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03 Jul 2019, 04:01
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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:
55%
(hard)
Question Stats:
54% (01:29) correct
46%
(01:15)
wrong
based on 403
sessions
History
Date
Time
Result
Not Attempted Yet
If lx + 3l = 4x - 5. Find the value(s) of x.
A. 2/5
B. 8/3
C. 8/5
D. 2/5, 8/3
E. None
A. 2/5
B. 8/3
C. 8/5
D. 2/5, 8/3
E. None
WiziusCareers1
Joined: 27 Apr 2009
Last visit: 21 Apr 2026
Posts: 175
Given Kudos: 35
Status:Not Applying
Location: India
Schools: HBS '14 (A)
GMAT 1: 730 Q51 V36
03 Jul 2019, 04:22
Kudos
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If lx + 3l = 4x - 5. Find the value(s) of x.
To solve an absolute value equation, take possible cases.
Case I: When x + 3 > 0
=> x + 3 = 4x - 5
=> 3 + 5 = 4x - x
=> 8/3 = x
Case II: When x + 3 < 0
=> -(x + 3) = 4x - 5
=> -x - 3 = 4x - 5
=> -3 + 5 = 4x + x
=> 2 = 5x
=> x = 2/5
However, of the two values only x = 8/3 satisfies the equation.
The answer is (B).
Alternate approach:
Use the answer choices
If x = 2/5, then |x + 3| = |2/5 + 3| = 17/5
whereas 4x - 5 = 4(2/3) - 5 = -17/5
Not equal
If x = 8/3, then |x + 3| = 17/3
and 4x - 5 = 17/3
hence, the answer is (B).
To solve an absolute value equation, take possible cases.
Case I: When x + 3 > 0
=> x + 3 = 4x - 5
=> 3 + 5 = 4x - x
=> 8/3 = x
Case II: When x + 3 < 0
=> -(x + 3) = 4x - 5
=> -x - 3 = 4x - 5
=> -3 + 5 = 4x + x
=> 2 = 5x
=> x = 2/5
However, of the two values only x = 8/3 satisfies the equation.
The answer is (B).
Alternate approach:
Use the answer choices
If x = 2/5, then |x + 3| = |2/5 + 3| = 17/5
whereas 4x - 5 = 4(2/3) - 5 = -17/5
Not equal
If x = 8/3, then |x + 3| = 17/3
and 4x - 5 = 17/3
hence, the answer is (B).
03 Jul 2019, 06:15
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Bookmarks
Dillesh4096
Another (fast) approach is to test the answer choices
A. x = 2/5 = 0.4
We get: |0.4 + 3| = 4(0.4) - 5
Simplify: 3.4 = 1.6 - 5
Simplify: 3.4 = some NEGATIVE number
Doesn't work!
ELIMINATE A & D
B. x = 8/3
We get: |8/3 + 3| = 4(8/3) - 5
Simplify: |8/3 + 9/3| = 32/3 - 15/3
Simplify: |17/3| = 17/3
WORKS!
Answer: B
Cheers,
Brent
