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Manager  Joined: 14 Apr 2010
Posts: 128
Is the product of x and y a prime number?  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 65% (01:12) correct 35% (01:05) wrong based on 210 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
Director  Status: Apply - Last Chance
Affiliations: IIT, Purdue, PhD, TauBetaPi
Joined: 17 Jul 2010
Posts: 573
Schools: Wharton, Sloan, Chicago, Haas
WE 1: 8 years in Oil&Gas
Re: Is the product of x and y a prime number?  [#permalink]

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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...
Director  Status: Apply - Last Chance
Affiliations: IIT, Purdue, PhD, TauBetaPi
Joined: 17 Jul 2010
Posts: 573
Schools: Wharton, Sloan, Chicago, Haas
WE 1: 8 years in Oil&Gas
Re: Is the product of x and y a prime number?  [#permalink]

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Excellent Bunuel. it is the x=1 case that does the complication. Thanks for all your time and help!
Intern  Joined: 08 Nov 2009
Posts: 13
Is the product of x and y a prime number?  [#permalink]

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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

My question is , why do we need to know whether the other non-prime number is 1 or not .
Why isn't statement 2 sufficient , that a prime * non-prime is always non-prime
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Joined: 11 Sep 2015
Posts: 4318
Re: Is the product of x and y a prime number?  [#permalink]

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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
_________________ Re: Is the product of x and y a prime number?   [#permalink] 23 Apr 2018, 05:46
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