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by anuptvm » Wed Dec 29, 2010 7:53 am
If x and y are positive integers, is y a prime number?

(1) xy is a prime number.

(2) y2 is even.


Could someone answer this,

My answer was E, the OG is C. If it has to be C then the question isn't worded correctly
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Source: — Data Sufficiency |
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by anshumishra » Wed Dec 29, 2010 8:05 am
anuptvm wrote:If x and y are positive integers, is y a prime number?

(1) xy is a prime number.

(2) y2 is even.


Could someone answer this,

My answer was E, the OG is C. If it has to be C then the question isn't worded correctly
Y -> prime ?

Statement 1:
xy = prime
=> either x or y = 1 and the other number is prime. -> Not sufficient

Statement 2 :
Y^2 = even
Y can be anything : 2,4, 6..... -> Not sufficient

Combine both :

Clearly X = 1 (as y^2 = even , y can't be 1), So Y = prime (which is 2 here).
Thanks
Anshu

(Every mistake is a lesson learned )
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by Anurag@Gurome » Wed Dec 29, 2010 8:05 am
anuptvm wrote:If x and y are positive integers, is y a prime number?

(1) xy is a prime number.

(2) y2 is even.
I assume this means y^2

Statement 1: xy is prime.
Therefore either (x is prime and y = 1) or (x = 1 and y is prime)

Not sufficient.

Statement 2: y^2 is even => y is even
y = 2 => y is prime
y = any other even integer => y is not prime

Not sufficient.

1 & 2 Together: From 2 consider y is an even integer other than 2, then statement 1 doesn't hold. Therefore y must be equal to 2. Thus y is prime.

Sufficient.

The correct answer is C.
Anurag Mairal, Ph.D., MBA
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