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# M04#07 If x is an integer, what is the value of x?

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Intern
Joined: 10 Jan 2014
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M04#07 If x is an integer, what is the value of x? [#permalink]

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26 Feb 2014, 02:45
If x is an integer, what is the value of x?
(1) |23x| is a prime number.

(2) 2√x² is a prime number.

___________________________________________________________

My choice was B although I knew it was probably E (which it turned out it was). Here's my problem with statement 2: if we know what that 2√x²=prime number, then why can't we conclude that x=1? Let's assume that x= -1, then according to the equation we would have 2√x²=positive value. but knowing that x= -1 we know that the equation would become 2*(-1)= -2 # 2 (since we know we would have to use the negative root since x= -1). but from statement 2 we know that it must be positive so x can only be positive 1. I know that technically the definition for √x² is |x| but in this case it does not make sense for me. for statement 1 it's no problem, since |x| dictates to multiply by (-1) if negative, but in the case of statement 2, x should only be positive, since otherwise we would have to take the negative square root and then the result would not be positive anymore. I hope I made it clear why I am confused. Maybe someone could help me

cheers,

Max

Last edited by damamikus on 26 Feb 2014, 03:23, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 38858
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Kudos [?]: 106060 [0], given: 11607

Re: M04#07 If x is an integer, what is the value of x? [#permalink]

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26 Feb 2014, 02:50
damamikus wrote:
If x is an integer, what is the value of x?
(1) |23x| is a prime number.

(2) 2√x² is a prime number.

My choice was B although I knew it was probably E (which it turned out it was). Here's my problem with statement 2: if we know what that 2√x²=prime number, then why can't we conclude that x=1? Let's assume that x= -1, then according to the equation we would have 2√x²=positive value. but knowing that x= -1 we know that the equation would become 2*(-1)= -2 # 2 (since we know we would have to use the negative root since x= -1). but from statement 2 we know that it must be positive so x can only be positive 1. I know that technically the definition for √x² is |x| but in this case it does not make sense for me. for statement 1 it's no problem, since |x| dictates to multiply by (-1) if negative, but in the case of statement 2, x should only be positive, since otherwise we would have to take the negative square root and then the result would not be positive anymore. I hope I made it clear why I am confused. Maybe someone could help me

cheers,

Max

If $$x=-1$$, then $$2\sqrt{x^2}=2\sqrt{(-1)^2}=2\sqrt{1}=2$$.

Complete solution:

If x is an integer, what is the value of x?

(1) $$|23x|$$ is a prime number. From this statement it follows that x=1 or x=-1. Not sufficient.

(2) $$2\sqrt{x^2}$$ is a prime number. The same here: x=1 or x=-1. Not sufficient.

(1)+(2) x could be 1 or -1. Not sufficient.

Hope it's clear.
_________________
Intern
Joined: 10 Jan 2014
Posts: 22
Followers: 0

Kudos [?]: 3 [0], given: 6

Re: M04#07 If x is an integer, what is the value of x? [#permalink]

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26 Feb 2014, 03:07
I think i get it now: since 2√x² must be positive, i am taking the positive square root out of the square-root expression x². but the value that lead to the positive expression inside the square root could be negative or positive. --> x²=z --> 2√z=positive, hence z=positive. but what lead to z being positive (--> x ) could be either negative or positive, since in both cases z would be positive. hope this reasoning is correct

thanks!
Manager
Joined: 09 Nov 2013
Posts: 90
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Kudos [?]: 11 [0], given: 30

Re: M04#07 If x is an integer, what is the value of x? [#permalink]

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03 Mar 2014, 05:49
Bunuel wrote:
damamikus wrote:
If x is an integer, what is the value of x?
(1) |23x| is a prime number.

(2) 2√x² is a prime number.

My choice was B although I knew it was probably E (which it turned out it was). Here's my problem with statement 2: if we know what that 2√x²=prime number, then why can't we conclude that x=1? Let's assume that x= -1, then according to the equation we would have 2√x²=positive value. but knowing that x= -1 we know that the equation would become 2*(-1)= -2 # 2 (since we know we would have to use the negative root since x= -1). but from statement 2 we know that it must be positive so x can only be positive 1. I know that technically the definition for √x² is |x| but in this case it does not make sense for me. for statement 1 it's no problem, since |x| dictates to multiply by (-1) if negative, but in the case of statement 2, x should only be positive, since otherwise we would have to take the negative square root and then the result would not be positive anymore. I hope I made it clear why I am confused. Maybe someone could help me

cheers,

Max

If $$x=-1$$, then $$2\sqrt{x^2}=2\sqrt{(-1)^2}=2\sqrt{1}=2$$.

Complete solution:

If x is an integer, what is the value of x?

(1) $$|23x|$$ is a prime number. From this statement it follows that x=1 or x=-1. Not sufficient.

(2) $$2\sqrt{x^2}$$ is a prime number. The same here: x=1 or x=-1. Not sufficient.

(1)+(2) x could be 1 or -1. Not sufficient.

Hope it's clear.

Dear Bunuel

If x = -1 or x=1 then it will give -23 or 23. Can negative numbers be prime numbers?

Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 38858
Followers: 7728

Kudos [?]: 106060 [0], given: 11607

Re: M04#07 If x is an integer, what is the value of x? [#permalink]

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03 Mar 2014, 05:52
sidpopy wrote:
Bunuel wrote:
damamikus wrote:
If x is an integer, what is the value of x?
(1) |23x| is a prime number.

(2) 2√x² is a prime number.

My choice was B although I knew it was probably E (which it turned out it was). Here's my problem with statement 2: if we know what that 2√x²=prime number, then why can't we conclude that x=1? Let's assume that x= -1, then according to the equation we would have 2√x²=positive value. but knowing that x= -1 we know that the equation would become 2*(-1)= -2 # 2 (since we know we would have to use the negative root since x= -1). but from statement 2 we know that it must be positive so x can only be positive 1. I know that technically the definition for √x² is |x| but in this case it does not make sense for me. for statement 1 it's no problem, since |x| dictates to multiply by (-1) if negative, but in the case of statement 2, x should only be positive, since otherwise we would have to take the negative square root and then the result would not be positive anymore. I hope I made it clear why I am confused. Maybe someone could help me

cheers,

Max

If $$x=-1$$, then $$2\sqrt{x^2}=2\sqrt{(-1)^2}=2\sqrt{1}=2$$.

Complete solution:

If x is an integer, what is the value of x?

(1) $$|23x|$$ is a prime number. From this statement it follows that x=1 or x=-1. Not sufficient.

(2) $$2\sqrt{x^2}$$ is a prime number. The same here: x=1 or x=-1. Not sufficient.

(1)+(2) x could be 1 or -1. Not sufficient.

Hope it's clear.

Dear Bunuel

If x = -1 or x=1 then it will give -23 or 23. Can negative numbers be prime numbers?

Thanks

No, only positive integers can be primes (the smallest prime is 2).

Now, if x=-1, then $$|23x|=|23*(-1)|=|-23|=23$$. I think you missed modulus sign there |23x|.

Hope it helps.
_________________
Re: M04#07 If x is an integer, what is the value of x?   [#permalink] 03 Mar 2014, 05:52
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# M04#07 If x is an integer, what is the value of x?

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