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Is x^1/2 a prime number?

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Is x^1/2 a prime number? [#permalink] New post   Updated on: 11 Jul 2013, 01:50
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Is x^1/2 a prime number?

(1) |3x - 7| = 2x + 2
(2) x^2 = 9x
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C

Originally posted by GMATmission on 24 Aug 2011, 23:41.
Last edited by Bunuel on 11 Jul 2013, 01:50, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: number properties [#permalink] New post   25 Aug 2011, 00:05
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the answer is C

1 |3x-7|=2x+2

--> -(3x-7)=2x+2
on solving this we get x=1
--> +(3x-7)=2x+2
on solving this we get x=9
so insufficient

B ) x^2=9x
x^2-9x=0
x(x-9)=0
hence x=0,9
insuff

combining both will give x=9
hence sqroot(9) will give 3 which is a prime number
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Re: number properties [#permalink] New post   25 Aug 2011, 04:28
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(1) mod (3x-7) = 2x+2
3x-7=2x+2
x=9

-3x+7=2x+2
x=1
x can be 9 or 1, 9^1/2 is 3 (prime) while 1^1/2 is 1 (not prime)
INSUFFICIENT

(2) x^2 = 9x
x(x-9)=0
x can only have two solutions 0 or 9
INSUFFICIENT

But combining the two statements we have 9 in both so the answer is 9
9^1/2 = 3, which is prime
So the answer is C
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Re: number properties [#permalink] New post   26 Aug 2011, 08:45
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abhi398 wrote:
the answer is C

1 |3x-7|=2x+2

--> -(3x-7)=2x+2
on solving this we get x=1
--> +(3x-7)=2x+2
on solving this we get x=9
so insufficient

B ) x^2=9x
x^2-9x=0
x(x-9)=0
hence x=0,9
insuff

combining both will give x=9
hence sqroot(9) will give 3 which is a prime number


OA is C. I was wondering whether we should consider negative values. Sq root of 9 = +/-3. +3 is prime and -3 is not. What do you say?
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Re: number properties [#permalink] New post   26 Aug 2011, 09:15
When we take the square root of a number in the GMAT the answer is always positive.
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Re: number properties [#permalink] New post   27 Aug 2011, 14:42
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GMATmission wrote:
OA is C. I was wondering whether we should consider negative values. Sq root of 9 = +/-3. +3 is prime and -3 is not. What do you say?


nammers wrote:
When we take the square root of a number in the GMAT the answer is always positive.



x has 2 roots i.e. sqrt(x) and - sqrt(x).

The question is asking about positive root i.e. sqrt(x). so sqrt(x) has always a +ve value.

Similarly sqrt(9) = 3.
-sqrt(9) = -3.
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Re: Is x^1/2 a prime number? [#permalink] New post   10 Jul 2014, 01:40
GMATmission wrote:
Is x^1/2 a prime number?

(1) |3x - 7| = 2x + 2
(2) x^2 = 9x


Hi Bunnel,

Could you please provide your comments on this?

I am using following logic

|3x-7| = 2x +2. here L.H.S is positive so 2x+2 >= 0---> 2x>=-2--> x>=-1

so if if x>= -1 then |3x-7| = -3x+7 = 2x+2

-5x = -5
x = 1

only 1 value so sufficient. Ans A ( my question is why we are considering other scenario to get 9)

in st2

x^2 = 9x
x^2-9x = 0
x(x-9) = 0
x= 0 or 9

here we are getting 2 values so not sufficient.
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Re: Is x^1/2 a prime number? [#permalink] New post   10 Jul 2014, 02:04
Expert Reply
PathFinder007 wrote:
GMATmission wrote:
Is x^1/2 a prime number?

(1) |3x - 7| = 2x + 2
(2) x^2 = 9x


Hi Bunnel,

Could you please provide your comments on this?

I am using following logic

|3x-7| = 2x +2. here L.H.S is positive so 2x+2 >= 0---> 2x>=-2--> x>=-1

so if if x>= -1 then |3x-7| = -3x+7 = 2x+2

-5x = -5
x = 1

only 1 value so sufficient. Ans A ( my question is why we are considering other scenario to get 9)

in st2

x^2 = 9x
x^2-9x = 0
x(x-9) = 0
x= 0 or 9

here we are getting 2 values so not sufficient.


2 questions:

1. Does x=9 satisfy the equation?
2. Why do you say that when x>=-1, then |3x-7| = -(3x-7)?
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Re: Is x^1/2 a prime number? [#permalink] New post   10 Jul 2014, 03:14
Bunuel wrote:
PathFinder007 wrote:
GMATmission wrote:
Is x^1/2 a prime number?

(1) |3x - 7| = 2x + 2
(2) x^2 = 9x


Hi Bunnel,

Could you please provide your comments on this?

I am using following logic

|3x-7| = 2x +2. here L.H.S is positive so 2x+2 >= 0---> 2x>=-2--> x>=-1

so if if x>= -1 then |3x-7| = -3x+7 = 2x+2

-5x = -5
x = 1

only 1 value so sufficient. Ans A ( my question is why we are considering other scenario to get 9)

in st2

x^2 = 9x
x^2-9x = 0
x(x-9) = 0
x= 0 or 9

here we are getting 2 values so not sufficient.


2 questions:

1. Does x=9 satisfy the equation?
2. Why do you say that when x>=-1, then |3x-7| = -(3x-7)?


Hi Bunnel,

1. Yes x=9 satisfy the equation.
2. I told x>= -1 because in st1 it is given that |3x-7| = 2x+2. Here LHS. is in modulus so it is >=0. so RHS should be >=0 2x+2>= 0 --> 2x>=-2-->x>=-1


Thanks
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Is x^1/2 a prime number? [#permalink] New post   10 Jul 2014, 03:56
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PathFinder007 wrote:
Bunuel wrote:
PathFinder007 wrote:
Hi Bunnel,

Could you please provide your comments on this?

I am using following logic

|3x-7| = 2x +2. here L.H.S is positive so 2x+2 >= 0---> 2x>=-2--> x>=-1

so if if x>= -1 then |3x-7| = -3x+7 = 2x+2

-5x = -5
x = 1

only 1 value so sufficient. Ans A ( my question is why we are considering other scenario to get 9)

in st2

x^2 = 9x
x^2-9x = 0
x(x-9) = 0
x= 0 or 9

here we are getting 2 values so not sufficient.


2 questions:

1. Does x=9 satisfy the equation?
2. Why do you say that when x>=-1, then |3x-7| = -(3x-7)?


Hi Bunnel,

1. Yes x=9 satisfy the equation.
2. I told x>= -1 because in st1 it is given that |3x-7| = 2x+2. Here LHS. is in modulus so it is >=0. so RHS should be >=0 2x+2>= 0 --> 2x>=-2-->x>=-1


Thanks


You did not understand my second question. Yes, from (1) x>=-1 BUT why does that mean that |3x-7| = -(3x-7)?

P.S. It's Bunuel not Bunnel. :-D
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Re: Is x^1/2 a prime number? [#permalink] New post   10 Jul 2014, 06:07
Hey Bunuel I know I was using Bunnel bcz in my area where I live in india its mean wise. So I used this word for you.

i think i got confusion here |3x-7| = -(3x-7) as i thought putting -1 makes it negative in modulus |-3-7| . but I think this is not the case and it should be |3x-7| = 3x-7.

Thanks Bunuel for all your replies. Please clarify this
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Re: Is x^1/2 a prime number? [#permalink] New post   10 Jul 2014, 12:30
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PathFinder007 wrote:
Hey Bunuel I know I was using Bunnel bcz in my area where I live in india its mean wise. So I used this word for you.

i think i got confusion here |3x-7| = -(3x-7) as i thought putting -1 makes it negative in modulus |-3-7| . but I think this is not the case and it should be |3x-7| = 3x-7.

Thanks Bunuel for all your replies. Please clarify this


That's not correct.

|3x-7| = 3x-7, when x > 7/3.
|3x-7| = -(3x-7), when x <= 7/3.

x>=-1 is not sufficient info to say whether |3x-7| = 3x-7 or |3x-7| = -(3x-7). For example, if x=0<7/3, then |3x-7| = -(3x-7) but if x=100>7/3, then |3x-7| = 3x-7.

Hope it's clear.
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Is x^1/2 a prime number? [#permalink] New post   01 Sep 2014, 03:25
Hey bunuel, In Manhattan gmat book its written that absolute values have +ve or -ve value. For +ve value the sign after solving is positive then its a correct soln, same goes for -ve. But here when we solve for +ve value we get +9, thats a correct soln, but for -ve soln we get +1, which isnt negative, so its not a legitimte soln and hence should be ignored, acc to MGMAT. Plz help !
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Re: Is x^1/2 a prime number? [#permalink] New post   01 Sep 2014, 03:35
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sunaimshadmani wrote:
Hey bunuel, In Manhattan gmat book its written that absolute values have +ve or -ve value. For +ve value the sign after solving is positive then its a correct soln, same goes for -ve. But here when we solve for +ve value we get +9, thats a correct soln, but for -ve soln we get +1, which isnt negative, so its not a legitimte soln and hence should be ignored, acc to MGMAT. Plz help !


Not sure I understand what you mean there.

As for the roots of |3x - 7| = 2x + 2: both x = 1 and x = 9 satisfy this equation, thus both are valid solutions.

Maybe if you could show your work, I'd be able to say more.
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Re: Is x^1/2 a prime number? [#permalink] New post   06 Sep 2014, 11:05
abhi398 wrote:
the answer is C

1 |3x-7|=2x+2

--> -(3x-7)=2x+2
on solving this we get x=1
--> +(3x-7)=2x+2
on solving this we get x=9
so insufficient

B ) x^2=9x
x^2-9x=0
x(x-9)=0
hence x=0,9
insuff

combining both will give x=9
hence sqroot(9) will give 3 which is a prime number




why cant we take x^2=9x as x.x=9.x
so x on both sides get cancelled
hence x=9
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Re: Is x^1/2 a prime number? [#permalink] New post   29 Aug 2023, 09:47
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Re: Is x^1/2 a prime number? [#permalink]
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