I signed up for the coaching service for the GRE and when looked through the questions I struggled with elementary number theory. What's the(adsbygoogle = window.adsbygoogle || []).push({}); most efficient wayto deal deal with the following kind of questions.

1. Positive integer Z_1 divided by 7 gives a remainder of 5 and Z_2 divided by 4 leaves a remainder of 3. Some constraint on Z_1 and Z_2 (e.g., they are equal and should be minimum [e.g., Z_1 = Z_2, min(Z_1)], or they should be in a certain range [e..g, Z_1 element of {235-256}], or Z_2 is a defined in terms of Z_1 [e.g., Z_2 = Z_1+2]).

2. f(x)= (x+2)*(x+7)*(x+8), for x element of Z^{+}. Is f(x) evenly divisible by 9?

3. x a positive integer and y is an odd positive integer

Find the remainder when (x+1)*(y+2) is divided by 7

4. How do I deal with questions that define long numbers with the last few digits similar to the one in the other number, e.g.,

What's larger: 9000014*131818or 9000818*131014

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# Efficient way to solve basic high school level number theory questions?

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