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 Please explain in detail

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.

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 Mitch's approach is great. Here's another (longer) 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

Here's another way to visualize it:

One last approach: .0015/.0300 * 10�� = 5 * 10� 15/300 * 10�� = 5 * 10� 15 * 10�� = 5 * 300 * 10� 10�� = 5 * 20 * 10� 10�� = 100 * 10� so (m - k) = 9

Matt@VeritasPrep wrote:One last approach: .0015/.0300 * 10�� = 5 * 10� 15/300 * 10�� = 5 * 10� 15 * 10�� = 5 * 300 * 10� 10�� = 5 * 20 * 10� 10�� = 100 * 10� so (m - k) = 9 HI THERE CAN YOU EXPLAIN THE LAST FEW STEPS BELOW? i THINK I MAYBE MISSING A FUNDAMENTAL HERE. PLEASE EXPLAIN AND GIVE ANOTHER EXAMPLE DEMONSTRATING THE SAME STEP YOU USED. THANK YOU i REALLY APPRECIATE IT. 10�� = 100 * 10� so (m - k) = 9[/quote]

Hi oquiella, It's common in 'exponent' questions for you to have to 'rewrite' a given number to get to the correct answer. For example: (9^2) can be rewritten as (3^2)^2, which can then be rewritten as 3^4. In this prompt, when we get to... (5)(20)(10^7) We can multiply the 5 and the 20 to get... 100, which can be rewritten as 10^2 When we multiply (10^2) and (10^7), we end up with 10^9 So 10�� = 10^9 (m-k) = 9 GMAT assassins aren't born, they're made, Rich

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