tenaman10 wrote:

What is the remainder when the positive integer x is divided by 8?

(1) When x is divided by 12, the remainder is 5.

(2) When x is divided by 18, the remainder is 11.

In many remainders questions, it's enough just to find a couple of numbers that 'work' with the given information, and if you simply list the first few numbers that satisfy each statement, it's easy to judge if the statements together are sufficient:

1) x = 5, 17, 29, 41, 53, 65, 77, 89 ...

2) x = 11, 29, 47, 65, 83, 101 ...

Since 29 and 65 give different remainders when you divide by 8, the answer is E.

More abstractly, when combining two statements like the above, the pattern will be based on the LCM of the two divisors. Here, we can consider dividing x by 36 = LCM(12, 18).

Notice that, if Statement 1 is true, the remainder will be 5, 17 or 29 when x is divided by 36.

If Statement 2 is true, the remainder will be 11 or 29 when x is divided by 36.

If both Statements are true, the remainder therefore must be 29 when x is divided by 36.

That's still not sufficient, as above; x could be 29, or x could be 65.

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