If x,y,z are different prime numbers. What is the value of y?

Question

1)xy is even
2)yz is even

acegmat123 · Answer

Statement 1:

Insufficient

Statement 2:

Insufficient

Statement 1&2:

Then y has to be 2.

Sufficient

IMO C

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BrentGMATPrepNow · Answer

Target question :    What is the value of y?

Given : x,y,z are different prime numbers.

Statement 1 : xy is even   
Let's TEST some values.
There are several values of x and y that satisfy statement 1. Here are two: 
Case a: x = 2 and y = 3. Here xy = (2)(3) = 6, which is even. In this case  y = 3 
Case b: x = 2 and y = 5. Here xy = (2)(5) = 10, which is even. In this case  y = 5 
Since we cannot answer the  target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : yz is even  
Let's TEST some values.
There are several values of y and z that satisfy statement 2. Here are two: 
Case a: y = 3 and z = 2. Here yz = (3)(2) = 6, which is even. In this case  y = 3 
Case b: y = 2 and z = 3. Here yz = (2)(3) = 6, which is even. In this case  y = 2 
Since we cannot answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined    
If a product of two prime numbers is even, we can be certain that one of those prime number is 2 (since 2 is the only even prime)
So, from statement 1, we can conclude that either x or y is equal to 2.
From statement 2, we can conclude that either y or z is equal to 2.
When we combine the statements, the only possibility is that y = 2
Why is this? Well, we're told that x, y, and z are  different  prime numbers. So, we can't have one value (x or y) equal 2 in statement 1, and then have have different value (y or z) equal 2 in statement 2. 
So,  y must equal 2 
Since we can answer the  target question  with certainty, the combined statements are SUFFICIENT

Answer:  C

Cheers,
Brent

Gauravji21 · Answer

x , y, z are all different prime numbers. It is to be kept in mind that 2 is the smallest prime number and the only even number which is prime.

St1: xy is even. So, either x =2 or y =2. No unique answer.Both can't be even as it is given that z, y, z are all different prime numbers and we have only one even prime number.So, statement is insufficient.

St2: yz is even.So, either z =2 or y =2. No unique answer.So, statement is insufficient

St1 + St2
Y is even in both the cases. so we can say that Y=2. Hence, answer is "C".

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TestPrepUnlimited · Answer

Statement 1: 
One of x or y must be even. There is only one even prime number, so either x or y is 2. We don't know which one is 2 so insufficient.

Statement 2: 
Same as above. Insufficient.

Combined: 
We can deduct y must be 2 as it is the only common factor of xy and yz. Sufficient.

If x,y,z are different prime numbers. What is the value of y?

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GMAT Data Sufficiency (DS) Questions

If x,y,z are different prime numbers. What is the value of y?

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