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16 Sep 2015, 09:48
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B
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% (02:08) correct
41%
(02:40)
wrong
based on 594
sessions
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What is the sum of all possible solutions to \(|x-3|^2 - |x-3| = 20\)?
A) -1
B) 6
C) 7
D) 12
E) 14
Source: GMAT Prep Now - https://www.gmatprepnow.com/module/gmat- ... video/1018
A) -1
B) 6
C) 7
D) 12
E) 14
Source: GMAT Prep Now - https://www.gmatprepnow.com/module/gmat- ... video/1018
16 Sep 2015, 11:42
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skylimit
Let, |x-3| = y
i.e. \(|x-3|^2 - |x-3| = 20\) ---> y^2 - y = 20
i.e. y(y-1) = 20
i.e. Product of two consecutive Numbers = 20
but 5*(5-1)= 20 and also (-4)*(-4-1) = 20
i.e. y = 5 or (-4)
but \(|x-3|\) can't be Negative i.e. can't be (-4)
Hence, \(|x-3| = 5\)
i.e. x = 8 or -2
Sum of these two solutions = 8+(-2) = 6
Answer: option B
16 Sep 2015, 12:24
Kudos
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skylimit
Important Property:\(\sqrt{x^2}=|x|\)
Since \(|x-3|=\sqrt{(x-3)^2}\), \(|x-3|^2= (x-3)^2\)
When \(x>3, |x-3|=x-3\) and when \(x<3, |x-3|=3-x\).
When \(x>3\), \((x-3)^2-(x-3)=20\) yields two solutions \(x=-1\) or \(x=8\), but since \(x=-1\) is not in the range \(x>3\), this solution should be rejected.
When \(x<3\), \((x-3)^2-(3-x)=20\) yields two solutions \(x=-2\) or \(x=7\), but since \(x=7\) is not in the range \(x<3\), this solution should be rejected.
The valid solutions are \(x=-2\) and \(x=8.\) Their sum is 6.
