n is an integer greater than 0
Quantity A: The number of different prime factors of 9n
Quantity B: The number of different prime factors of 8nQuantity A is greater.,
Quantity B is greater.,
The two quantities are equal.,
The relationship cannot be determined from the information given.
2 Explanations
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Carolina Seigler
Hi there, I was just wondering why there is no explanation for the previous question, Question #8? Thanks!
First, let's think about what happens if n=1. If that's the case, then QA has 1 prime factor (3). And QB also has 1 prime factor (2).
Now, if n=3, then QA still only has 1 unique prime factor (3). But QB now has two different prime factors (2 and 3). So in this case, QB is greater. So we have QA < QB.
But let's think about what happens if n=2. In this case, QA would have two different prime factors (2 and 3). And QB would still just have one unique prime factor (2). So in this case the QA is greater, so we'd have QA > QB.
So essentially, the signs flip when we plug in different numbers for n.
2 Explanations