lukaswelker wrote:
What is the remainder when the positive integer x is divided by 3?
(1) when x is divided by 6, the remainder is 2.
(2) when x is divided by 15, the remainder is 2.
Statement 1: When x is divided by 6, the remainder is 2.
In other words, x is 2 more than a multiple of 6:
x = 6a + 2, where a is a nonnegative integer.
Options for x: 2, 8, 14, 20...
Dividing these option by 3, we get:
2/3 = 0 R2.
8/3 = 2 R2.
14/3 = 2 R2.
Since the remainder in each case is the same, SUFFICIENT.
Statement 2: When x is divided by 15, the remainder is 2.
In other words, x is 2 more than a multiple of 15:
x = 15a + 2, where a is a nonnegative integer.
Options for x: 2, 17, 32, 47...
Dividing these options by 3, we get:
2/3 = 0 R2.
17/3 = 5 R2.
32/3 = 10 R2.
Since the remainder in each case is the same, SUFFICIENT.
The correct answer is
D.
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