<p>What would be the best most efficient way to get the answer here?
x = 1, 0, or 2
y = 1, 0, or -1
z = 0, 1, or 3
How many different values can x+yz possibly take on?</p>
<p>Write the combination of yz down (and pay attention to the zero impact) and then add the x combination. Again, paying attention to the zero.</p>
<p>PS It is helpful to list the source of the problem. Some problems reported here are not worth solving. :)</p>
<p>Do you think this problem is not worth solving? I got it from private tutoring. Am I wasting my time with these problems?</p>
<p>I also got this one:
For positive integers a and b, a mod b is equal to the remainder when a is divided by b. If q-2 is any odd integer in the interval -1 < q -2 < 10, what are all possible values of (q-1)^2 mod 3? (I) 0 (II) 1 (III) 2 (IV) 3</p>
<p>If you are asking if these problems are similar to SAT problems, the answer is no. A case could be made that the first one might be useful to solve. The language used in the second problem will never appear on an SAT (in its present form).</p>
<p>Anyway, here’s a solution to the second one.</p>
<p>q-2 is either 1,3,5,7, or 9. So q-1 is 2,4,6,8, or 10. So (q-1)^2 is 4, 16, 36, 64, or 100. </p>
<p>4, 16, 64, and 100 are 1 more than a multiple of 3, and 36 is divisible by 3. So the possible remainders are 0 and 1. </p>
<p>I just did it by brute force. I haven’t thought about if there is a quicker, more clever way to do this.</p>