AAPL 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?
(1) If the integer is divided by 45, the remainder is 30.
(2) The integer is divisible 2.
The OA is A.
Let x = the integer.
If a certain positive integer is divided by 9, the remainder is 3.
In other words, x is 3 more than a multiple of 9:
x = 9a + 3 =
3, 12, 21, 30....
Statement 1: If the integer is divided by 45, the remainder is 30.
In other words, x is 30 more than a multiple of 45:
x = 45b + 30 = 30, 75, 120....
Every value in the list above is viable, since each is 3 more than a multiple of 9:
30 = 27 + 3
75 = 72 + 3
120 = 117 + 3
Since every option for x is a multiple of 5, dividing x by 5 will yield a remainder of 0.
SUFFICIENT.
Statement 2: The integer is divisible by 2
In the blue list above, both x=12 and x=30 are divisible by 2.
If x=12, then dividing x by 5 will yield a remainder of 2.
If x=30, then dividing x by 5 will yield a remainder of 0.
Since the remainder can be different values, INSUFFICIENT.
The correct answer is
A.
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