If x, y, and z are positive integers, is 3x 5y + z even?

Question

If x, y, and z are positive integers, is 3x – 5y + z even?

(1) x + 3y + z is even

(2) x – y + z is even

gmatophobia · Answer

Statement 1

(1) x + 3y + z is even

Note: The coefficient for x, y, and z is odd. Hence  x + 3y + z = 	ext{even}  under two circumstances

1) When x, y, and z are even
2) When among x, y, and z two variables are odd and one is even.

In both cases,

3x – 5y + z = 	ext{even}

Hence, statement 1 is sufficient, and we can eliminate B, C, and E.

Statement 2

(2) x – y + z is even

Note: Similar to statement 1, the coefficient for x, y, and z is odd. Hence  x – y + z = 	ext{even}  under two circumstances

1) When x, y, and z are even
2) When among x, y, and z two variables are odd and one is even.

In both cases,

3x – 5y + z = 	ext{even}

Hence, statement 2 is sufficient.

Option D

Yosemite98 · Answer

Let me try to give a simple solution to this:

We want to see whether 3x – 5y + z is even:

(1) x + 3y + z is even

3x – 5y + z = (x + 3y + z) +2x -8y -> (even) + even - even -> Even sufficient

which ever number multiplied by a multiple of 2 will be even

(2) x – y + z is even

3x – 5y + z = ( x – y + z ) +2x -4y -> (even) + even - even -> Even sufficient

which ever number multiplied by a multiple of 2 will be even

Hope it helps.

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