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OG 13 227-Simpler Solution

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by Brent@GMATPrepNow » Fri Jul 05, 2013 10:52 am
if (0.0015 x 10^m) / (0.03 x 10^k) = 5 x 10^7, then m - k = ?

a. 9
b. 8
c. 7
d. 6
e. 5
Here's one approach:

First rewrite the equation as:
(0.0015/0.03) x (10^m)/(10^k) = 5 x 10^7
Simplify to get: (0.0015/0.03) x 10^(m-k) = 5 x 10^7

Aside: A quick way to simplify 0.0015/0.03 is to multiply top and bottom by 10,000 to get 15/300.
Simplify to get 1/20

So, we now have (1/20) x 10^(m-k) = 5 x 10^7
Isolate 10^(m-k) by multiplying both sides by 20 to get:
10^(m-k) = (20)(5) (10^7)
Simplify: 10^(m-k) = (100)(10^7)
Simplify: 10^(m-k) = (10^2)(10^7)
Simplify: 10^(m-k) = 10^9

So, m-k must equal 9

Answer: A

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by GMATGuruNY » Sat Jul 06, 2013 2:31 am
if (0.0015 x 10^m) / (0.03 x 10^k) = (5 x 10^7), then m - k = ?

a. 9
b. 8
c. 7
d. 6
e. 5
Let k=0.
(0.0015 * 10^m) / (0.03* 10^0) = (5 * 10^7)

Convert the decimals to integers:
(15 * 10^(-4) * 10^m / (3 * 10^(-2) * 1) = (5 * 10^7)

Divide the integers and subtract the exponents:
5 * 10^(-2) * 10^m = 5 * 10^7

Cancel the 5's and divide each side by 10^(-2):
10^m = 10^9
m = 9.

Thus:
m-k = 9-0 = 9.

The correct answer is A.
Last edited by GMATGuruNY on Sat Aug 17, 2013 7:33 am, edited 1 time in total.
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by vipulgoyal » Fri Aug 16, 2013 1:25 am
alt approach

.03x.05x10^m/.03x10^k = 5x10^7
5x10^m/10^k+2 = 5x10^7
m-k-2=7
m-k=9
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by lunarpower » Sat Aug 17, 2013 6:08 am
[email protected] wrote:While I have understood the solution given in OG, I feel there can be a simpler solution :(
If you plug in k = 2, then the denominator of the fraction just becomes 3. So you'll get an easier equation to solve.

If you solve that equation, you'll get m = 11.
So then m - k = 11 - 2 = 9.
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