Yesterday, Integrated Learning posted a 700 level GMAT question on our blog. Today, they have followed up with the answer:
This is a tough problem to know exactly where to start. The best place is to realize that any number divided by 10 will produce a remainder that is the same as the units digit of that number. For example, 34 divided by 10 yields a remainder of 4, 96 divided by 10 yields a remainder of 6, etc. We can predict what the units digit of 19p will be just by looking at what the units digit of powers of 9 are:
91 = 9, units digit: 9
92 = 81, units digit: 1
93 = 729, units digit: 9
94 = 6561, units digit: 1
What we see from this list is that the pattern of the units digit for any number ending in nine is simply to alternate 9, 1, 9, 1, 9, 1, and that pattern is correlated with whether or not the power is even or odd: all even powers yield a units digit of 1, all odd powers yield a units digit of 9.
So now we just want to know whether or not p is even or odd. Statement 1 tells us that p a multiple of 5, that could be either even or odd; insufficient. Statement 2 tells us that p is a multiple of 6, which will ALWAYS be even. That is sufficient.
So B is the right answer.
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