i go about this question?
I considered various options, but none seems attractive to me:
|x + 1| < |x^2 + 2x + 2|
A: (-infinity, +infinity)
B: (-1, +infinity)
C: (-infinity, -1)
D: no solutions
E: (-1, 1)
I considered various options, but none seems attractive to me:
|x + 1| < |x^2 + 2x + 2|
A: (-infinity, +infinity)
B: (-1, +infinity)
C: (-infinity, -1)
D: no solutions
E: (-1, 1)
\(|x + 1| < |x^2 + 2x + 2|\) since \(x^2 + 2x + 2 = (x+1)^2 +1\) which is always > 0
=> \(|x + 1| < (x+1)^2 +1\) take \(|x+1| = y\)
=> \(y<y^2 +1\) => \(y^2 +1 - y>0\)
\((y-\frac{1}{2})^2 +\frac{3}{4}>0\)
This is true for all values of y, hence it is true for all values of x.
Hence A
General Discussion
24 Sep 2010, 12:05
Kudos
Bookmarks
gmatbull
please how do i go about this question?
I considered various options, but none seems attractive to me:
|x + 1| < |x^2 + 2x + 2|
A: (-infinity, +infinity)
B: (-1, +infinity)
C: (-infinity, -1)
D: no solutions
E: (-1, 1)
I considered various options, but none seems attractive to me:
|x + 1| < |x^2 + 2x + 2|
A: (-infinity, +infinity)
B: (-1, +infinity)
C: (-infinity, -1)
D: no solutions
E: (-1, 1)
Lets try plugin and POE as alternative to the other solution- this is pretty quick as the math isnt hard at all and the answer choices given are super easy to pick easy numbers 1/2
POE:
A. lets skip this for now since if any number doesn't work this will fail.
B. try -2 since it is supposed to be "invalid". |-2+1| < |(-2)^2 + 2*-2 +2| = 1 <2 which is VALID so NO B
C. try 1 since it is out of scopre - |1+1| < |1^2 + 2*1 +2| = 2 < 5 which is VALID so no C
D. obviously no from above examples (and in general on test "no solutions" is a trap
E. from trying -2 from B we know this is false
So we derived A with POE.
