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Math Expert V
Joined: 02 Sep 2009
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Difficulty:   15% (low)

Question Stats: 69% (00:38) correct 31% (00:44) wrong based on 321 sessions

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If $$x$$ and $$y$$ are integers is $$xy$$ a prime number?

(1) $$x^2 = 1$$

(2) $$y$$ is a prime number and $$x$$ is a positive number but not a prime number.

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Math Expert V
Joined: 02 Sep 2009
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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.

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Joined: 18 Sep 2014
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Concentration: General Management, Technology
GMAT 1: 710 Q50 V37 GMAT 2: 710 Q49 V38 GMAT 3: 760 Q49 V45 GPA: 3.74

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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 V
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varun72 wrote:
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?

But the question asks whether xy is prime not x alone.
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Joined: 22 Dec 2016
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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.
Math Expert V
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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).
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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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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?
Math Expert V
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abhinavsareen1 wrote:
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?

_______________
Yes, it does.
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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

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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
Math Expert V
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shobhiitgupta wrote:
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

The question asks whether xy is prime not the value of xy.
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