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If 0.0015*10^m/0.03*10^k=5*10^7, then m - k =

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If 0.0015*10^m/0.03*10^k=5*10^7, then m - k = [#permalink] New post 31 Dec 2012, 04:41
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If \frac{0.0015*10^m}{0.03*10^k}=5*10^7, then m - k =

(A) 9
(B) 8
(C) 7
(D) 6
(E) 5
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Re: If 0.0015*10^m/0.03*10^k=5*10^7, then m - k = [#permalink] New post 31 Dec 2012, 04:45
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Walkabout wrote:
If \frac{0.0015*10^m}{0.03*10^k}=5*10^7, then m - k =

(A) 9
(B) 8
(C) 7
(D) 6
(E) 5


\frac{0.0015*10^m}{0.03*10^k}=5*10^7;

\frac{15*10^{-4}*10^m}{3*10^{-2}*10^k}=5*10^7;

5*\frac{10^{m-4}}{10^{k-2}}=5*10^7;

10^{(m-4)-(k-2)}=10^7;

(m-4)-(k-2)=7;

m-k=9.

Answer: A.
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Re: If 0.0015*10^m/0.03*10^k=5*10^7, then m - k = [#permalink] New post 31 Dec 2012, 06:24
Walkabout wrote:
If \frac{0.0015*10^m}{0.03*10^k}=5*10^7, then m - k =

(A) 9
(B) 8
(C) 7
(D) 6
(E) 5



Rearrange the decimals : (15*10^-4*10^m)/(3*10^-2*10^k) = 5*10^7

After adjusting and cancelling 5 from each side : 10^(m-k-2) = 10^7
=> m-k-2=7 => m-k = 9
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Re: If 0.0015*10^m/0.03*10^k=5*10^7, then m - k = [#permalink] New post 03 Jan 2013, 12:49
rewrite the expression like this:

15(10)^-4 (10)^m / 3(10)^-2 (10)^k = 5(10)^7

When you simplify the expression you are left with: (10)^m / (10)^k = 10^9

Therefore m-k = 9
Answer: A
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Re: If 0.0015*10^m/0.03*10^k=5*10^7, then m - k = [#permalink] New post 14 Jul 2013, 14:50
I solved this question by cross multiplying.

15*10^-4m=15*10^-14k
-4m-14k=0
-4(7)-14(-2)=0
-28+28=0
m-k
7-(-2)= 9


sambam wrote:
rewrite the expression like this:

15(10)^-4 (10)^m / 3(10)^-2 (10)^k = 5(10)^7

When you simplify the expression you are left with: (10)^m / (10)^k = 10^9

Therefore m-k = 9
Answer: A
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Re: If 0.0015*10^m/0.03*10^k=5*10^7, then m - k = [#permalink] New post 26 Jul 2013, 22:11
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josemnz83 wrote:
I solved this question by cross multiplying.

15*10^-4m=15*10^-14k
-4m-14k=0
-4(7)-14(-2)=0
-28+28=0
m-k
7-(-2)= 9


Hello josemnz84 - I was looking at the alternate ways to solve this problem and I don't quite understand what you did here. Can you please explain? Specifically how did you get 10^{-14k}. I feel this is incorrect, but please correct me if my calculations are off.

If you want to cross multiply, the problem would be done this way:

\frac{15*10^{-4 + m}}{3*10^{-2+k}} = 5*10^7

15*10^{-4 + m}=15*10^{5 + k} - when you multiple powers of 10, you multiply the whole numbers and add the powers of 10 (you seemed to have multiplied the exponents rather than adding to get 10^-14 in your answer). See this: http://www.dummies.com/how-to/content/m ... ation.html

After cancelling out the "15 x 10^" (essentially 10^1) from both sides, you are left with:

-4 + m = 5 + k

m - k = 5 + 4

m - k = 9

Answer: A

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plz help in solving this!! [#permalink] New post 25 Oct 2013, 22:27
if (0.0015 . 10)^m/0.03 . 10^k = 5 . 10^7, then (m-k) =

a. 9
b.8
c.7
d.6
e.5
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Re: plz help in solving this!! [#permalink] New post 26 Oct 2013, 02:20
Expert's post
krithikaram89 wrote:
if (0.0015 . 10)^m/0.03 . 10^k = 5 . 10^7, then (m-k) =

a. 9
b.8
c.7
d.6
e.5


Merging similar topics. Please refer to the solutions above.

P.S. All OG13 questions with solutions are here: the-official-guide-quantitative-question-directory-143450.html
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: If 0.0015*10^m/0.03*10^k=5*10^7, then m - k = [#permalink] New post 26 Feb 2014, 01:42
Removing decimal point & solving ahead,

5 . 10^(m+2-4-k) = 5 . 10^7

Equating , m-k = 9 = Answer = A
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Re: If 0.0015*10^m/0.03*10^k=5*10^7, then m - k =   [#permalink] 26 Feb 2014, 01:42
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