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Is x^1/2 a prime number? [#permalink]
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24 Aug 2011, 23:41
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Is ￼x^1/2 a prime number? (1) 3x  7 = 2x + 2 (2) ￼x^2 = 9x
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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]
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25 Aug 2011, 00:05
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the answer is C
1 3x7=2x+2
> (3x7)=2x+2 on solving this we get x=1 > +(3x7)=2x+2 on solving this we get x=9 so insufficient
B ) x^2=9x x^29x=0 x(x9)=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]
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25 Aug 2011, 04:28
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(1) ￼mod (3x7) = 2x+2 3x7=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(x9)=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]
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26 Aug 2011, 08:45
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abhi398 wrote: the answer is C
1 3x7=2x+2
> (3x7)=2x+2 on solving this we get x=1 > +(3x7)=2x+2 on solving this we get x=9 so insufficient
B ) x^2=9x x^29x=0 x(x9)=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]
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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]
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27 Aug 2011, 14:42
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]
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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 3x7 = 2x +2. here L.H.S is positive so 2x+2 >= 0> 2x>=2> x>=1 so if if x>= 1 then 3x7 = 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^29x = 0 x(x9) = 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]
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10 Jul 2014, 02:04



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Re: Is x^1/2 a prime number? [#permalink]
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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 3x7 = 2x +2. here L.H.S is positive so 2x+2 >= 0> 2x>=2> x>=1 so if if x>= 1 then 3x7 = 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^29x = 0 x(x9) = 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 3x7 = (3x7)? Hi Bunnel, 1. Yes x=9 satisfy the equation. 2. I told x>= 1 because in st1 it is given that 3x7 = 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]
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10 Jul 2014, 03:56
PathFinder007 wrote: Bunuel wrote: PathFinder007 wrote: Hi Bunnel,
Could you please provide your comments on this?
I am using following logic
3x7 = 2x +2. here L.H.S is positive so 2x+2 >= 0> 2x>=2> x>=1
so if if x>= 1 then 3x7 = 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^29x = 0 x(x9) = 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 3x7 = (3x7)? Hi Bunnel, 1. Yes x=9 satisfy the equation. 2. I told x>= 1 because in st1 it is given that 3x7 = 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 3x7 = (3x7)? P.S. It's Bunuel not Bunnel.
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Re: Is x^1/2 a prime number? [#permalink]
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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 3x7 = (3x7) as i thought putting 1 makes it negative in modulus 37 . but I think this is not the case and it should be 3x7 = 3x7.
Thanks Bunuel for all your replies. Please clarify this



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Re: Is x^1/2 a prime number? [#permalink]
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10 Jul 2014, 12:30



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Is x^1/2 a prime number? [#permalink]
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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]
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01 Sep 2014, 03:35
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]
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06 Sep 2014, 11:05
abhi398 wrote: the answer is C
1 3x7=2x+2
> (3x7)=2x+2 on solving this we get x=1 > +(3x7)=2x+2 on solving this we get x=9 so insufficient
B ) x^2=9x x^29x=0 x(x9)=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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