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firas92
Current Student
Joined: 16 Jan 2019
Last visit: 02 Dec 2024
Posts: 616
Given Kudos: 142
Location: India
Concentration: General Management
Schools: Tepper '23 (M$) Foster '23 (D)
GMAT 1: 740 Q50 V40
WE:Sales (Other)
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16 Feb 2020, 08:06
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
51% (01:13) correct
49%
(01:26)
wrong
based on 95
sessions
History
Date
Time
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If \(\sqrt{x^2}=x\), what is the value of \(x\)?
1. \(|x|=-x\)
2. \(x^2=-x\)
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1. \(|x|=-x\)
2. \(x^2=-x\)
Posted from my mobile device
16 Feb 2020, 08:40
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For all values of x, positive and negative (and zero), the following is true:
\(\\
\sqrt{x^2} = |x|\\
\)
Also if x > 0, then |x| = x, and if x < 0, |x| = -x.
So the equation in the stem just tells us |x| = x. That equation tells us that x is zero or greater. The equation in Statement 1, |x| = -x, tells us x is zero or smaller. If x is zero or greater and is also zero or smaller, x can only be zero. So Statement 1 is sufficient.
In Statement 2, since we know from the stem x is zero or greater, we know that the right side of the equation, -x, is zero or smaller. But the left side, x^2, is a square, so it is zero or greater. A number zero or smaller can only equal a number zero or greater if both numbers are zero, so Statement 2 also tells us x = 0, and is also sufficient.
You can also analyze Statement 2 by solving it as a quadratic (it only has two solutions, 0 and -1) and plugging each solution back into the equation in the stem to see which of them works -- only x = 0 does.
So the answer is D.
\(\\
\sqrt{x^2} = |x|\\
\)
Also if x > 0, then |x| = x, and if x < 0, |x| = -x.
So the equation in the stem just tells us |x| = x. That equation tells us that x is zero or greater. The equation in Statement 1, |x| = -x, tells us x is zero or smaller. If x is zero or greater and is also zero or smaller, x can only be zero. So Statement 1 is sufficient.
In Statement 2, since we know from the stem x is zero or greater, we know that the right side of the equation, -x, is zero or smaller. But the left side, x^2, is a square, so it is zero or greater. A number zero or smaller can only equal a number zero or greater if both numbers are zero, so Statement 2 also tells us x = 0, and is also sufficient.
You can also analyze Statement 2 by solving it as a quadratic (it only has two solutions, 0 and -1) and plugging each solution back into the equation in the stem to see which of them works -- only x = 0 does.
So the answer is D.
16 May 2021, 02:45
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