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If x and y are both prime, is xy = 323?

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If x and y are both prime, is xy = 323?  [#permalink]

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New post 23 Apr 2014, 08:36
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If x and y are both prime, is xy = 323?

(1) x is the first prime after 18.
(2) y is the last prime before 180.
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Re: If x and y are both prime, is xy = 323?  [#permalink]

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New post 23 Apr 2014, 09:51
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tusharGupta1 wrote:
If x and y are both prime, is xy = 323?

(1) x is the first prime after 18.
(2) y is the last prime before 180.


323 = 19 x 17. There are only four factors of 323...1, 17, 19, 323.

Statement 1: x is the first prime after 18. It means X=19. For xy = 323, y should be 17. But y can take any prime value ....2, 3, 5 etc. Not sufficient

Statement 2: y is the last prime before 180. It means y=179. Now x can take any prime value but product of 179 and any other number cannot be 323. Therefor, xy cannot be 323. Sufficient

Answer is B
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Re: If x and y are both prime, is xy = 323?  [#permalink]

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New post 23 Apr 2014, 20:55
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tusharGupta1 wrote:
If x and y are both prime, is xy = 323?

(1) x is the first prime after 18.
(2) y is the last prime before 180.



You have x and y are prime. You need to find whether xy = 323.

(1) x is the first prime after 18.

This means x is 19. But what is y? We don't know. So should we move on right away that this statement alone is not sufficient? No. What if 19 is not a factor of 323? Since both x and y are integers, if 19 were not a factor of 323, it would be sufficient to say that xy is not 323.
323/19 = 17. So if y is 17, xy will be 323. If y is any other value, xy will not be 323.
Not sufficient alone.

(2) y is the last prime before 180.
We don't need to find the last prime before 180 as long as we know that it would be 179 or 173 etc. We don't really need to find it exactly. What we do know is that last prime before 180 is certainly not 19. y is something like 179/173 etc and since 323 does not have 2 as a factor, xy will certainly not be 323. Hence this statement alone is sufficient to say that xy is NOT 323.

Answer (B)
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Re: If x and y are both prime, is xy = 323?  [#permalink]

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New post 31 Jan 2018, 19:38
tusharGupta1 wrote:
If x and y are both prime, is xy = 323?

(1) x is the first prime after 18.
(2) y is the last prime before 180.


Statement I:

\(x = 19\), y can be 2,3,5,7,11,17,.... etc. So, Insufficient.

Statement II:

\(y = 179\). When we factorize \(323\) we have \(323 = 17*19\). So, one number has to be either of them. But as this statement one number is 179. Hence, their product wont be equal to 323.

So, Sufficient.
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Re: If x and y are both prime, is xy = 323?  [#permalink]

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New post 31 Jan 2018, 23:41
Factors of 323 are: {1, 17 ,19 ,323}

(1) x= 19 and and y can be any prime number{2,3,5,7,11,13,17...}
If x= 19 and y=17 then [Yes]
If x=19 and y= 2 then [No]
We need confirm answer either yes or no [Insuff]

(2)Y=180 and x can be any prime number{2,3,5,7,11,13,17....}
In all these cases, product of xy can never be 323

So we have confirmed no answer. [Suff]

Answer: B.
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Re: If x and y are both prime, is xy = 323? &nbs [#permalink] 31 Jan 2018, 23:41
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