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To find m-k

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by gmattesttaker2 » Thu Feb 06, 2014 11:19 pm
Hello,

For the following:

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

OA: A

However, I am getting E.

Can you please assist with this?

Thanks,
Sri
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by Brent@GMATPrepNow » Thu Feb 06, 2014 11:22 pm
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

Cheers,
Brent
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by Brent@GMATPrepNow » Thu Feb 06, 2014 11:33 pm
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
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 = [spoiler]9 = A[/spoiler]

Cheers,
Brent
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by batwaraanirudh » Thu Feb 06, 2014 11:39 pm
Another approach is to assign k a "nice" value.
Let's see what happens when k = 0
I used an approach similar to the first approach that you have mentioned, but I must say the second approach is interesting. Might be useful when one is getting stuck with long calculations...
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by GMATGuruNY » Fri Feb 07, 2014 1:04 am
gmattesttaker2 wrote:Hello,

For the following:

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
Slightly different approach:

Let k=2.
(0.0015 * 10^m) / (0.03* 10^2) = 5 * 10^7

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

Divide 15 by 3:
5 * 10^(-4) * 10^m = 5 * 10^7

Cancel the 5's and divide each side by 10^(-4):
10^m = 10^11
m = 11.

Thus:
m-k = 11-2 = 9.

The correct answer is A.
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