VP Algebra Challenge

Ans 11

This is how I approaced - kept dividing 177147 by 3 and found 177147 = 3^11

since question says 3^x*4^y means y=0

x-y =11

Theres a couple of ways to do this one. Easiest, I think, is to realize that they are asking you to express 177,147 as the product of some 3's and 4's. Well, even if there was only one 4 thrown in there, then 177,147, the product, would have to be even. It's not, so we know that there are no 4's, or y=0. If y=0, then x must be 11.

If that didn't come to you, you could at least throw out answer choices [D] and [E] because they clearly don't make any sense. 177,147 is divisible by 3 (sum of digits is divisible by 3), then x=0 and undefined don't make sense either.

Hope this helps.

Here is what I did if it helps

Look at answers. It can't be undefined and the weird big numbers in D & E. So its between B & C

Lets say its B '0'

X-Y=11 and X=0 means Y =-11 that means 4 ^ -11 = 177147 Can it be? No

Ans must be C 11

Another sanity check, if X=11 and X-Y=11 means Y=0

now is 3 ^ 11 = 177147??

We dont have to solve the whole thing as this is just sanity check

3 ^ 1=3; 3 ^ 2=9 ; 3 ^ 3 =27; 3 ^4=81;

3^ 5 =243; 3 ^6= 729; 3^7=....7; 3^8=.....1

3^9=....3; 3^10=....9 ; 3 ^11=....7; 3 ^12=...1

HTH