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06 Jan 2021, 01:15
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D
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Difficulty:
45%
(medium)
Question Stats:
68% (02:01) correct
32%
(01:59)
wrong
based on 265
sessions
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Is x > 0 ?
(1) |x - 5| = 7x - 11
(2) |x + 5| = |x - 9|
M36-89
(1) |x - 5| = 7x - 11
(2) |x + 5| = |x - 9|
M36-89
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12 Nov 2021, 03:03
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Bunuel
Official Solution:
Is \(x > 0\) ?
(1) \(|x - 5| = 7x - 11\)
The right hand side (\(7x - 11\)) equals to the absolute value, so it must be non-negative: \(7x - 11 \geq 0\). This gives: \(x \geq \frac{11}{7}\). So, \(x\) is positive. Sufficient.
(2) \(|x + 5| = |x - 9|\)
The above means that \(x\) is equidistant from -5 and 9 (the distance between \(x\) and -5 is equal to the distance between \(x\) and 9), so \(x=\frac{-5+9}{2}=2\). Sufficient.
Answer: D
12 Nov 2021, 07:15
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Bunuel
Bunuel uses some great number sense to solve this question.
Here's a more traditional approach....
Target question: Is x > 0 ?
Statement 1: |x - 5| = 7x - 11
There are 3 steps to solving equations involving ABSOLUTE VALUE:
1. Apply the rule that says: If |x| = k, then x = k or x = -k
2. Solve the resulting equations
3. Plug solutions into original equation to check for extraneous roots
So, for the equation |x - 5| = 7x - 11, we must examine two cases:
Case a: x - 5 = 7x - 11. Solve to get x = 1. However, when we plug x = 1 into the original equation and simplify we get |-4| = -4, which is not true. So, x = 1 is NOT a solution
Case b: x - 5 = -(7x - 11). Solve to get x = 2. When we plug x = 2 into the original equation and simplify we get |-3| = 3, which is true. So, x = 2 is a solution.
So, the answer to the target question is YES, x is positive
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: |x + 5| = |x - 9|
Once again we must solve two equations...
Case a: x + 5 = x - 9. This equation has no solution
Case b: x + 5 = -(x - 9). Solve to get x = 2 (we already learned in statement 1 that x = 2 satisfies the original equation. So, we need not confirm this again)
So, the answer to the target question is YES, x is positive
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
