If 5^21 x 4^11 = 2 x 10^n what is the value of n?

[joe]

If 5^21 x 4^11 = 2 x 10^n what is the value of n?

A - 11
B - 21
C - 22
D - 23
E - 24

Hi Stacey, this first question on the Prep CAT really threw me for a loop. Maybe it's obvious and I'm just not seeing it yet, but how is the answer (B) 21? Much thanks,

Joe

[RonPurewal]

tricky-exponents-t1187.html

[tm03]

Here is how I solved it:

5^21 x 4^11=2 x 10^n

5^21 x ((2)^2)^11=2^1 x (2 x 5)^n
5^21 x 2^22= 2^1 x 2^n x 5^n
2^22=2^1+n , 22=1+n, n=21
5^21=5^n , n=21

I hope you find it helpful

[RonPurewal]

the solution above is good. it's also pretty much identical to the solution in the post linked above it.

here's the essential takeaway here:
if you see POWERS OF SPECIFIC WHOLE NUMBERS, then you should BREAK THE WHOLE NUMBERS DOWN INTO PRIMES.

i don't think i've ever seen a gmat problem featuring powers of whole numbers for which this doesn't work.