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# Is x a prime number?

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Math Expert
Joined: 02 Sep 2009
Posts: 50058
Is x a prime number?  [#permalink]

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16 Feb 2015, 06:54
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65% (hard)

Question Stats:

50% (01:18) correct 50% (01:25) wrong based on 220 sessions

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Is x a prime number?

(2) y^2=x
(1) 2x/x^2 = 1

Kudos for a correct solution.

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Re: Is x a prime number?  [#permalink]

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16 Feb 2015, 07:56
3
2
I'm guessing there is a typo and that $$y^2=x$$ is actually statement 1.

(1) $$y^2=x$$ [Insufficient] We are not told that y is an integer. If y is an integer, then x is not prime. Otherwise, y could be the square root of a prime such as $$\sqrt{2}$$
(2) $$2x/x^2 = 1$$ [Sufficient] From this statement, we can see that x is not zero. Multiplying both sides by $$x^2$$, we get $$2x = x^2$$. Dividing both sides by x, we are left with x = 2, which is a prime number.

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Joined: 11 Feb 2015
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Re: Is x a prime number?  [#permalink]

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16 Feb 2015, 09:27
My answer was C. Neither statement is sufficient:
In stmt 1, "y" can be 0,1, or the square root of a prime as stated above. Multiple possibilities, not sufficient
In stmt 2, "x" can be 1 or 2 and (2x / x^2) will equal 1. Multiple possibilities, not sufficient.

The problem never specified that x or y must be integers.
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Re: Is x a prime number?  [#permalink]

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16 Feb 2015, 11:59
Robcarr65 wrote:
In stmt 2, "x" can be 1 or 2 and (2x / x^2) will equal 1.

x cannot be 1 as $$(2*1)/(1^2) = 2/1 = 2$$

This may be confusing if you aren't familiar with the ^ sign. It means "raised to the power of".
So 2^3 = $$2^3$$ = 8
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Re: Is x a prime number?  [#permalink]

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16 Feb 2015, 14:06
sterling19 wrote:
Robcarr65 wrote:
In stmt 2, "x" can be 1 or 2 and (2x / x^2) will equal 1.

x cannot be 1 as $$(2*1)/(1^2) = 2/1 = 2$$

This may be confusing if you aren't familiar with the ^ sign. It means "raised to the power of".
So 2^3 = $$2^3$$ = 8

Thank you. Careless mistake on my part.
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Re: Is x a prime number?  [#permalink]

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17 Feb 2015, 03:17
Is x a prime number?

(2) y^2=x
(1) 2x/x^2 = 1

Statement 1 is sufficient- 2x/x^2=1.
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Re: Is x a prime number?  [#permalink]

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19 Feb 2015, 23:39
2
Statement 1 is insufficient:
y^2=x
If y is an integer then x is not prime.
If y is not an integer like sqrt2,sqrt3…. then x is prime.
So not sufficient.
Statement 2 is sufficient:
2/x=1
So x is 2. Which is prime.
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Is x a prime number?  [#permalink]

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20 Feb 2015, 01:12
1
(1) it states that x is positive but doesn't provide any detail of x being prime

Not Sufficient

(2) 2x/x^2=1 x can hold only one value I.e. 2 as x can not be 0

Sufficient

IMO (B)
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Posts: 50058
Re: Is x a prime number?  [#permalink]

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22 Feb 2015, 11:17
Bunuel wrote:
Is x a prime number?

(2) y^2=x
(1) 2x/x^2 = 1

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION

I. y could be 1, giving us a NO answer to the question (since 1 is not prime), or it could be (2)−−−√, giving us a YES answer to the question (since 2 is prime). Insufficient.

II. If you cross-multiply this equation, you'll get 2x = x². There are two solutions to this equation 0 and 2, but we can rule out 0, because that would put 0 in the denominator of the fraction in the original form of the equation, and putting 0 in the denominator is not allowed; it is undefined.

Therefore, x must be 2, a prime, giving us a YES in answer to the question. Sufficient.
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Re: Is x a prime number?  [#permalink]

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06 Aug 2016, 15:40
Bunuel wrote:
Bunuel wrote:
Is x a prime number?

(2) y^2=x
(1) 2x/x^2 = 1

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION

I. y could be 1, giving us a NO answer to the question (since 1 is not prime), or it could be (2)−−−√, giving us a YES answer to the question (since 2 is prime). Insufficient.

II. If you cross-multiply this equation, you'll get 2x = x². There are two solutions to this equation 0 and 2, but we can rule out 0, because that would put 0 in the denominator of the fraction in the original form of the equation, and putting 0 in the denominator is not allowed; it is undefined.

Therefore, x must be 2, a prime, giving us a YES in answer to the question. Sufficient.

Hi!
st1) doesnt matter at all y could be anything.......... ok?
st2) can x as a variable be reduced.. as its an equation rather inequality.. and hence coming up B as an answer...
thanks
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Re: Is x a prime number?  [#permalink]

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07 Aug 2016, 09:19
Bunuel wrote:
Is x a prime number?

(2) y^2=x
(1) 2x/x^2 = 1

Kudos for a correct solution.

Statement 2: If we take x^2 to the opposite side, 2x=x^2 and x^2-2x=0
x(x-2)=0.Therefore, x=0 or 2. How can we determine?

Thanks
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Re: Is x a prime number?  [#permalink]

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07 Aug 2016, 09:34
KS15 wrote:
Bunuel wrote:
Is x a prime number?

(2) y^2=x
(1) 2x/x^2 = 1

Kudos for a correct solution.

Statement 2: If we take x^2 to the opposite side, 2x=x^2 and x^2-2x=0
x(x-2)=0.Therefore, x=0 or 2. How can we determine?

Thanks

Once you have got the value of x as 0 and 2, you need to put the value in the actual statement to see if it works.

So, if you put x=0, you will have 0/0 form, which is NOT DEFINED. Hence, x cannot be 0, thus x=2 only. Hence, sufficient.
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Re: Is x a prime number?  [#permalink]

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16 Oct 2016, 03:32
We need to get if x is prime or not
statement 1 =>
x=y^2
If y is an integer then x wont be prime ( Primes can never be factorised)
Else if y=√2 then x=2 => Prime
Hence since no clue of y is given => Not suff
Statement 2 =>
2x/x^2=1
here x can never be 0 as something /0 => not defined
hence x^2=2x=> x=2 which is a prime number
Therefore suff

Hence B
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Re: Is x a prime number? &nbs [#permalink] 16 Oct 2016, 03:32
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