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.
In math terms:
x = 6a + 2, where a is a non-negative integer.
Options for x:
2, 8, 14, 20...
What is the remainder when the positive integer x is divided by 3?
Testing our options for x, we get:
2/3 = 0 R2.
8/3 = 2 R2.
14/3 = 4 R2
20/3 = 6 R2.
In every case, the remainder is 2.
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.
In math terms:
x = 15b + 2, where b is a non-negative integer.
Options for x:
2, 17, 32, 47...
What is the remainder when the positive integer x is divided by 3?
Testing our options for x, we get:
2/3 = 0 R2.
15/3 = 5 R2.
32/3 = 10 R2
47/3 = 15 R2.
In every case, the remainder is 2.
SUFFICIENT.
The correct answer is
D.
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