Bunuel wrote:
If a certain positive integer is divided by 9, the remainder is 3. What is the remainder when the integer is divided by 5?
Given that \(x=9q+3\). x could be: 3, 12, 21, 30, 39, 42, ...
(1) If the integer is divided by 45, the remainder is 30 --> \(x=45p+30=5(9p+6)\). So, x is a multiple of 5, which means that the remainder when x is divided by 5 is 0. Sufficient.
(2) The integer is divisible by 2 --> x is even. If x is 12, then the remainder is 2 but if x is 30, then the remainder is 0. Not sufficient.
Answer: A.
As for your doubt: the values of x which satisfies both equations are: 30, 75, 120, ...
Hope it helps.
Hi Bunuel,
One question. With statement 1, are the following inferences all valid?
- N is divisible by 5 since --> n = 5 (9q + 6)
- N is also divisible by 3 since --> n = 3 (15q + 10)
- N is therefore also divisible by 15 since --> n = 15 (3q + 2)
I know this goes beyond the scope of answering this question. I just wanna check if my reasoning is correct for future problems such as this one.
Thanks,