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M31-50

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Bunuel
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M31-50 [#permalink] New post   20 Jun 2015, 12:14
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What is the value of \(x\)?


(1) \((|x| + 9)(x - 9) = 0\)

(2) \((|x| - 9)(x + 9) = 0\)
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A
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Re M31-50 [#permalink] New post   20 Jun 2015, 12:14
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Official Solution:


What is the value of \(x\)?

(1) \((|x| + 9)(x - 9) = 0\)

For the product of two factors to equal 0, at least one of them must be 0. Since \(|x| + 9\) is the sum of a nonnegative and a positive value, it will always be positive and cannot be 0. Therefore, \(x - 9 = 0\), which implies \(x = 9\). Sufficient.

(2) \((|x| - 9)(x + 9) = 0\)

Either \(|x| - 9 = 0\) or \(x + 9 = 0\). This means \(x\) can be either 9 or -9. Not sufficient.


Answer: A
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Re: M31-50 [#permalink] New post   06 May 2023, 02:42
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re: M31-50 [#permalink] New post   03 Jul 2023, 03:45
This does tend to confuse me. But the in the case of (A), how can we assume that the value inside the mod is non-negative? If X is less than or equal to a negative value, then it would mean that we'd have to consider a negative value. The in-consistent application of this principle in questions does tend to confuse me.
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Re: M31-50 [#permalink] New post   03 Jul 2023, 04:53
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okrahulnambiar wrote:
This does tend to confuse me. But the in the case of (A), how can we assume that the value inside the mod is non-negative? If X is less than or equal to a negative value, then it would mean that we'd have to consider a negative value. The in-consistent application of this principle in questions does tend to confuse me.


Where we assumed that "the value inside the mod is non-negative"? The solution says that |x| + 9 is the sum of a nonnegative and a positive value, thus positive. It does not say x is nonnegative, it says |x| is nonnegative.
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Re: M31-50 [#permalink] New post   26 Jul 2023, 11:15
hello Bunuel,

Can you please share the link to understand the concept of absolute value as these questions always tend to confuse me.

thank you
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Re: M31-50 [#permalink] New post   26 Jul 2023, 11:18
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Road2MSx wrote:
hello Bunuel,

Can you please share the link to understand the concept of absolute value as these questions always tend to confuse me.

thank you


10. Absolute Value



For more check Ultimate GMAT Quantitative Megathread



Hope it helps.
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gmatclubot
Re: M31-50 [#permalink]
26 Jul 2023, 11:18
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Bunuel
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