number system

[vipulgoyal]

Is z even number ??
1. 5z is an even number
2. 3z is an even number

C

[sanjoy18]

(1): 5z = 2, z = 2/5; 5z = 10, z = 2... Not sufficient
(2): 3z = 2, z = 2/3; 3z = 6, z = 2... Not sufficient

Combining: Subtract the two: 2z = even - even = even

Subtracting again: 3z - 2z = even - even so z is even ... Ans. C

[ganeshrkamath]

Is z even number ??
1. 5z is an even number
2. 3z is an even number

C

1. z = 2/5, z = 2
Not sufficient.

2. z = 2/3, z = 2
Not sufficient.

Both: 5z - 3z = 2z
Since 2z and 3z are both even numbers, z is an even number.

Choose C

Cheers

[Brent@GMATPrepNow]

I thought I'd point out that ganeshrkamath and sanjoy18 are both using versions of a nice divisibility rule that says:
If integers A and B are both divisible by k, then A+B is divisible by k, and A-B is divisible by k

In this question, k = 2 (that is, a number is even if it is divisible by 2)
So, if 5z is divisible by 2, and 3z is divisible by 2, then 5z-3z is divisible by 2
In other words, 2z is divisible by 2.

Furthermore, if 3z is divisible by 2, and 2z is divisible by 2, then 3z-2z is divisible by 2
In other words, z is divisible by 2.

Cheers,
Brent