Yesterday, Integrated Learning posted a 700 level GMAT question on our blog. Today, they have followed up with the answer:
This is a tough remainder question. First off, we can see right away that the answer cannot be A, B, or D, since each statement refers to only part of the question. Now we simply need to figure out if they can work together to secure a consistent answer.
The key is to realize that if we divide p by 3, the only remainders that are possible or 1 or 2. If we divided p by 4, the only options are 1, 2, or 3. So the options are limited. We just need to see what p could be, and figure out if the remainders always work in one way or another.
Do a quick little chart on your paper. This won’t take long, and you’ll have the answer right away.
p 1 2 3 4 5 6 7
q 1 2 0 1 2 0 1
r 1 2 3 0 1 2 3
Since q and r must be positive integers, we can eliminate all instances where they are 0. But we can still see that q can be either larger, smaller, or equal to r, so there is no way to answer this question.
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