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Math Expert V
Joined: 02 Sep 2009
Posts: 59586
If xy + x is a prime number, is xy + x a multiple of 3?  [#permalink]

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5 00:00

Difficulty:   95% (hard)

Question Stats: 37% (02:21) correct 63% (02:24) wrong based on 131 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

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Retired Moderator D
Joined: 25 Feb 2013
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If xy + x is a prime number, is xy + x a multiple of 3?  [#permalink]

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2
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
SVP  V
Joined: 26 Mar 2013
Posts: 2343
If xy + x is a prime number, is xy + x a multiple of 3?  [#permalink]

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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

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.

Retired Moderator D
Joined: 25 Feb 2013
Posts: 1159
Location: India
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Re: If xy + x is a prime number, is xy + x a multiple of 3?  [#permalink]

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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
SVP  V
Joined: 26 Mar 2013
Posts: 2343
If xy + x is a prime number, is xy + x a multiple of 3?  [#permalink]

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

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

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

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1
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
SVP  V
Joined: 26 Mar 2013
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Re: If xy + x is a prime number, is xy + x a multiple of 3?  [#permalink]

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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
Math Expert V
Joined: 02 Sep 2009
Posts: 59586
Re: If xy + x is a prime number, is xy + x a multiple of 3?  [#permalink]

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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

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

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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

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]

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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]

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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]

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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

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 Re: If xy + x is a prime number, is xy + x a multiple of 3?   [#permalink] 08 Oct 2019, 04:46
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