Bunuel wrote:
If x and y are integers, is x divisible by 3?
(1) x - y is divisible by 3.
(2) x + y is divisible by 3.
Case 2: (x + y) is divisible by 3: The only way this statement to be true is when 3 is added to x. Therefore, we can say that value of y has to be 3. Now let us figure out the value of x:
x =......., -3, -2, -1, 0, 1, 2, 3 ...... and value of y = 3.Based on the above scenario, the value will be as follows:
1) x = 0 and y = 3, we get (0+3)/3 = 3/3 = 1 (Hence, divisible)
2) x = 1 and y = 3, we get (1+3)/3 = 4/3 (Not divisible)
3) x = 2 and y = 3, we get (2+3)/3 = 5/3 (Not divisible)
4) x = 3 and y = 3, we get (3+3)/3 = 6/3 = 2 (Hence, divisible)
In terms of negative numbers, the equation will follow the same logic. But after dividing, the quotient will be negative but the pattern will be the same.
we can see that the possible values of x when this equation (x + y)/3 satisfy is when value of y is 3 and value of x is 3n where n = 1,2,3......
There since the value of x has to be 3n then we can say that
x is divisible by 3, hence, satisfied.Case 1: (x-y) is divisible by 3: The only way this statement to be true is when 3 is subtracted. Therefore, we can say that value of y has to be 3. Now let us figure out the value of x:
x =..........., -3, -2, -1, 0, 1, 2, 3.................. and value of y = 3.Based on the above scenario, the value will be as follows:
1) x = 0 and y = 3, we get (0-3)/3 = -3/3 = -1 (Hence, divisible)
2) x = 1 and y = 3, we get (1-3)/3 = -2/3 (Not divisible)
3) x = 2 and y = 3, we get (2-3)/3 = -1/3 (Not divisible)
4) x = 3 and y = 3, we get (3-3)/3 = 0/3 = 0 (Hence, divisible)
In terms of negative numbers, the equation will follow the same logic. But after dividing, the quotient will be negative but the pattern will be the same.
we can see that the possible values of x when this equation (x-y)/3 satisfy is when value of y is 3 and value of x is 3n where n = 1,2,3......
There since the value of x has to be 3n then we can say that
x is divisible by 3, hence, satisfied.Since both Case 1 and Case 2 are satisfied, therefore, the answer is option D. Kindly correct me if I am wrong. Thank you.