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
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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
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Brent Hanneson – Creator of greenlighttestprep.com

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