Carcass wrote:

If x and y are integers and x = 50y + 69, which of the following

must be odd?

A) xy

B) x + y

C) x + 2y

D) 3x — 1

E) 3x + 1

The key word here is

MUSTSo, if we can show that an answer choice

CAN be false, we can

eliminate it.

If x = 50y + 69, then one possible solution is y = 0 and x = 69

In other words

x is ODD and

y is EVENNow check the answer choices...

A) xy = (

ODD)(

EVEN) = EVEN

ELIMINATE A

B) x + y =

ODD +

EVEN = ODD

KEEP B for now

C) x + 2y =

ODD + (2)(

EVEN)

= ODD + EVEN

= ODD

KEEP C for now

D) 3x — 1 = (3)(

ODD) - 1

= (ODD)(

ODD) - ODD

= ODD - ODD

= EVEN

ELIMINATE D

E) 3x + 1 = (3)(

ODD) + 1

= (ODD)(

ODD) + ODD

= ODD + ODD

= EVEN

ELIMINATE E

We're now left with answer choices B and C

So let's test another pair of values...

If x = 50y + 69, then another possible solution is y = 1 and x = 119

In other words

x is ODD and

y is ODDNow check the remaining answer choices...

B) x + y =

ODD +

ODD = EVEN

ELIMINATE B

By the process of elimination, the correct answer is C

Cheers,

Brent

_________________

Brent Hanneson – Creator of greenlighttestprep.com

Sign up for our free GRE Question of the Day emails