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If 0.018*10^r/0.0003*10^w=6*10^7, the r-w=
[#permalink]
02 Sep 2021, 09:50
02 Sep 2021, 09:50
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Question Stats:
73% (01:27) correct
26% (01:18) wrong based on 23 sessions
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If \(\frac{0.018*10^r}{0.0003*10^w}=6*10^7\), the \(r-w=
\)
(A) 6
(B) 7
(C) 8
(D) 9
(E) 15
\)
(A) 6
(B) 7
(C) 8
(D) 9
(E) 15
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If 0.018*10^r/0.0003*10^w=6*10^7, the r-w=
[#permalink]
02 Sep 2021, 10:11
02 Sep 2021, 10:11
Carcass wrote:
If \(\frac{0.018*10^r}{0.0003*10^w}=6*10^7\), the \(r-w=
\)
(A) 6
(B) 7
(C) 8
(D) 9
(E) 15
\)
(A) 6
(B) 7
(C) 8
(D) 9
(E) 15
Useful property: \(\frac{AB}{CD}=(\frac{A}{C})(\frac{B}{D})\)
Given: \(\frac{0.018*10^r}{0.0003*10^w}=6*10^7\)
Apply the above property to get: \((\frac{0.018}{0.0003})(\frac{10^r}{10^w})=6*10^7\)
Simplify both fractions: \((60)(10^{r-w})=6*10^7\)
Divide both sides of the equation by \(6\) to get: \((10)(10^{r-w})=10^7\)
Divide both sides of the equation by \(10\) to get: \(10^{r-w}=10^6\)
Since both sides of the equation have the same base, the exponents must be equal: \(r-w=6\)
Answer: A
General Discussion
Re: If 0.018*10^r/0.0003*10^w=6*10^7, the r-w=
[#permalink]
03 Sep 2021, 23:18
03 Sep 2021, 23:18
GreenlightTestPrep wrote:
Carcass wrote:
If \(\frac{0.018*10^r}{0.0003*10^w}=6*10^7\), the \(r-w=
\)
(A) 6
(B) 7
(C) 8
(D) 9
(E) 15
\)
(A) 6
(B) 7
(C) 8
(D) 9
(E) 15
Useful property: \(\frac{AB}{CD}=(\frac{A}{C})(\frac{B}{D})\)
Given: \(\frac{0.018*10^r}{0.0003*10^w}=6*10^7\)
Apply the above property to get: \((\frac{0.018}{0.0003})(\frac{10^r}{10^w})=6*10^7\)
Simplify both fractions: \((60)(10^{r-w})=6*10^7\)
Divide both sides of the equation by \(6\) to get: \((10)(10^{r-w})=10^7\)
Divide both sides of the equation by \(10\) to get: \(10^{r-w}=10^6\)
Since both sides of the equation have the same base, the exponents must be equal: \(r-w=6\)
Answer: A
GreenlightTestPrep
Hi sir,
In the Simplify both fractions step, shouldn't it be 0.6 instead of 60. I'm getting the answer as 8.
Thanks in advance!
