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M01-30

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M01-30  [#permalink]

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New post 16 Sep 2014, 00:16
1
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C
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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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M01-30  [#permalink]

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New post 16 Sep 2014, 00:16
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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M01-30  [#permalink]

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New post 03 Mar 2015, 07:17
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?
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Re: M01-30  [#permalink]

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New post 03 Mar 2015, 07:29
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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Re: M01-30  [#permalink]

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New post 02 Aug 2017, 03:02
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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New post 02 Aug 2017, 07:25
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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Re: M01-30  [#permalink]

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New post 02 Aug 2017, 07:41
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: M01-30  [#permalink]

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New post 02 Aug 2017, 07:44
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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Re: M01-30  [#permalink]

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New post 02 Aug 2017, 23:41
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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: M01-30  [#permalink]

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New post 11 Apr 2018, 16:11
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: M01-30 &nbs [#permalink] 11 Apr 2018, 16:11
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