sk8ternite wrote:What is the remainder when the positive integer x is divided by 6?
(1) When x is divided by 2, the remainder is 1l and when x is divided by 3, the remainder is 0.
(2) When x is divided by 12, the remainder is 3.
Answer is d. Why not c
Statement 1: Cause when 3 is divided by 6, remainder is 6, but when 9 is divided by 3, remainder is 3
First, when 3 is divided by 6, the remainder is 3, not 6, since
3/6 = 0 with 3 left over.
In fact, when you divide by integer n, the greatest possible remainder is n-1, so there's no way that any integer divided by 6 would leave you with a remainder of 6.
For example, if you divide by 4, the possible remainders are 0, 1, 2 and 3; if you divide by 6 the possible remainders are 0, 1, 2, 3, 4 and 5.
(2) is much simpler, so let's start here: x/12 has remainder of 3.
Therefore, x = 3, 15, 27, 39, ...
For each of these numbers, when we divide by 6, we get a remainder of 3: sufficient.
(1) x/2 has remainder 1 and x/3 has remainder 0.
Let's break those up into two different statements:
x/2 has remainder 1... therefore, x is odd.
x/3 has a remainder 0... therefore, x is a multiple of 3.
Together: x is an odd multiple of 3, i.e. 3, 9, 15, 21, 27, ...
For each of these numbers, when we divide by 6, we get a remainder of 3: sufficient.
Each of (1) and (2) are sufficient alone: choose D.
