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If 0.063*10^w/(0.0007*10^k) = 9*10^5, then w - k =

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If 0.063*10^w/(0.0007*10^k) = 9*10^5, then w - k =  [#permalink]

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New post 15 Jan 2018, 06:02
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E

Difficulty:

  45% (medium)

Question Stats:

68% (01:22) correct 32% (01:43) wrong based on 86 sessions

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Math Expert
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Re: If 0.063*10^w/(0.0007*10^k) = 9*10^5, then w - k =  [#permalink]

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New post 15 Jan 2018, 06:03
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Re: If 0.063*10^w/(0.0007*10^k) = 9*10^5, then w - k =  [#permalink]

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New post 19 Jan 2018, 16:00
1
Bunuel wrote:
If \(\frac{0.063*10^w}{0.0007*10^k} = 9*10^5\), then w - k =

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

\(\frac{0.063*10^w}{0.0007*10^k} = 9*10^5\)

\(\frac{.063 * 10^4}{.0007 * 10^4} * \frac{10^w}{10^k}= 9*10^5\)

\(\frac{630}{7} * 10^{(w-k)} = 9 * 10^5\)

\(90 * 10^{(w-k)} = 9 * 10^5\)

\(9 *10^1*10^{(w-k)} = 9 * 10^5\)

\(9 * 10^{(w-k)+1} = 9 * 10^5\)

\((w - k) + 1 = 5\)

\(w - k = 4\)

Answer B

If you don't want to clear decimals for .063 and .0007, these numbers factor/cancel easily:

\(\frac{\frac{63}{1,000}}{\frac{7}{10,000}} = (\frac{63}{1,000} * \frac{10,000}{7} )= 90\) . . .
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Re: If 0.063*10^w/(0.0007*10^k) = 9*10^5, then w - k = &nbs [#permalink] 19 Jan 2018, 16:00
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