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# If x is an integer, then is x a prime number?

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Manager
Joined: 24 Dec 2009
Posts: 219
If x is an integer, then is x a prime number? [#permalink]

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04 May 2012, 20:51
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If x is an integer, then is x a prime number?

(1) x is a multiple of a prime number.
(2) x is a product of two integers.
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 39656
Re: If x is an integer, then is x a prime number? [#permalink]

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04 May 2012, 21:38
If x is an integer, then is x a prime number?

(1) x is a multiple of a prime number --> if x=2 then the asnwer is Yes, but if x=4 then the answer is NO. Not sufficient.

(2) x is a product of two integers --> the same here: if x=1*2=2 then the asnwer is Yes, but if x=1*4=4 then the answer is NO. Not sufficient.

(1)+(2) The same xample: if x=2 then the asnwer is Yes, but if x=4 then the answer is NO. Not sufficient.

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Joined: 18 Oct 2010
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Re: If x is an integer, then is x a prime number? [#permalink]

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05 May 2012, 17:01
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Bunuel wrote:
If x is an integer, then is x a prime number?

(1) x is a multiple of a prime number --> if x=2 then the asnwer is Yes, but if x=4 then the answer is NO. Not sufficient.

(2) x is a product of two integers --> the same here: if x=1*2=2 then the asnwer is Yes, but if x=1*4=4 then the answer is NO. Not sufficient.

(1)+(2) The same xample: if x=2 then the asnwer is Yes, but if x=4 then the answer is NO. Not sufficient.

let me just further elaborate on Bunuel
(1) let the prime number be 2 then 2*1= 2 this is a prime number
again 2*2 =4 this is not a prime number so both 2 and 4 are multiples of the prime number 2, but 2 is a prime number and 4 is not so (1) is not sufficient

similarly 6 is a product of 2 integers 3*2 and 6 is not a prime number
but 2 is also a multiple of 2 integers 1*2 and 2 is a prime number
so (2) is also not sufficient

Taking both (1) and (2)
First number 2 , (1) Is a multiple of a prime no.( 2*1)
(2) is the product of 2 integers (2*1)
and 2 is a prime number

second number 6, (1) Is a multiple of a prime no.( 3*2)
(2) is the product of 2 integers (3*2)

and 6 is not a prime number

as both 1 and 2 together do not give a consistent answer the answer is e

Hope I have understood it correctly ,

Thanks Bunuel
Manager
Status: Kitchener
Joined: 03 Oct 2013
Posts: 98
Concentration: Finance, Finance
GPA: 2.9
WE: Education (Education)
If x is an integer, then is x a prime number? [#permalink]

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06 Feb 2015, 09:26
Bunuel wrote:
If x is an integer, then is x a prime number?

(1) x is a multiple of a prime number --> if x=2 then the asnwer is Yes, but if x=4 then the answer is NO. Not sufficient.

(2) x is a product of two integers --> the same here: if x=1*2=2 then the asnwer is Yes, but if x=1*4=4 then the answer is NO. Not sufficient.

(1)+(2) The same xample: if x=2 then the asnwer is Yes, but if x=4 then the answer is NO. Not sufficient.

Dear Bunuel, Ireally confused here in statement 1 (x is a multiple of a prime number )

in the case 2*1= 2. where is x here ? does it is 1 or 2 ?

Does the statement 1 mean that 2k=x? where k any integre.
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Math Expert
Joined: 02 Sep 2009
Posts: 39656
Re: If x is an integer, then is x a prime number? [#permalink]

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06 Feb 2015, 09:36
1
KUDOS
Expert's post
23a2012 wrote:
Bunuel wrote:
If x is an integer, then is x a prime number?

(1) x is a multiple of a prime number --> if x=2 then the asnwer is Yes, but if x=4 then the answer is NO. Not sufficient.

(2) x is a product of two integers --> the same here: if x=1*2=2 then the asnwer is Yes, but if x=1*4=4 then the answer is NO. Not sufficient.

(1)+(2) The same xample: if x=2 then the asnwer is Yes, but if x=4 then the answer is NO. Not sufficient.

Dear Bunuel, Ireally confused here in statement 1 (x is a multiple of a prime number )

in the case 2*1= 2. where is x here ? does it is 1 or 2 ?

Does the statement 1 mean that 2k=x? where k any integre.

x is a multiple of a prime number --> x = prime*k = 2*1.
_________________
Manager
Status: Kitchener
Joined: 03 Oct 2013
Posts: 98
Concentration: Finance, Finance
GPA: 2.9
WE: Education (Education)
Re: If x is an integer, then is x a prime number? [#permalink]

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06 Feb 2015, 09:44
Thank you Bunuel +1 KUDOS
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Re: If x is an integer, then is x a prime number?   [#permalink] 06 Feb 2015, 09:44
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