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 - founder of Greenlight Test PrepSign up for our GRE Question of the Day emails