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

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

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New post 01 Oct 2017, 23:28
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  65% (hard)

Question Stats:

38% (01:53) correct 63% (01:49) wrong based on 32 sessions

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

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New post 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

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

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New post 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.


Can you elaborate please????

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Re: If xy + x is a prime number, is xy + x a multiple of 3? [#permalink]

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New post 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.


Can you elaborate please????


Hi Mo2men

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

Kudos [?]: 306 [0], given: 39

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

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New post 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.


Can you elaborate please????


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.

Kudos [?]: 302 [0], given: 166

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

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New post 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 \(2*\frac{1}{2}+2 =1+2=3\)

Kudos [?]: 306 [0], given: 39

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

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New post 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?

Kudos [?]: 302 [0], given: 166

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Re: If xy + x is a prime number, is xy + x a multiple of 3? [#permalink]

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New post 03 Oct 2017, 02:30
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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

Kudos [?]: 306 [1], given: 39

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Re: If xy + x is a prime number, is xy + x a multiple of 3? [#permalink]

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New post 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 :-D

kudos to you

Kudos [?]: 302 [0], given: 166

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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