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Is x = 4 ? (1) (x^2)^(1/2) = 4 (2) |x| = -x

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nevilpat1
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Is x = 4 ? (1) (x^2)^(1/2) = 4 (2) |x| = -x [#permalink] New post   Updated on: 01 Oct 2021, 06:26
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Is x = 4 ?

(1) \(\sqrt{x^2}\) = 4

(2) \(|x| = -x\)
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B

Originally posted by nevilpat1 on 04 Sep 2014, 16:30.
Last edited by Bunuel on 01 Oct 2021, 06:26, edited 2 times in total.
Renamed the topic and edited the question.
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Re: Is x = 4 ? (1) (x^2)^(1/2) = 4 (2) |x| = -x [#permalink] New post   04 Sep 2014, 16:47
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Is x = 4 ?

(1) \(\sqrt{x^2}\) = 4 --> x^2 =16 --> x = 4 or x = -4. Not sufficient.

(2) \(|x| = -x\). This is only possible when \(x\leq{0}\), so x cannot be 4. Sufficient.

Answer: B.

P.S. Please name topics properly. Check rule 3 here: rules-for-posting-please-read-this-before-posting-133935.html Thank you.
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Re: Is x = 4 ? (1) (x^2)^(1/2) = 4 (2) |x| = -x [#permalink] New post   08 Sep 2014, 02:50
Bunuel wrote:
Is x = 4 ?

(1) \(\sqrt{x^2}\) = 4 --> x^2 =16 --> x = 4 or x = -4. Not sufficient.

(2) \(|x| = -x\). This is only possible when \(x\leq{0}\), so x cannot be 4. Sufficient.

Answer: B.

P.S. Please name topics properly. Check rule 3 here: rules-for-posting-please-read-this-before-posting-133935.html Thank you.



Hi
Could you please explain this in greater details?
My thought was

1) sqrt{x^2} = 4 --> x^2 =16 --> x = 4 or x = -4. However the answer itself says that Sq rt( x^2 ) = 4 , so does it not imply that x = 4 (and not -4)

2) |x| = -x -----------------clearly says that x is negative

Hence answer should be D (both statements alone are sufficient to answer the question)?
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Re: Is x = 4 ? (1) (x^2)^(1/2) = 4 (2) |x| = -x [#permalink] New post   08 Sep 2014, 04:05
Expert Reply
mayankpant wrote:
Bunuel wrote:
Is x = 4 ?

(1) \(\sqrt{x^2}\) = 4 --> x^2 =16 --> x = 4 or x = -4. Not sufficient.

(2) \(|x| = -x\). This is only possible when \(x\leq{0}\), so x cannot be 4. Sufficient.

Answer: B.

P.S. Please name topics properly. Check rule 3 here: rules-for-posting-please-read-this-before-posting-133935.html Thank you.



Hi
Could you please explain this in greater details?
My thought was

1) sqrt{x^2} = 4 --> x^2 =16 --> x = 4 or x = -4. However the answer itself says that Sq rt( x^2 ) = 4 , so does it not imply that x = 4 (and not -4)

2) |x| = -x -----------------clearly says that x is negative

Hence answer should be D (both statements alone are sufficient to answer the question)?


Why? Plug -4, there. Does it satisfy the equation? Yes. So, x could be -4.

One more way to look at it: \(\sqrt{x^2}=|x|\), so we have that |x| = 4, which means that x = 4 or x = -4.

Hope it's clear.
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123Avi
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Re: Is x = 4 ? (1) (x^2)^(1/2) = 4 (2) |x| = -x [#permalink] New post   08 Sep 2014, 05:55
Bunuel wrote:
mayankpant wrote:
Bunuel wrote:
Is x = 4 ?

(1) \(\sqrt{x^2}\) = 4 --> x^2 =16 --> x = 4 or x = -4. Not sufficient.

(2) \(|x| = -x\). This is only possible when \(x\leq{0}\), so x cannot be 4. Sufficient.

Answer: B.

P.S. Please name topics properly. Check rule 3 here: rules-for-posting-please-read-this-before-posting-133935.html Thank you.



Hi
Could you please explain this in greater details?
My thought was

1) sqrt{x^2} = 4 --> x^2 =16 --> x = 4 or x = -4. However the answer itself says that Sq rt( x^2 ) = 4 , so does it not imply that x = 4 (and not -4)

2) |x| = -x -----------------clearly says that x is negative

Hence answer should be D (both statements alone are sufficient to answer the question)?


Why? Plug -4, there. Does it satisfy the equation? Yes. So, x could be -4.

One more way to look at it: \(\sqrt{x^2}=|x|\), so we have that |x| = 4, which means that x = 4 or x = -4.

Hope it's clear.



yes it does.... thanks :)
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Re: Is x = 4 ? (1) (x^2)^(1/2) = 4 (2) |x| = -x [#permalink] New post   13 Sep 2014, 21:30
Bunuel wrote:
mayankpant wrote:
Bunuel wrote:
Is x = 4 ?

(1) \(\sqrt{x^2}\) = 4 --> x^2 =16 --> x = 4 or x = -4. Not sufficient.

(2) \(|x| = -x\). This is only possible when \(x\leq{0}\), so x cannot be 4. Sufficient.

Answer: B.

P.S. Please name topics properly. Check rule 3 here: rules-for-posting-please-read-this-before-posting-133935.html Thank you.



Hi
Could you please explain this in greater details?
My thought was

1) sqrt{x^2} = 4 --> x^2 =16 --> x = 4 or x = -4. However the answer itself says that Sq rt( x^2 ) = 4 , so does it not imply that x = 4 (and not -4)

2) |x| = -x -----------------clearly says that x is negative

Hence answer should be D (both statements alone are sufficient to answer the question)?


Why? Plug -4, there. Does it satisfy the equation? Yes. So, x could be -4.

One more way to look at it: \(\sqrt{x^2}=|x|\), so we have that |x| = 4, which means that x = 4 or x = -4.

Hope it's clear.




Why is the answer B.

I mean I understood the reasoning behind statement 1 that X = 4, -4

But in case of statement 2, why have we taken the value of X = -4, Nothing in statement 2 states that there is a definite value for X except that it is a negative value.

Please clear my doubt
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Re: Is x = 4 ? (1) (x^2)^(1/2) = 4 (2) |x| = -x [#permalink] New post   14 Sep 2014, 17:25
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Ashishmathew01081987 wrote:
Why is the answer B.

I mean I understood the reasoning behind statement 1 that X = 4, -4

But in case of statement 2, why have we taken the value of X = -4, Nothing in statement 2 states that there is a definite value for X except that it is a negative value.

Please clear my doubt


This is not a value question. It's a YES/NO question.

The question asks whether x is 4. From (2) we get that x is negative, so the answer to the question whether x is 4, is definite NO.

Hope it's clear.
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Re: Is x = 4 ? (1) (x^2)^(1/2) = 4 (2) |x| = -x [#permalink] New post   16 Sep 2014, 14:31
how can an absolute value be negative?
can someone explain?
we can plug in -4 to check it, |4|=-4, I understand that |-4|=4, but vice versa? this is the first time I see smth like this.
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Re: Is x = 4 ? (1) (x^2)^(1/2) = 4 (2) |x| = -x [#permalink] New post   16 Sep 2014, 14:36
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mvictor wrote:
how can an absolute value be negative?
can someone explain?


An absolute value cannot be negative. Because of that |x| = -x does not mean that |x| is negative, it means that -x must be more than or equal to 0: \(-x\geq{0}\) --> \(x\leq{0}\), so x is 0 or less. For example: |-2| = -(-2) = 2 = posiitve.
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Re: Is x = 4 ? (1) (x^2)^(1/2) = 4 (2) |x| = -x [#permalink] New post   01 Oct 2021, 04:43
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Is x = 4 ?

(1) \(\sqrt{x^2}\) = 4
Square both sides \(x^2=16\)
So x can be 4 or -4.

(2) \(|x| = -x\)
As absolute modulus is always non negative, -x is also non negative.
\(-x\geq 0\)
Multiply by -1, and change the inequality sign.
\(-x*-1\leq -1*0\)
\(x\leq 0\)
So x cannot be 4.
Sufficient



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Re: Is x = 4 ? (1) (x^2)^(1/2) = 4 (2) |x| = -x [#permalink]
01 Oct 2021, 04:43
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