Understanding "Fours and Fives" CAT Exam Math Problem

[s.victerian]

I believe the explanation for the Math problem "Fours and Fives" contradicts the correct answer. Please correct me if I am wrong. The explanation compares the unit digit of Quantity A) 13x13^14 to Quantity B) 19x19^19, saying that the unit digit for the 13 answer is greater (which it is). However the problem is actually comparing 13x13^13 (not ^14) and 19x19^19.

Perhaps I am misunderstanding the explanation? Can someone please review this?

Thanks in advance!!

[tommywallach]

Hey S,

Yeah, you're thinking of this wrong:

13 * 13^13 = 13^14

This is because 13 = 13^1

So we have: 13^1 * 13^13

And whenever you have the same base and multiple like this, you add the exponents. The same goes for:

19 * 19^19 = 19^1 * 19^19 = 19^20

In general, I'd encourage you to assume that the error lies in your work, not our tests. We certainly make mistakes (many, in fact!), but the odds are still against it. I've retitled this post to clarify, just because I don't want people thinking there's an error where there isn't!

-t