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# Is the product of x and y a prime number?

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Manager
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Is the product of x and y a prime number?  [#permalink]

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12 Aug 2010, 23:11
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62% (01:12) correct 38% (01:03) wrong based on 167 sessions

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Is the product of x and y a prime number?

(1) x^2 = 1
(2) y is positive and prime; x is positive but not prime

(C) 2008 GMAT Club - m01#30
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Joined: 30 May 2010
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Re: Is the product of x and y a prime number?  [#permalink]

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13 Aug 2010, 00:10
A) $$x^2$$=1 => x = 1 or -1, y can be anything. Let y=4 => xy= 4 or -4 which is not a prime
B) Let y=3 and x=9 => xy=27, which is not a prime.

C)x=1 and y is positive & prime
=> xy = y which is prime.

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Re: Is the product of x and y a prime number?  [#permalink]

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13 Aug 2010, 09:16
1) clearly unsuf
2) if x=1, y=2, xy prime,
if x=6, y=2, xy not prime. Uns
1)+2)
x=1
y is prime, so xy prime also
(C)
Am i right that eliminated "-1" when consider (1)+(2)?
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Re: Is the product of x and y a prime number?  [#permalink]

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13 Aug 2010, 10:59
1

If Y is positive and prime, and X is positive and not prime then xy will always be a non-prime number, right?

What am I missing?
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Re: Is the product of x and y a prime number?  [#permalink]

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13 Aug 2010, 11:51
I go with C

For a product of numbers to be prime, the other number has to be 1.

1) You can get positive or negative. Prime numbers are always positive. YES for 1 No for -1 Not Suff.

2) Tells us that Y is prime and that the other number is positive (it could be any number). Not Suff

1 + 2 = 1. YES
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Re: Is the product of x and y a prime number?  [#permalink]

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14 Aug 2010, 00:47
C :

1) x^2 = 1 => x can be -1 or 1 and it doesn't tell us anything about y, hence insufficient
2) y>0 and y prime, x>0 and x prime Gives two possibilities:
x=1 (1 is not a prime number) & y=3 => xy = 3 is prime
or
x=4 & y=3 => xy = 12 which is not prime

Together:
from 1) we know that x= 1 or -1 and from 2) (x>0) we are sure that it is 1
And if y is prime, x=1 then xy=y and the result is prime
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Re: Is the product of x and y a prime number?  [#permalink]

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14 Aug 2010, 07:57
OA = C
While combining the two statements, I didn't pay attention to "x is positive" part..
such a stupid mistake
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Re: Is the product of x and y a prime number?  [#permalink]

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14 Aug 2010, 08:28
1
I don't understand.
1. x = 1 or -1, I get the insuf part
2. y=prime, x=not prime, right here xy we know is NOT prime.
Why cannot I stop at B? I don't need the A part anymore.
If I look at C, then ok x=1, xy=y, y is prime, ok xy is prime. But my question is why do I have to go to C.. Is it not that if I can answer with less information, I go with that option?

I also hear that the options cannot contradict each other, which means that x=1 and hence I am forced to use that information to go with C? Bunuel please enlighten...
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Re: Is the product of x and y a prime number?  [#permalink]

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14 Aug 2010, 09:51
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bibha wrote:
Is the product of x and y a prime number?
1)x^2 = 1
2) y is positive and prime; x is positive but not prime
(C) 2008 GMAT Club - m01#30

I have a small confusion with this.. Will tell you after you get the answer.

Couple of things:
1. Only positive integers can be prime numbers;
2. 1 is not prime number.

Next, product of two integers $$x$$ and $$y$$ to be prime: either one of them must be $$1$$ and another $$prime$$, for example (1,3), (1,7)... OR one of them must be $$-1$$ and another $$-prime$$, for example (-1,-7), (-1,-13) ....

Back to the original question:

Is the product of x and y a prime number?

Question: is $$xy=prime$$?

(1) $$x^2=1$$ --> $$x=1$$ or $$x=-1$$. Not sufficient.

(2) $$y=prime$$; $$x>0\neq{prime}$$ --> if $$y=prime$$ and $$x=1$$ then answer would be YES but if $$y=prime$$ and $$x=4$$ (or any other non-prime integer >1 or some fractions) then answer would be NO. Not sufficient.

(1)+(2) as from (1) $$x=1$$ or $$x=-1$$ and from (2) $$x>0$$ then $$x=1$$, so $$xy=1*prime=prime$$. Sufficient.

Hope it's clear.
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Re: Is the product of x and y a prime number?  [#permalink]

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14 Aug 2010, 10:03
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Excellent Bunuel. it is the x=1 case that does the complication. Thanks for all your time and help!
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Re: Is the product of x and y a prime number?  [#permalink]

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15 Aug 2010, 18:54
Is the product of x and y a prime number?
1)x^2 = 1
2) y is positive and prime; x is positive but not prime

stat 1: no y value, not sufficient
stat 2: depends on the value of x, for ex if x=1 xy is prime number, if x=2 xy is not prime
from stat 1 and 2
x=1
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Re: Is the product of x and y a prime number?  [#permalink]

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24 Sep 2011, 21:59
Bunuel wrote:
bibha wrote:
Is the product of x and y a prime number?
1)x^2 = 1
2) y is positive and prime; x is positive but not prime
(C) 2008 GMAT Club - m01#30

I have a small confusion with this.. Will tell you after you get the answer.

Couple of things:
1. Only positive integers can be prime numbers;
2. 1 is not prime number.

Next, product of two integers $$x$$ and $$y$$ to be prime: either one of them must be $$1$$ and another $$prime$$, for example (1,3), (1,7)... OR one of them must be $$-1$$ and another $$-prime$$, for example (-1,-7), (-1,-13) ....

Back to the original question:

Is the product of x and y a prime number?

Question: is $$xy=prime$$?

(1) $$x^2=1$$ --> $$x=1$$ or $$x=-1$$. Not sufficient.

(2) $$y=prime$$; $$x>0\neq{prime}$$ --> if $$y=prime$$ and $$x=1$$ then answer would be YES but if $$y=prime$$ and $$x=4$$ (or any other non-prime integer >1 or some fractions) then answer would be NO. Not sufficient.

(1)+(2) as from (1) $$x=1$$ or $$x=-1$$ and from (2) $$x>0$$ then $$x=1$$, so $$xy=1*prime=prime$$. Sufficient.

Hope it's clear.

Hi Bunnel,

In the second statement example... We cant take x = 2 since it is given x is positive and not prime but 2 is prime...
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Re: Is the product of x and y a prime number?  [#permalink]

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25 Sep 2011, 04:04
bibha wrote:
Is the product of x and y a prime number?
1)x^2 = 1
2) y is positive and prime; x is positive but not prime
(C) 2008 GMAT Club - m01#30

I have a small confusion with this.. Will tell you after you get the answer.

1) x^2 = 1 means x=1 or x=-1
y can be any number
So x*y may or may not be prime.
Hence we can eliminate A and D

2) y = +ve and prime, so y = 2,3,5...
x = +ve and not non-prime, so x=1,4,6...
So, x*y = (2, 3, 6, 12...) may or may not be prime.
Hence we can eliminate B

3) Combining both
x can only be 1 and y can only be a prime number
Hence x*y = prime.
We can eliminate E.

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Re: Is the product of x and y a prime number?  [#permalink]

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23 Apr 2018, 06:46
Top Contributor
bibha wrote:
Is the product of x and y a prime number?

(1) x² = 1
(2) y is positive and prime; x is positive but not prime

Target question: Is the product xy a prime number?

Statement 1: x² = 1
This tells us that either x = 1 or x = -1, but it provides NO INFORMATION about y.
Consider these two possible cases:
Case a: x = 1 and y = 3. In this case, xy = (1)(3) = 3, which is prime. So, the answer to the target question is YES, the product xy IS prime
Case b: x = 1 and y = 6. In this case, xy = (1)(6) = 6, which is NOT prime. So, the answer to the target question is NO, the product xy is NOT prime
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y is positive and prime; x is positive but not prime
Let's test some possible cases again...
Case a: x = 1 (aside: 1 is NOT prime) and y = 3. In this case, xy = (1)(3) = 3, which is prime. So, the answer to the target question is YES, the product xy IS prime
Case b: x = 4 and y = 3. In this case, xy = (4)(3) = 12, which is NOT prime. So, the answer to the target question is NO, the product xy is NOT prime
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that either x = 1 or x = -1
Statement 2 tells us that x is POSITIVE, so we now know that x MUST equal 1
If x = 1, then the product xy = (1)(y) = y
Statement 2 also tells us that y is PRIME, and we just concluded that the product xy = y
This means the product xy MUST BE PRIME
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Cheers,
Brent
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Re: Is the product of x and y a prime number? &nbs [#permalink] 23 Apr 2018, 06:46
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