MBA.com prep software, practice test #1, Quant question #1

[Guest]

Can't type exponents, please read and note exponents:

If 5 to the 21st times 4 to the 11th = 2 times 10 to the Nth, what is N?

A) 11
B) 21
C) 22
D) 23
E) 32

Answer says B, but offers no explanation. I had guessed B (add the exponents after combining to get 20 on each side, but wrong wrong wrong!)

[Paul]

This is actually not as bad as it looks, here is how you approach this problem:
(let's rewrite the whole thing algebraically)

(5^21)(4^11) = (2^1)(10^n)

Now, break down the bases (ex: 4 and 10) into factors

(5^21) (2^22) = (2^1) (2^n)(5^n) -->(2^1)(2^n) =>2^1+n

This is what you end up with:

(5^21) (2^22) = (2^1+n)(5^n)

Now you just have to look at the common bases (ie. 5 and 2), equate them and then just look at the exponents alone :

5^21 = 5^n --> 21 = n

OR

2^22 = 2^n+1 --> 22=n+1 --> 21=n

[RonPurewal]

This is actually not as bad as it looks, here is how you approach this problem:
(let's rewrite the whole thing algebraically)

(5^21)(4^11) = (2^1)(10^n)

Now, break down the bases (ex: 4 and 10) into factors

(5^21) (2^22) = (2^1) (2^n)(5^n) -->(2^1)(2^n) =>2^1+n

This is what you end up with:

(5^21) (2^22) = (2^1+n)(5^n)

Now you just have to look at the common bases (ie. 5 and 2), equate them and then just look at the exponents alone :

5^21 = 5^n --> 21 = n

OR

2^22 = 2^n+1 --> 22=n+1 --> 21=n

beautifully done.

to the original poster:
* i'm moving this thread to the gmatprep math folder, where it belongs;
* when you post gmatprep problems, please (1) post them in the correct folder and (2) title them correctly, using the first 6-8 words of the problem statement, as stipulated in the forum rules.
thank you.