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

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Math Expert
Joined: 02 Sep 2009
Posts: 58453
If 0.063*10^w/(0.0007*10^k) = 9*10^5, then w - k =  [#permalink]

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15 Jan 2018, 06:02
00:00

Difficulty:

45% (medium)

Question Stats:

68% (01:20) correct 32% (01:41) wrong based on 92 sessions

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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

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Math Expert
Joined: 02 Sep 2009
Posts: 58453
Re: If 0.063*10^w/(0.0007*10^k) = 9*10^5, then w - k =  [#permalink]

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15 Jan 2018, 06:03
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

Similar question from OG: https://gmatclub.com/forum/if-0-0015-10 ... 45032.html
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Posts: 3554
Re: If 0.063*10^w/(0.0007*10^k) = 9*10^5, then w - k =  [#permalink]

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19 Jan 2018, 16:00
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

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

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

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

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

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

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

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

$$w - k = 4$$

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 =   [#permalink] 19 Jan 2018, 16:00
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