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If (0.016*10^n)/(0.4*10^m)=4*10^4, then m-n=?

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If (0.016*10^n)/(0.4*10^m)=4*10^4, then m-n=?  [#permalink]

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New post 11 Apr 2017, 07:24
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A
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E

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Question Stats:

63% (01:05) correct 38% (01:27) wrong based on 80 sessions

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If \(\frac{0.016 \times 10^n}{0.4 \times 10^m} = 4 \times 10^4\), then \(m-n=\)

A. 6
B. 4
C. 0
D. -4
E. -6

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Re: If (0.016*10^n)/(0.4*10^m)=4*10^4, then m-n=?  [#permalink]

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New post 11 Apr 2017, 09:20
\(0.016 * 10^n / 0.4 * 10^m = 4 * 10^4\)

=> \((0.016/0.4) * 10^(^n^-^m^) = 4 * 10^4\)
\(=> 10^(^n^-^m^) = 4*10^4 * (0.4/0.016)\)
\(=> 10^(^n^-^m^) = 4*10^4 * 400 / 16\)
\(=> 10^(^n^-^m^) = 10^6\)
\(=> (n-m) = 6\)
\(=> m-n = -6\)
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Re: If (0.016*10^n)/(0.4*10^m)=4*10^4, then m-n=?  [#permalink]

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New post 11 Apr 2017, 12:06
nguyendinhtuong wrote:
If \(\frac{0.016 \times 10^n}{0.4 \times 10^m} = 4 \times 10^4\), then \(m-n=\)

A. 6
B. 4
C. 0
D. -4
E. -6

Source: GMAT Free

\(\frac{0.016 \times 10^n}{0.4 \times 10^m} = 4 \times 10^4\), then \(m-n=\)

Or, \(0.04*10^{n - m} = 4*10^4\)

Or, \(\frac{4}{10^2}*10^{n - m} = 4*10^4\)

Or, \(4*10^{n - m -2} = 4*10^4\)

So, \(n - m - 2 = 4\)

Or, \(n - m = 6\)

Now, \(-1 ( n - m ) = -1 ( 6 )\)

Or, \(m - n = -6\)

Hence, answer must be (E) \(m - n = -6\)
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Re: If (0.016*10^n)/(0.4*10^m)=4*10^4, then m-n=?  [#permalink]

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New post 15 Apr 2018, 12:02
+1 for E. Simplify and get the solution. m-n=-6.
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Re: If (0.016*10^n)/(0.4*10^m)=4*10^4, then m-n=? &nbs [#permalink] 15 Apr 2018, 12:02
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