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04 Oct 2021, 08:45
Kudos
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
74% (01:23) correct
26%
(01:13)
wrong
based on 61
sessions
History
Date
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If \(\frac{0.018*10^r}{0.0003*10^w}=6*10^7\), then \(r-w=\)?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 15
(A) 6
(B) 7
(C) 8
(D) 9
(E) 15
04 Oct 2021, 09:05
Kudos
Bookmarks
This can be simplified as
> 18 X 10^r-3 / 3x10^w-4 = 6 x 10^7
> 6 X 10^r-w+1 = 6 X 10^7
> r-w+1 = 7
> r-w = 6
> 18 X 10^r-3 / 3x10^w-4 = 6 x 10^7
> 6 X 10^r-w+1 = 6 X 10^7
> r-w+1 = 7
> r-w = 6
04 Oct 2021, 09:43
Kudos
Bookmarks
Bunuel
Useful property: \(\frac{AB}{CD}=\frac{A}{C} \times \frac{B}{D}\)
Given: \(\frac{(0.018)(10^r)}{(0.0003)(10^w)}=(6)(10^7)\)
Apply the above property to the left side to get: \(\frac{0.018}{0.0003} \times \frac{10^r}{10^w}=(6)(10^7)\)
Aside: An easy way to evaluate \(\frac{0.018}{0.0003}\) is to first eliminate the decimals by multiplying numerator and denominator by \(10,000\) to get the equivalent fraction \(\frac{180}{3}\), which equals \(60\).
So we now have: \(60 \times \frac{10^r}{10^w}=(6)(10^7)\)
From here, let's divide both sides by \(60\) to get: \(\frac{10^r}{10^w}=\frac{(6)(10^7)}{60}\)
Simplify the right side: \(\frac{10^r}{10^w}=10^6\)
Finally, we can apply the quotient law to the left side to get: \(10^{r-w} = 10^6\)
Since the bases are equal, we can conclude that the exponents are equal to get: \(r-w=6\)
Answer: A
