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

Question

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

M36-56

Bunuel · Accepted Answer

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 
eq 0  and thus  xy + x 
eq 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

niks18 · Answer

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

Mo2men · Answer

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????

niks18 · Answer

Hi  Mo2men

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

Mo2men · Answer

Hi  niks18 ,

If I use your example above....then x * y does not equal 3 as per statement 1.

niks18 · Answer

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

Mo2men · Answer

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?

niks18 · Answer

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

Mo2men · Answer

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

Bunuel · Answer

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

Ypsychotic · Answer

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.

UdayPratapSingh · Answer

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

fitzpratik · Answer

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

Kinshook · Answer

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

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