GMAT Prep Exponent question

Question

Hello all,

I was wondering if anyone had insight on how to solve this problem from a GMATPrep test.

5^21 x 4^11 = 2 x 10^n (What is the value of n?)

I first thought to make the bases the same so:

5^21 x 2^22 = 2 x 10^n

The correct answer is n = 21?

Thanks in advance for all your help.. Gmat in 13 days..

chiya · Answer

Yes its 21.. 5^21 x 4^11 = 2 x 10^n => 5^21 x 2^22 = 2 x 10^n =>5^21 x 2^21 x 2= 2 x 10^n => 10^21 x2 =2 x 10^n =>n=21 All the best for exam :-D

StartupAddict · Answer

n=21

First convert 4^11 to 2^22 (4^11 = (2^2)^11 = 2^22)

divide both sides by 2

5^21*2^21=10^n
(5*2)^21=10^n
10^21=10^n
n=21

AK79 · Answer

Chiya and StartupAddict (and anyone else who posts after this!),

Thanks fellas, I really appreciate it. It stumped the hell out of me. Forgot to figure out to make the exponents the same to manipulate them out. Thanks again for the help and good wishes.. :-D

StartupAddict · Answer

No sweat! Yah you should practise exponent questions, I find from GMATPrep that when the difficulty goes up, they like to throw some nasty ones at you. The real test is almost the same as GMATprep too, so expect to see some nasty exponent ones...... here's one:

if M = 4^1/2 + 4^1/3 + 4^1/4, what is M?


a. between 0.5 and 1.5
b. between 1.5 and 2.5
c. between 3.5 and 4
d. greater than 4

something like that

i just did approximations in my head.... 2 + 1.6 + 1.4

GMATBLACKBELT · Answer

Aprox is a good idea, especially if u don't know what to do. Even if u get stuck btwn C and D, u still eliminated 2 answers.

Sumithra Sen · Answer

Hey Startupaddict

Is the answer your exponent question D?

Greater than 4?

beny · Answer

That question seems relatively easy...

You know sqrt(4) = 2....

You know that 4^1/3 and 4^1/4 each have to be bigger than 1...

summed, they must be greater than 4. 10 second problem.

troy3626 · Answer

Since you have to multiply numbers with the same base, you can simply add the exponents. 

1/2 + 1/3 + 1/4 = 13/12 or 1 and 1/12

4^1 and 1/12

Answer: D

ywilfred · Answer

yup..
5^21 * 2*22 = 5^21 * 2^21 * 2 = 2*10^21.

AK79 · Answer

Thanks all... This is a great place to be...

GMAT Prep Exponent question

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