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Is the product of x and y a prime number?
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12 Aug 2010, 23:11
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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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Re: Is the product of x and y a prime number?
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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.
So answer should be C



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Re: Is the product of x and y a prime number?
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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?
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13 Aug 2010, 10:59
Why isn't the answer B?
If Y is positive and prime, and X is positive and not prime then xy will always be a nonprime number, right?
What am I missing?



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Re: Is the product of x and y a prime number?
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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?
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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?
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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?
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14 Aug 2010, 08:28
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?
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14 Aug 2010, 09:51
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 nonprime 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. Answer: C. Hope it's clear.
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Re: Is the product of x and y a prime number?
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14 Aug 2010, 10:03
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?
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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 so answer is c



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Re: Is the product of x and y a prime number?
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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 nonprime 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. Answer: C. 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?
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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 nonprime, 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. So answer should be C.
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Re: Is the product of x and y a prime number?
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23 Apr 2018, 06:46
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 primeCase 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 primeSince 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 primeLet'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 primeCase 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 primeSince 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 1If 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 = yThis means the product xy MUST BE PRIMESince we can answer the target question with certainty, the combined statements are SUFFICIENT Answer: C Cheers, Brent
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