If 0.0015*10^m/0.03*10^k=5*10^7, then m - k = : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 19 Feb 2017, 18:06

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 178
Followers: 5

Kudos [?]: 2425 [0], given: 0

If 0.0015*10^m/0.03*10^k=5*10^7, then m - k = [#permalink]

### Show Tags

31 Dec 2012, 04:41
16
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

68% (02:07) correct 32% (01:24) wrong based on 911 sessions

### HideShow timer Statistics

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
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 37024
Followers: 7226

Kudos [?]: 96066 [5] , given: 10706

Re: If 0.0015*10^m/0.03*10^k=5*10^7, then m - k = [#permalink]

### Show Tags

31 Dec 2012, 04:45
5
KUDOS
Expert's post
3
This post was
BOOKMARKED
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

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

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

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

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

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

$$m-k=9$$.

_________________
Intern
Joined: 21 Mar 2009
Posts: 21
Followers: 0

Kudos [?]: 21 [0], given: 0

Re: If 0.0015*10^m/0.03*10^k=5*10^7, then m - k = [#permalink]

### Show Tags

31 Dec 2012, 06:24
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
Manager
Joined: 18 Oct 2011
Posts: 90
Location: United States
Concentration: Entrepreneurship, Marketing
GMAT Date: 01-30-2013
GPA: 3.3
Followers: 2

Kudos [?]: 69 [0], given: 0

Re: If 0.0015*10^m/0.03*10^k=5*10^7, then m - k = [#permalink]

### Show Tags

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
Manager
Joined: 30 Jun 2012
Posts: 84
Location: United States
GMAT 1: 510 Q34 V28
GMAT 2: 580 Q35 V35
GMAT 3: 640 Q34 V44
GMAT 4: 690 Q43 V42
GPA: 3.61
WE: Education (Education)
Followers: 13

Kudos [?]: 124 [0], given: 16

Re: If 0.0015*10^m/0.03*10^k=5*10^7, then m - k = [#permalink]

### Show Tags

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
Intern
Joined: 23 Mar 2011
Posts: 30
Followers: 0

Kudos [?]: 4 [1] , given: 9

Re: If 0.0015*10^m/0.03*10^k=5*10^7, then m - k = [#permalink]

### Show Tags

26 Jul 2013, 22:11
1
KUDOS
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:

$$-4 + m = 5 + k$$

$$m - k = 5 + 4$$

$$m - k = 9$$

~ Im2bz2p345
Intern
Joined: 07 Sep 2013
Posts: 4
Followers: 0

Kudos [?]: 1 [0], given: 0

plz help in solving this!! [#permalink]

### Show Tags

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
Math Expert
Joined: 02 Sep 2009
Posts: 37024
Followers: 7226

Kudos [?]: 96066 [0], given: 10706

Re: plz help in solving this!! [#permalink]

### Show Tags

26 Oct 2013, 02:20
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
_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1858
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 49

Kudos [?]: 1981 [1] , given: 193

Re: If 0.0015*10^m/0.03*10^k=5*10^7, then m - k = [#permalink]

### Show Tags

26 Feb 2014, 01:42
1
KUDOS
Removing decimal point & solving ahead,

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

Equating , m-k = 9 = Answer = A
_________________

Kindly press "+1 Kudos" to appreciate

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13870
Followers: 589

Kudos [?]: 167 [0], given: 0

Re: If 0.0015*10^m/0.03*10^k=5*10^7, then m - k = [#permalink]

### Show Tags

13 Mar 2015, 08:44
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13870
Followers: 589

Kudos [?]: 167 [0], given: 0

Re: If 0.0015*10^m/0.03*10^k=5*10^7, then m - k = [#permalink]

### Show Tags

10 May 2016, 05:39
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Director
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 607
Location: United States (CA)
Followers: 23

Kudos [?]: 245 [0], given: 2

Re: If 0.0015*10^m/0.03*10^k=5*10^7, then m - k = [#permalink]

### Show Tags

10 May 2016, 06:11
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

We start by simplifying the numerator and denominator of the given fraction. First, we simplify the numerator:

(0.0015)(10^m)

It will be helpful to convert 0.0015 to an integer. To do so we must move the decimal point in 0.0015 four places to the right. Since we are making 0.0015 larger by four decimal places we must make 10^m, smaller by four decimal places. Thus, 10^m now becomes 10^(m-4). Thus, the numerator becomes (15)(10^(m-4)).

Next we can simplify the denominator:

(0.03)(10^k)

It will be helpful to convert 0.03 to an integer. To do so we must move the decimal point in 0.03 two places to the right. Since we are making 0.03 larger by two decimal places we must make 10^k, smaller by two decimal places. Thus, 10^k now becomes 10^(k-2). The denominator can thus be re-expressed as (3)(10^(k-2)).

So now we are left with:

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

Dividing 15 by 3 on the left hand side of the equation, we have 15/3 = 5. Recall that when we divide powers of like bases, we subtract the exponents, so 10^(m-4)/10^(k-2) =
10^((m-4) – (k-2)) = 10^(m-k-2). Therefore, we have

5(10^(m-k-2)) = (5)(10^7)

5 will cancel out from both sides of the equation, leaving us with:

10^(m-k-2)=10^7

Because we are left with a base of 10 on both the right-hand side and the left-hand side of the equation, we can drop the base and set the exponents equal and hence determine the value of m – k:

m – k – 2 = 7

m – k = 9

_________________

Jeffrey Miller
Scott Woodbury-Stewart
Founder and CEO

VP
Joined: 11 Sep 2015
Posts: 1044
Followers: 116

Kudos [?]: 995 [1] , given: 169

Re: If 0.0015*10^m/0.03*10^k=5*10^7, then m - k = [#permalink]

### Show Tags

30 Nov 2016, 16:56
1
KUDOS
Top Contributor
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

Another approach is to assign k a "nice" value.

Let's see what happens when k = 0

We get: (0.0015 x 10^m) / (0.03 x 10^0) = 5 x 10^7

Simplify: (0.0015 x 10^m) / (0.03 x 1) = 5 x 10^7

Simplify: (0.0015 x 10^m) / (0.03) = 5 x 10^7

Multiply both sides by 0.03 to get: 0.0015 x 10^m = 0.15 x 10^7

Eliminate blue decimals by multiplying both sides by 10,000 to get: 15 x 10^m = 1500 x 10^7

Divide both sides by 15 to get: 1 x 10^m = 100 x 10^7

Rewrite 100 as 10^2: 1 x 10^m = 10^2 x 10^7

Simplify: 10^m = 10^9

So, m = 9

In other words, when k = 0, m = 9
So, m - k = 9 - 0 = 9

Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

Re: If 0.0015*10^m/0.03*10^k=5*10^7, then m - k =   [#permalink] 30 Nov 2016, 16:56
Similar topics Replies Last post
Similar
Topics:
3 If k and m are numbers such that k + m = 20 and k^2 + m^2 = 289, then 4 15 Feb 2017, 11:08
4 If m and n are positive integers, and m=2n and k=3m, then - 4 27 Aug 2014, 05:51
12 If k is a multiple of 3 and k = (m^2)n, where m and n are 9 04 Feb 2013, 12:34
3 If k=m(m+4)(m+5) k and m are positive integers. Which of the 10 17 Apr 2010, 00:44
7 If a, b, k, and m are positive integers, is a^k factor of b 5 06 Nov 2009, 22:12
Display posts from previous: Sort by