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# If xy + x is a prime number, is xy + x a multiple of 3?

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Math Expert
Joined: 02 Sep 2009
Posts: 43792
If xy + x is a prime number, is xy + x a multiple of 3? [#permalink]

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01 Oct 2017, 23:28
1
KUDOS
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Difficulty:

65% (hard)

Question Stats:

36% (01:53) correct 64% (01:53) wrong based on 33 sessions

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Fresh GMAT Club Tests' Challenge Question:

If xy + x is a prime number, is xy + x a multiple of 3?

(1) xy = 3
(2) x = 2
[Reveal] Spoiler: OA

_________________
PS Forum Moderator
Joined: 25 Feb 2013
Posts: 919
Location: India
GPA: 3.82
If xy + x is a prime number, is xy + x a multiple of 3? [#permalink]

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02 Oct 2017, 03:10
Bunuel wrote:

Fresh GMAT Club Tests' Challenge Question:

If xy + x is a prime number, is xy + x a multiple of 3?

(1) xy = 3
(2) x = 2

as $$xy+x$$ is a prime no, so $$x$$ cannot be $$0$$ and only prime that is a multiple of $$3$$ is $$3$$ itself so the question is asking is $$xy+x=3$$

Statement 1: $$xy=3$$, add $$x$$ to both sides, $$xy+x=3+x$$

as explained earlier $$x$$ is not equal to $$0$$ so $$3+x$$ cannot be equal to $$3$$, hence $$xy+x$$ is not a multiple of $$3$$. Sufficient

Statement 2: substitute the value of $$x$$ in question stem to get $$2y+2$$

Now if $$y=\frac{1}{2}$$, then $$xy+x=3$$ and if $$y=\frac{3}{2}$$, then $$xy+x=5$$. Hence no unique answer. Insufficient

Option A
VP
Joined: 26 Mar 2013
Posts: 1427
If xy + x is a prime number, is xy + x a multiple of 3? [#permalink]

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03 Oct 2017, 01:56
Bunuel wrote:

Fresh GMAT Club Tests' Challenge Question:

If xy + x is a prime number, is xy + x a multiple of 3?

(1) xy = 3
(2) x = 2

Bunuel

Is the question correct? or is there any typo?

Statement 1: xy = 3

Let x =1 & y = 3...........xy+x = 3+1= NOT Prime ........condition highlighted failed.

Let x =3 & y = 1...........xy+x = 3+3 = NOT Prime ........condition highlighted failed.

Let x =3/2 & y = 2...........xy+x = 3 +3/2= NOT Prime ........condition highlighted failed.

Let x =3 & y = 3/2...........xy+x = 3/2+2 = NOT Prime ........condition highlighted failed.

PS Forum Moderator
Joined: 25 Feb 2013
Posts: 919
Location: India
GPA: 3.82
Re: If xy + x is a prime number, is xy + x a multiple of 3? [#permalink]

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03 Oct 2017, 02:14
Mo2men wrote:
Bunuel wrote:

Fresh GMAT Club Tests' Challenge Question:

If xy + x is a prime number, is xy + x a multiple of 3?

(1) xy = 3
(2) x = 2

Bunuel

Is the question correct? or is there any typo?

Statement 1: xy = 3

Let x =1 & y = 3...........xy+x = 3+1= NOT Prime ........condition highlighted failed.

Let x =3 & y = 1...........xy+x = 3+3 = NOT Prime ........condition highlighted failed.

Let x =3/2 & y = 2...........xy+x = 3 +3/2= NOT Prime ........condition highlighted failed.

Let x =3 & y = 3/2...........xy+x = 3/2+2 = NOT Prime ........condition highlighted failed.

Hi Mo2men

use x=2 & y=1/2 then you will get xy+x=3=Prime
VP
Joined: 26 Mar 2013
Posts: 1427
If xy + x is a prime number, is xy + x a multiple of 3? [#permalink]

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03 Oct 2017, 02:17
niks18 wrote:
Mo2men wrote:
Bunuel wrote:

Fresh GMAT Club Tests' Challenge Question:

If xy + x is a prime number, is xy + x a multiple of 3?

(1) xy = 3
(2) x = 2

Bunuel

Is the question correct? or is there any typo?

Statement 1: xy = 3

Let x =1 & y = 3...........xy+x = 3+1= NOT Prime ........condition highlighted failed.

Let x =3 & y = 1...........xy+x = 3+3 = NOT Prime ........condition highlighted failed.

Let x =3/2 & y = 2...........xy+x = 3 +3/2= NOT Prime ........condition highlighted failed.

Let x =3 & y = 3/2...........xy+x = 3/2+2 = NOT Prime ........condition highlighted failed.

Hi Mo2men

use x=2 & y=1/2 then you will get xy+x=3=Prime

Hi niks18,

If I use your example above....then x * y does not equal 3 as per statement 1.
PS Forum Moderator
Joined: 25 Feb 2013
Posts: 919
Location: India
GPA: 3.82
If xy + x is a prime number, is xy + x a multiple of 3? [#permalink]

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03 Oct 2017, 02:21
Quote:
If I use your example above....then x * y does not equal 3 as per statement 1.

Hi Mo2men

(xy+x) is prime and not xy so if x=2 & y=1/2, then $$2*\frac{1}{2}+2 =1+2=3$$
VP
Joined: 26 Mar 2013
Posts: 1427
If xy + x is a prime number, is xy + x a multiple of 3? [#permalink]

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03 Oct 2017, 02:26
niks18 wrote:
Quote:
If I use your example above....then x * y does not equal 3 as per statement 1.

Hi Mo2men

(xy+x) is prime and not xy so if x=2 & y=1/2, then $$2*\frac{1}{2}+2 =1+2=3$$

Maybe I can't see something. Can you help me with statement 1 and come up with example that maintain both Statement 1 xy =3 & condition in the stem xy+x = Prime?
PS Forum Moderator
Joined: 25 Feb 2013
Posts: 919
Location: India
GPA: 3.82
Re: If xy + x is a prime number, is xy + x a multiple of 3? [#permalink]

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03 Oct 2017, 02:30
1
KUDOS
Mo2men wrote:
niks18 wrote:
Quote:
If I use your example above....then x * y does not equal 3 as per statement 1.

Hi Mo2men

(xy+x) is prime and not xy so if x=2 & y=1/2, then $$2*\frac{1}{2}+2 =1+2=3$$

Maybe I can't see something. Can you help me with statement 1 and come up with example that maintain both Statement 1 xy =3 & condition in the stem xy+x = Prime?

Hi Mo2men
x=2 & y =3/2, then xy=2*3/2=3=Prime and xy+x=3+2=5=Prime
VP
Joined: 26 Mar 2013
Posts: 1427
Re: If xy + x is a prime number, is xy + x a multiple of 3? [#permalink]

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03 Oct 2017, 02:39
niks18 wrote:

Hi Mo2men
x=2 & y =3/2, then xy=2*3/2=3=Prime and xy+x=3+2=5=Prime

Hi niks18

Thanks for bearing with me. I know where I got wrong. I totally missed up my 4th example when asked Bunuel. It seems my brain get burned after some study

kudos to you
Re: If xy + x is a prime number, is xy + x a multiple of 3?   [#permalink] 03 Oct 2017, 02:39
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