GMAT Practice Paper 1 n0. 1

[mimi77]

Please help me find a solution to this problem:

5*4^11=2*10^n. What is the value of n.

thanks

[Suyog]

5*4^11=2*10^n
i.e. 5*2^22 = 2*10^n
i.e. 10*2^21 = 2*10^n
i.e. 10*2^20 = 10^n
i.e. 2^20 = 10^(n-1)
approx 10^6 = 10^(n-1)
approx 5

let me know...

[mimi77]

Thank you so much!

[mimi77]

thank you so much Suyog

[mimi77]

I am sorry Suyog, the answer should be 21. I thanked you before I had reviewed your answer

[Suyog]

can you confirm the second expression...
it is..2*10^n or 2^n*10
let me know...

[moneyman]

Hello Mimi,
If this question is from the GMAT Testprep then you have posted it wrongly.


Its actually 5^21*4^11=2*10^n and the answer would be as follows


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

5^11*5^10*4^11=2*10^n

20^11*5^10=2*10^n

20^10*20^1*5^10=2*10^n

100^10*20^1=2*10^n

10^20*2*10=2*10^n ( Because 100 is 10^2 and 20 is 2*10)

10^21*2=2*10^n and therefore n is 21

Hope I am clear Mimi!!

[showoff16884]

I guess this is a much simpler way to look at it...

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

5^21*2^22 = 2*2^n*5^n
5^21*2^21*2 = 5^n*2^n*2

hence, n = 21

I hope you guys understand!

Cheers!

[mimi77]

thanks guys....I understsand both concepts

[jcan-gmatter]

Are we trying to get all the values to the same base or so that we can equate the powers? For example, in moneyman's response ..

5^21*4^11=2*10^n becomes 5^11*5^10*4^11=2*10^n

AND

20^11*5^10=2*10^n becomes 20^10*20^1*5^10=2*10^n

Why not 20^8 * 20^3, for instance? I'm guessing because then we couldn't do the 20^10 * 5^10 to get 100^10 calculation.

Seems to be random. Are there any guiding principles when answering these questions?