Explanation

Construct the following table


Remember:

even + odd = odd
even+ even= even
odd + odd = even


even * even = even
even* odd = even
odd*odd = odd

y	x= 50y + 69	A) xy	B) x + y	C) x + 2y	D) 3x — 1	E) 3x + 1
even	odd	even	odd	odd	even	even
odd	odd	odd	even	odd	even	even

Hence option C is the only correct choice. As other option may or maynot be odd
_________________

The key word here is MUST

So, 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 EVEN

Now 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 ODD

Now 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
_________________

If x and y are integers and x = 50y + 69, which of the following must be odd?

We don't know whether y is odd or even but we can conclude that X will always be odd from the previous equation

Why?
50 times y will be even no matter what. Even + odd (69) is odd. (ie 1+2=3, 3+4=7, etc.)

Answer:
C) x + 2y

C will always be odd. X is odd + even (2*even or odd - either case) = odd.

The faster way I would approach this problem after reviewing the solution
From this information x = 50y + 69, you know 100% that x is ODD, y can't be determined odd or even with this information
Glance through 5 answer choices, you see that each choice is either multiplication or sum (either sum of two positive numbers or negative numbers or 1 positive & 1 negative)
Given that x and 3x are ODD => you must find an answer which gives you another term that is 100% EVEN

A) xy : eliminate A since y is not 100% even

B) x + y : eliminate B since y is not 100% even

C) x + 2y : Correct, since 2y is 100% even

D) 3x — 1 : eliminate D since -1 is odd

E) 3x + 1: eliminate E since 1 is odd

Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.