Compare:
A: (100,210)(90,021)
B: (100,021)(90,210)
I ran into problems like this a few times in my practice tests (PowerPrep), and only thing I could do to compare A and B is by multiplying out. Now, here is a quicker way to do this:
A: (100,210)(90,021) = (100,000 + 210)(90,000+21) = (100,000)(90,000) + (100,000)(21) + (210)(90,000) + (210)(21)
B: (100,021)(90,210) = (100,000 + 21)(90,000+210) = (100,000)(90,000) + (100,000)(210) + (21)(90,000) + (21)(210)
Now, we're down to comparing
A: (100,000)(90,000) + (100,000)(21) + (210)(90,000) + (210)(21)
B: (100,000)(90,000) + (100,000)(210) + (21)(90,000) + (21)(210) Since those terms appear in both, we can strike 'em out.
Now, we're down to comparing
A: (100,000)(21) + (210)(90,000)
B: (100,000)(210) + (21)(90,000)
Let's do more factoring:
In A, factor out 21 and get: (21)[100,000 + (10)(90,000)] = (21)(1,000,000)
In B, factor out 21 and get: (21)[(10)(100,000) + 90,000] = (21)(1,090,000)
Now since both A and B are multiples of 21, We just need to compare 1,000,000 and 1,090,000. Which one's bigger? B!
I know it seems long, but I actually do this way much faster than straight multiplication. And if you're really good in math, you can probably skip a lot of the steps above and do them in your head, and arrive at the result much quicker.
Here's an exercise if anyone likes:
Compare:
A: (23)(784)
B: (24)(783)