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Alex75PAris
Joined: 16 Mar 2016
Last visit: 08 Mar 2017
Posts: 102
Location: France
Schools: Marshall '19 Darden '19 HKUST '19 Anderson '19
GMAT 1: 660 Q47 V33
GPA: 3.25
26 May 2016, 13:12
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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:
60% (02:04) correct
40%
(02:32)
wrong
based on 606
sessions
History
Date
Time
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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
A -1
B 6
C 7
D 12
E 14
26 May 2016, 13:28
Kudos
Bookmarks
Alex75PAris
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
A -1
B 6
C 7
D 12
E 14
First of all |x - 3|^2 = (x - 3)^2, so we have: (x - 3)^2 + |x - 3| = 20.
When x < 3, x - 3 is negative, thus |x - 3| = -(x - 3). In this case we'll have (x - 3)^2 - (x - 3) = 20 --> x = -1 or x = 8. Discard x = 8 because it's not in the range we consider (< 3).
When x >= 3, x - 3 is non-negative, thus |x - 3| = x - 3. In this case we'll have (x - 3)^2 + (x - 3) = 20 --> x = -2 or x = 7. Discard x = -2 because it's not in the range we consider (>= 3).
Thus there are two solutions: x = -1 and x = 7 --> the sum = 6.
Answer: B.
26 May 2016, 13:31
Kudos
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Alex75PAris
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
A -1
B 6
C 7
D 12
E 14
Another way.
Denote |x - 3| as y: y^2 + y = 20 --> y = -5 or y = 4. Discard the first solution since y = |x - 3|, so it's an absolute value and thus cannot be negative.
y = |x - 3| = 4 --> x = 7 or x = -1. The sum = 6.
Answer: B.
