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18 Dec 2005, 17:32
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This was the very first question in my GMATPrep software. I had no idea how to approach it which is scary for your first problem. Could someone please tell me how to approach this problem and walk me through steps to solve it?
(5^21)(4^11)=2(10^n)
What is the value of n?
PS - The answer is 21
(5^21)(4^11)=2(10^n)
What is the value of n?
PS - The answer is 21
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18 Dec 2005, 18:07
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(5^21)(4^11)=2(10^n)
5^21*2^11*2^11=2*5^n*2^n
5^21*2^22=5^n*2^(n+1)
==> n=21
Hope it makes sense.
5^21*2^11*2^11=2*5^n*2^n
5^21*2^22=5^n*2^(n+1)
==> n=21
Hope it makes sense.
18 Dec 2005, 18:17
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Yes, I agree with the previous solution. Another way to look at the problem is...
Instead of solving the whole problem, you can also note that on the right hand side, the only factors of 10 are 2 and 5. Hence, on the right hand side, the maximum power of 5 is n (because there are no other multiple of 5 on the right hand side). Now, equating n = the power of 5 on the left hand side, you get n = 21.
-Srinivas (mathguru).
Instead of solving the whole problem, you can also note that on the right hand side, the only factors of 10 are 2 and 5. Hence, on the right hand side, the maximum power of 5 is n (because there are no other multiple of 5 on the right hand side). Now, equating n = the power of 5 on the left hand side, you get n = 21.
-Srinivas (mathguru).
