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

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Bunuel
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If xy + x is a prime number, is xy + x a multiple of 3? [#permalink] New post   02 Oct 2017, 00:28
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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


M36-56

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Bunuel
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Re: If xy + x is a prime number, is xy + x a multiple of 3? [#permalink] New post   08 Nov 2021, 07:23
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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


M36-56


Official Solution:


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

There is only one prime which is a multiple of 3, 3 itself. So, the question basically asks whether \(xy + x=3\).

(1) \(xy = 3\)

The question becomes: does \(3+ x=3\)? Or: does \(x=0\)? If \(x\) were 0, then \(xy + x\) would be 0, which is NOT a prime number as given in the stem. So, \(x \neq 0\) and thus \(xy + x \neq 3\). Sufficient.

(2) \(x = 2\)

The question becomes: does \(2y+ 2=3\)? Or: does \(y=\frac{1}{2}\)? Well, we don't know that. \(y\) could be \(\frac{1}{2}\) but it might as well be some other number making \(xy + x\) a prime number, for example \(\frac{3}{2}\) or \(\frac{5}{2}\) or ... Not sufficient.


Answer: A
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Re: If xy + x is a prime number, is xy + x a multiple of 3? [#permalink] New post   02 Oct 2017, 04:10
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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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Re: If xy + x is a prime number, is xy + x a multiple of 3? [#permalink] New post   03 Oct 2017, 02:56
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] New post   03 Oct 2017, 03:14
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
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Re: If xy + x is a prime number, is xy + x a multiple of 3? [#permalink] New post   03 Oct 2017, 03:17
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.
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Re: If xy + x is a prime number, is xy + x a multiple of 3? [#permalink] New post   03 Oct 2017, 03:21
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 \(2*\frac{1}{2}+2 =1+2=3\)
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Re: If xy + x is a prime number, is xy + x a multiple of 3? [#permalink] New post   03 Oct 2017, 03:26
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?
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Re: If xy + x is a prime number, is xy + x a multiple of 3? [#permalink] New post   03 Oct 2017, 03:30
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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
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Re: If xy + x is a prime number, is xy + x a multiple of 3? [#permalink] New post   03 Oct 2017, 03:39
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
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Re: If xy + x is a prime number, is xy + x a multiple of 3? [#permalink] New post   24 Dec 2018, 02:57
Expert Reply
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


Par of GMAT CLUB'S New Year's Quantitative Challenge Set

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Re: If xy + x is a prime number, is xy + x a multiple of 3? [#permalink] New post   26 Dec 2018, 00:13
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


Statement 1) xy=3, If xy+x is a prime number, then 3+x is a prime number and for it to be divisible by 3, x has to be zero because all other prime numbers greater than 3 are not divisible by 3. But x can't be 0 as xy=3. So, xy+x isn't divisible by 3. Sufficient.

Statement 2) x=2. For y=1/2, xy+x=3, divisible by 3. For y=3/2, xy+x=5, not divisible by 3. Insufficient.

Hence, Option A is correct.
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Re: If xy + x is a prime number, is xy + x a multiple of 3? [#permalink] New post   26 Dec 2018, 21:46
If xy+x is a prime no. as given in question then we already know that it is not multiple of any other than 1 and itself.
We don't even need any of the two statements to say that. Then why isn't the answer 'D'?

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Re: If xy + x is a prime number, is xy + x a multiple of 3? [#permalink] New post   26 Dec 2018, 22:11
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UdayPratapSingh wrote:
If xy+x is a prime no. as given in question then we already know that it is not multiple of any other than 1 and itself.
We don't even need any of the two statements to say that. Then why isn't the answer 'D'?

Posted from my mobile device


xy+x is a prime number and is it a multiple of 3?

so, as it is a prime number, x(y+1) is a prime number

Now as 3 is a prime number, any prime number which is a multiple of 3 has to be 3.

Now x(y+1) = 3, so X cant be Zero....this is important!


A: xy = 3 and X is not 0, so Xy+ x is not a multiple of 3...............Sufficient

B: x=2 now substitute x= 2, and y as 1 we get xy+y = 3 ........a multiple of 3
x= 2, and y as 1/2 we get xy+y = 5..........NOT a multiple of 3..........Statement 2 ALONE is insufficient
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Re: If xy + x is a prime number, is xy + x a multiple of 3? [#permalink] New post   08 Oct 2019, 04:46
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


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

(1) xy = 3
Since xy+x is a prime number; xy is an integer; x is an integer
x = {0,2,4,8,10.....}
If x = 0; xy + x = 0 is NOT a prime number
For all other values of x; xy+x is NOT a multiple of 3
SUFFICIENT

(2) x = 2
2(y+1) is a prime number
y={0,.5,1.5,...}
For y = .5; xy+x is a multiple of 3
for all other values of y, xy+x is NOT a multiple of 3
NOT SUFFICIENT

IMO A
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Re: If xy + x is a prime number, is xy + x a multiple of 3? [#permalink] New post   08 Jul 2023, 06:32
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Re: If xy + x is a prime number, is xy + x a multiple of 3? [#permalink]
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