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Manager  Status: Bell the GMAT!!!
Affiliations: Aidha
Joined: 16 Aug 2011
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Concentration: Finance, General Management
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Is x^1/2 a prime number?  [#permalink]

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Difficulty:   75% (hard)

Question Stats: 51% (01:49) correct 49% (01:48) wrong based on 332 sessions

### HideShow timer Statistics Is ￼x^1/2 a prime number?

(1) |3x - 7| = 2x + 2
(2) ￼x^2 = 9x

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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.
Manager  Joined: 30 Sep 2009
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2
1

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
Manager  Joined: 19 Jul 2011
Posts: 90
Concentration: Finance, Economics
Schools: Duke '15
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2
(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
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Manager  Status: Bell the GMAT!!!
Affiliations: Aidha
Joined: 16 Aug 2011
Posts: 132
Location: Singapore
Concentration: Finance, General Management
GMAT 1: 680 Q46 V37 GMAT 2: 620 Q49 V27 GMAT 3: 700 Q49 V36 WE: Other (Other)

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1
abhi398 wrote:

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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Manager  Joined: 19 Jul 2011
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When we take the square root of a number in the GMAT the answer is always positive.
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Director  Joined: 03 May 2007
Posts: 758
Schools: University of Chicago, Wharton School

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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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Joined: 10 Mar 2014
Posts: 185
Re: Is x^1/2 a prime number?  [#permalink]

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GMATmission wrote:
Is ￼x^1/2 a prime number?

(1) |3x - 7| = 2x + 2
(2) ￼x^2 = 9x

Hi Bunnel,

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.
Math Expert V
Joined: 02 Sep 2009
Posts: 56300
Re: Is x^1/2 a prime number?  [#permalink]

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PathFinder007 wrote:
GMATmission wrote:
Is ￼x^1/2 a prime number?

(1) |3x - 7| = 2x + 2
(2) ￼x^2 = 9x

Hi Bunnel,

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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Joined: 10 Mar 2014
Posts: 185
Re: Is x^1/2 a prime number?  [#permalink]

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Bunuel wrote:
PathFinder007 wrote:
GMATmission wrote:
Is ￼x^1/2 a prime number?

(1) |3x - 7| = 2x + 2
(2) ￼x^2 = 9x

Hi Bunnel,

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
Math Expert V
Joined: 02 Sep 2009
Posts: 56300
Is x^1/2 a prime number?  [#permalink]

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1
PathFinder007 wrote:
Bunuel wrote:
PathFinder007 wrote:
Hi Bunnel,

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. _________________
Manager  B
Joined: 10 Mar 2014
Posts: 185
Re: Is x^1/2 a prime number?  [#permalink]

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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.

Math Expert V
Joined: 02 Sep 2009
Posts: 56300
Re: Is x^1/2 a prime number?  [#permalink]

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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.

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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GMAT 1: 630 Q42 V35 Is x^1/2 a prime number?  [#permalink]

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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 !
Math Expert V
Joined: 02 Sep 2009
Posts: 56300
Re: Is x^1/2 a prime number?  [#permalink]

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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]

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abhi398 wrote:

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]

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_________________ Re: Is x^1/2 a prime number?   [#permalink] 08 Jan 2019, 22:58
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