If xy = z , where x ,y and z are positive integers and x and y are pri

Question

If xy = z, where x, y and z are positive integers and x and y are prime numbers, what is the value of y?

(1) z is even 
(2) x is odd

lacktutor · Answer

x , y , and z — positive integers
x and y — prime numbers 
xy=z
 —> y=?

Statement1: 
z is even 
(Even=even*odd)
—> if z is even, one of the x and y should be 2.

But no info about whether y is 2
Insufficient

Statement2: 
x is odd.
x could any odd prime numbers:3,5,7...
But no info about y.

Insufficient

Taken together 1 and 2, 
y*ODD= EVEN
y should be EVEN—> only one even prime number satisfies the equation —2. 
Sufficient

The answer choice is C

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Archit3110 · Answer

given x&y are prime 
#1
z is even so x or y has to be even insufficient
#2
x is odd so y has to be 2 or any other no
insufficient
from 1 &2
y = 2
IMO C

CrackverbalGMAT · Answer

The fundamentals of the multiplication of positive integers is the concept being tested in this question here.

Remember,
Odd * Odd = Odd

Odd * Even = Even

Even * Even = Even

The product of any two positive integers will be even, if at least one of them is even. On the other hand, the product of any two positive integers will be odd only when both of them are odd.

From the question statement, we know that all three of x, y and z are positive integers. We also know that x and y are prime numbers. A couple of points to be noted from this data:

It is not given that x and y are distinct. So, we can take a case where x and y are same.
2 is an even prime number, so x and y CAN be even.

With this, let us look at the statements now.

From statement I, we know that z is even. This means that at least one among x and y is an even prime number. But, this is not sufficient for us to find a unique value of y. Statement I alone is insufficient.

Answer options A and D can be eliminated. Possible answer options at this stage are B, C or E.

From statement II, we know that x is odd. There is no data whatsoever about either z or y to help us find out a unique value for y. Statement II is insufficient. 
Answer option B can be ruled out.

Combining statements I and II, we know that z is even and x is odd. Since the product of x and y is yielding an even integer z, it follows that y HAS to be an even integer. But, y is also a prime number. 
Therefore, the value of y HAS to be 2. The combination of statements is sufficient to find a unique value of y.

The correct answer option is C.

Hope this helps!

freedom128 · Answer

x and y are prime positive integers. z is positive integer.

xy=z

#1
z is even, then either x or y can be even. y can be odd or even, depending on x. 
NOT SUFFICIENT

#2
No information about x and z
NOT SUFFICIENT

Combining #1 and #2
If z is even and x is odd, then y must be even. Y is given to be a prime positive integer , then y=2.

Answer is C

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If xy = z , where x ,y and z are positive integers and x and y are pri

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