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02 May 2021, 01:15
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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:
75%
(hard)
Question Stats:
46% (01:48) correct
54%
(01:22)
wrong
based on 197
sessions
History
Date
Time
Result
Not Attempted Yet
09 May 2021, 02:45
Kudos
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What is the value of x?
(1) |x + 9| = 2x.
The left hand side is an absolute value, so it cannot be negative, thus the right hand side also cannot be negative, which means that x is positive or 0. If \(x \geq 0\), then x + 9 > 0, thus |x + 9| = x + 9. So, we'd have that x + 9 = 2x. Solving gives x = 9. Sufficient.
(2) |2x − 9| = x.
2x - 9 = x --> x = 9. Plug back to verify this solution: |2*9 - 9| = 9 --> OK;
2x - 9 = -x --> x = 3. Plug back to verify this solution: |2*3 - 9| = 3 --> OK.
Not sufficient.
Note that we cannot use trick we used for (1) for (2): yes, |2x − 9| = x also implies that x must be positive but 2x - 9 could be positive as well as negative for positive x.
Answer: A.
(1) |x + 9| = 2x.
The left hand side is an absolute value, so it cannot be negative, thus the right hand side also cannot be negative, which means that x is positive or 0. If \(x \geq 0\), then x + 9 > 0, thus |x + 9| = x + 9. So, we'd have that x + 9 = 2x. Solving gives x = 9. Sufficient.
(2) |2x − 9| = x.
2x - 9 = x --> x = 9. Plug back to verify this solution: |2*9 - 9| = 9 --> OK;
2x - 9 = -x --> x = 3. Plug back to verify this solution: |2*3 - 9| = 3 --> OK.
Not sufficient.
Note that we cannot use trick we used for (1) for (2): yes, |2x − 9| = x also implies that x must be positive but 2x - 9 could be positive as well as negative for positive x.
Answer: A.
General Discussion
02 May 2021, 01:24
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Bunuel
1)
Case1:
x + 9 = 2x
-x = -9
x = 9
Case2:
-x - 9 = -2x
x = 9.
Sufficient
2)
Case1:
2x - 9 = x
x = 9
Case2:
-2x + 9 = x
-3x = -9
x = 3
Plug in the values of x to confirm if both the values satisfy the equation. It does.
So, two different values of x. Insufficient! (A)
