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What is the value of x ? (1) √x^2 = 19 (2) √19^2 = x

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Bunuel
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What is the value of x ? (1) √x^2 = 19 (2) √19^2 = x [#permalink] New post  09 Sep 2021, 01:30
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What is the value of x ?


(1) \(\sqrt{x^2} = 19\)

(2) \(\sqrt{19^2} = x\)

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What is the value of x ? (1) √x^2 = 19 (2) √19^2 = x [#permalink] New post  09 Sep 2021, 02:03
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Bunuel wrote:
What is the value of x ?


(1) \(\sqrt{x^2} = 19\)

(2) \(\sqrt{19^2} = x\)

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1) |x| = 19, x = +19, -19 -Insufficient!
2)x = 19 - Sufficient!

IMO, (B)!
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Re: What is the value of x ? (1) √x^2 = 19 (2) √19^2 = x [#permalink] New post  09 Sep 2021, 02:42
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Bunuel wrote:
What is the value of x ?


(1) \(\sqrt{x^2} = 19\)

(2) \(\sqrt{19^2} = x\)

Project DS Butler Data Sufficiency (DS3)


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x?
(1) \(\sqrt{x^2} = 19\)
Square both sides
x^2 = 381
x can be 19 or -19
insufficient

(2) \(\sqrt{19^2} = x\)
Square both sides

Answer B
x = 19
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Re: What is the value of x ? (1) √x^2 = 19 (2) √19^2 = x [#permalink] New post  09 Sep 2021, 16:30
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What is the value of x ?

(1) Statement 1 gives us two values. This is because sqrt of the sq of x is mod x. Which means RHS will have two values i.e. +ve and -ve
Insufficient

(2) Statement 2 gives us only 1 value. Sqrt of the sq of 19 only returns a positive value.
Sufficient
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Re: What is the value of x ? (1) √x^2 = 19 (2) √19^2 = x [#permalink] New post  09 Sep 2021, 19:00
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Bunuel wrote:
What is the value of x ?


(1) \(\sqrt{x^2} = 19\)

(2) \(\sqrt{19^2} = x\)

Project DS Butler Data Sufficiency (DS3)


For DS butler Questions Click Here


(1) \(\sqrt{x^2} = 19\) => |x| = 19
=> x = 19 or x = -19
=> insufficient

(2) \(\sqrt{19^2} = x\) => 19 = x
=> sufficient
=> B
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Re: What is the value of x ? (1) √x^2 = 19 (2) √19^2 = x [#permalink] New post  09 Sep 2021, 21:30
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(1)\( \sqrt{x^2}= 19 \)

\(=> |x| = 19\)

\(=> x = 19\) or \(x = -19\)

=> Insufficient

(2) \( \sqrt{19^2}= x \)

\(=> x = 19\)

=> Sufficient

=> Choice B
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Re: What is the value of x ? (1) √x^2 = 19 (2) √19^2 = x [#permalink] New post  10 Sep 2021, 07:40
1. Squaring both sides --> x gives 2 values +19,-19--> Not sufficent
2. X can only have positive values due to square root--> Sufficent

IMO B
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Re: What is the value of x ? (1) √x^2 = 19 (2) √19^2 = x [#permalink] New post  11 Sep 2021, 01:06
In
(i) (x)^2*1/2 = 19
(X)^1 = 19

Isn???t this right?

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Bunuel
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Re: What is the value of x ? (1) √x^2 = 19 (2) √19^2 = x [#permalink] New post  11 Sep 2021, 03:10
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rplrtnwt wrote:
In
(i) (x)^2*1/2 = 19
(X)^1 = 19

Isn???t this right?

Posted from my mobile device


That's not correct because \(\sqrt{x^2}=|x|\), not x.

Why?

The point here is that square root function cannot give negative result: which means that \(\sqrt{some \ expression}\geq{0}\).

So \(\sqrt{x^2}\geq{0}\). But what does \(\sqrt{x^2}\) equal to?

Let's consider following examples:
If \(x=5\) --> \(\sqrt{x^2}=\sqrt{25}=5=x=positive\);
If \(x=-5\) --> \(\sqrt{x^2}=\sqrt{25}=5=-x=positive\).

So we got that:
\(\sqrt{x^2}=x\), if \(x\geq{0}\);
\(\sqrt{x^2}=-x\), if \(x<0\).

What function does exactly the same thing? The absolute value function! That is why \(\sqrt{x^2}=|x|\)
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Re: What is the value of x ? (1) √x^2 = 19 (2) √19^2 = x [#permalink] New post  11 Sep 2021, 03:23
#1
Value of x raised to even power would always be +ve but value of x can be either + or -ve
Insufficient
#2
Value of x would +19 sufficient option B

Bunuel wrote:
What is the value of x ?


(1) \(\sqrt{x^2} = 19\)

(2) \(\sqrt{19^2} = x\)

Project DS Butler Data Sufficiency (DS3)


For DS butler Questions Click Here


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Re: What is the value of x ? (1) √x^2 = 19 (2) √19^2 = x [#permalink]
11 Sep 2021, 03:23
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