krishan wrote:
If x and y are positive integers , is the product xy even
(1) 5x - 4y is even
(2) 6x + 7y is even
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
EVENcase b: x is even and y is odd: In this case 5x-4y is
EVENcase 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 evenSince 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 evenLet's test all 4 cases
case a: x is even and y is even: In this case 6x+7y is
EVENcase 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
EVENcase 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 evenSince we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer = D
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