BTGModeratorVI wrote: ↑Thu Jul 23, 2020 6:38 am
If x and y are positive integers, is the product xy even ?
(1) 5x - 4y is even
(2) 6x + 7y is even
Answer:
D
Source: GMAT prep
Target question: Is xy even?
Statement 1: 5x - 4y is even
Let's test all 4 cases
case a: x is even and y is even: In this case 5x-4y is
EVEN
case b: x is even and y is odd: In this case 5x-4y is
EVEN
case c: x is odd and y is even: In this case 5x-4y is ODD
case d: x is odd and y is odd: In this case 5x-4y is ODD
So, cases a and b are both possible.
In both cases the product xy is even
So,
xy must be even
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Aside: If anyone is interested, we have a video (below) on testing possible cases for these question types
Statement 2: 6x+7y is even
Let's test all 4 cases
case a: x is even and y is even: In this case 6x+7y is
EVEN
case b: x is even and y is odd: In this case 6x+7y is ODD
case c: x is odd and y is even: In this case 6x+7y is
EVEN
case d: x is odd and y is odd: In this case 6x+7y is ODD
So, cases a and c are both possible.
In both cases the product xy is even
So,
xy must be even
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer = D
