BTGmoderatorDC wrote:If x and y are integers, is xy + 1 divisible by 3 ?
(1) When x is divided by 3, the remainder is 1.
(2) When y is divided by 9, the remainder is 8.
OA C
Source: Official Guide
Let's take each statement one by one.
(1) When x is divided by 3, the remainder is 1.
Say x = 3p + 1, where p = quotient
=> xy + 1 = (3p + 1)y + 1 = 3py + y + 1; though 3py is divisible by 3, (y + 1) may/may not be divisible by 3. Insufficient.
(2) When y is divided by 9, the remainder is 8.
Say y = 9q + 8, where q = quotient
=> xy + 1 = x(9q + 8) + 1 = 9qx + 8x + 1; though 9qx is divisible by 3, (8x + 1) may/may not be divisible by 3. Insufficient.
(1) and (2) together
=> xy + 1 = (3p + 1)(9q + 8) + 1 = 27pq + 9q + 24p + 8 + 1 = 27pq + 9q + 24p + 9. We see that each term is divisible by 3. Sufficient.
The correct answer:
C
Hope this helps!
-Jay
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