Bunuel wrote:
Official Solution:
Note: Positive integer \(a\) divided by positive integer \(d\) yields a reminder of \(r\) can always be expressed as \(a=qd+r\), where \(q\) is called a quotient and \(r\) is called a remainder, note here that \(0 \le r \lt d\) (remainder is non-negative integer and always less than divisor).
(1) When \(x\) is divided by 4 the remainder is 3. Not sufficient as no info about \(y\).
(2) When \(y\) is divided by 4 the remainder is 2. Not sufficient as no info about \(x\).
(1)+(2) From (1) \(x=4q+3\) and from (1) \(y=4p+2\), so \(xy=(4q+3)(4p+2)=16qp+8q+12p+6\): now, all terms but the last are divisible by 4 and the last term, 6, yields remainder of 2 when divided by 4. Sufficient.
Or another way: \(x\) can be: 3, 7, 11, ... and \(y\) can be: 2, 6, 10, 14, ... You can try several values to see that \(xy\) always yields remainder of 2 when divided by 4.
Answer: C
Thanks
Bunuel for your explanation. Where can I find similar questions like this?
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