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Joined: 02 Sep 2009
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Question Stats:
72% (00:33) correct 28% (00:35) wrong based on 212 sessions
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Math Expert
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Official Solution:If x and y are integers is xy a prime number?Notice that only positive integers can be prime numbers and that 1 is not a prime number. Next, product of two integers \(x\) and \(y\) to be a prime number: either one of them must be \(1\) and another \(\text{prime}\), for example (1,3), (1,7)... OR one of them must be \(1\) and another \(\text{prime}\), for example (1,7), (1,13) ... (1) \(x^2=1\). Either \(x=1\) or \(x=1\). Not sufficient. (2) \(y\) is a prime number and \(x\) is a positive number but not a prime number. If \(y=\text{prime}\) and \(x=1\) then \(xy=y=\text{prime}\) but if for example \(y=\text{prime}\) and \(x=4\) \(xy=4y \neq \text{prime}\). Not sufficient. (1)+(2) as from (1) \(x=1\) or \(x=1\) and from (2) \(x \gt 0\) then \(x=1\), so \(xy=1*\text{prime}=\text{prime}\). Sufficient. Answer: C
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Intern
Joined: 18 Sep 2014
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GMAT 1: 710 Q50 V37 GMAT 2: 710 Q49 V38 GMAT 3: 760 Q49 V45
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Hi,
I see your logic and yes 'c' seems like a logical answer. However do answer this for me:
When we explore option A we get two answers for x i.e. 1 and 1. Is 1 a prime? No. Is 1 a prime? No again. Doesn't this answer our question with a definite No and hence shouldnt we go for option A?



Math Expert
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Re: M0130
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03 Mar 2015, 06:29



Intern
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Re: M0130
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02 Aug 2017, 02:02
While solving the question, I took xy as a number rather taking it as x*y. I think the question maker should clarify this ambiguity while framing the question, as xy can represent a number of the form 10x+y.



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Re: M0130
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02 Aug 2017, 06:25



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Re: M0130
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02 Aug 2017, 06:41
Stmnt i) No info about y  Insuff
Stmnt 2) if x = 1 > xy is prime; If x takes any value other than 1 > xy is not prime
Combining both > x=1 and y is prime, so xy is prime



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Re: M0130
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02 Aug 2017, 06:44
Bunuel wrote: abhinavsareen1 wrote: While solving the question, I took xy as a number rather taking it as x*y. I think the question maker should clarify this ambiguity while framing the question, as xy can represent a number of the form 10x+y. While I understand what you mean, it's actually the other way around. If xy where two digit integer, then it would have been clearly mentioned. Without this xy can only mean x*y (only multiplication sign can be omitted this way). Does this mean whenever and wherever xy would be mentioned, it would mean x*y until and unless it is mentioned xy represents a 2 digit integer?



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02 Aug 2017, 22:41



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Re: M0130
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11 Apr 2018, 15:11
1) X^2 = 1
X can be equal 1 or 1
We don't have any information about Y.
Insufficient
2) Y= prime X = + not prime
If Y= 2 X = 1 Then, XY = (1)(2) = 2 YES
If Y= 3 X = 4 Then XY = (4)(3) = 12 NO
Insufficient
Taking both statements together.... X=1 Y=Prime XY= (1)(prime) = prime
Always YES Sufficient
Answer C



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Re: M0130
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28 Nov 2018, 22:20
I marked E on my tests because prime = 2,3,5,7 combining both statements we get x as 1 but still y can be any of the primes hence would not be a prime.
Somebody correct me where am i wrong



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28 Nov 2018, 22:24










