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Powers of numbers

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Powers of numbers

by marcusking » Wed Feb 11, 2009 11:53 am
If , (0.063*10^w)/(.0007*10^k) = 9*10^5 then w –k=

(A) 3 (B) 4(C) 5(D) 6(E) 71.

I keep getting D. 6

But the OA is B. 4

I think the answer given is wrong. I've tried plugging in numbers and I affirm my answer but maybe I'm approaching it wrong.
Last edited by marcusking on Wed Feb 11, 2009 12:34 pm, edited 1 time in total.
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by truplayer256 » Wed Feb 11, 2009 12:29 pm
The OA is incorrect... The correct answer is (C.)5. Here's why:
.063=6.3/100
.0007=7/10000
So, 6.3/100/(7/10000)=6.3/100*10000/7=6.3*100/7=6300/7=90
(90)(10^w-k)=9*10^6
Divide by 90 on both sides.
10^w-k=10^6*10^-1
10^w-k=10^6-1
10^w-k=10^5
w-k=5
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Re: Powers of numbers

by Stuart@KaplanGMAT » Wed Feb 11, 2009 12:30 pm
marcusking wrote:If , (0.063*10^w)/(.0007*10^k) = 9*10^5 then w –k=

(A) 3 (B) 4(C) 5(D) 6(E) 71.
(0.063*10^w)/(.0007*10^k) = 9*10^5

Let's break the left side up into two fractions:

(0.0630)/(0.0007) * 10^w/10^k = 9*10^5

multiplying the first fraction by 10000/10000, we get:

630/7 * 10^w/10^k = 9*10^5

90 * 10^w/10^k = 9*10^5

10^w/10^k = 9*10^5/9*10^1

10^(w-k) = 10^(5-1)
w - k = 5 - 1
w - k = 4

[edited after original question was edited]
Last edited by Stuart@KaplanGMAT on Wed Feb 11, 2009 12:58 pm, edited 1 time in total.
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by marcusking » Wed Feb 11, 2009 12:36 pm
Thank you both for your answers, I didn't enter the equation correctly it should have been = 9*10^5 I have made the correction in bold.

But the same principal applies and I get the correct answer after seeing how you've solved it. I made the mistake of thinking .063/.0007 = 9 when really it is 90 thus throwing off the power I needed to multiply by.

Thanks again!
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