If x is a positive integer, what is the remainder when x is divided by

Target question: What is the remainder when x is divided by 7?

Statement 1: The remainder when x is divided by 4 is 3
When it comes to remainders, we have a nice rule that says:
If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

So, if the remainder when x is divided by 4 is 3, then some possible values of x are: 3, 7, 11, 15, 19, 23, etc
Let's examine some of these possible values of x
Case a: If x = 3, then the remainder when x is divided by 7 is 3
Case b: If x = 7, then the remainder when x is divided by 7 is 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The remainder when x is divided by 5 is 1
Some possible values of x are: 1, 6, 11, 16, 21, 26, 31, etc
Let's examine some of these possible values of x
Case a: If x = 1, then the remainder when x is divided by 7 is 1
Case b: If x = 6, then the remainder when x is divided by 7 is 6
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that some possible values of x are: 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, etc
Statement 2 tells us that some possible values of x are: 1, 6, 11, 16, 21, 26, 31, etc
Since we already have 2 possible x-values that BOTH statements share, let's examine the following cases:

Case a: If x = 11, then the remainder when x is divided by 7 is 4
Case b: If x = 31, then the remainder when x is divided by 7 is 3
Since we still cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer:

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