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

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Senior CR Moderator
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11 Apr 2017, 06:24
1
00:00

Difficulty:

45% (medium)

Question Stats:

60% (01:45) correct 40% (01:49) wrong based on 86 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

Source: GMAT Free

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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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11 Apr 2017, 08:20
$$0.016 * 10^n / 0.4 * 10^m = 4 * 10^4$$

=> $$(0.016/0.4) * 10^(^n^-^m^) = 4 * 10^4$$
$$=> 10^(^n^-^m^) = 4*10^4 * (0.4/0.016)$$
$$=> 10^(^n^-^m^) = 4*10^4 * 400 / 16$$
$$=> 10^(^n^-^m^) = 10^6$$
$$=> (n-m) = 6$$
$$=> m-n = -6$$
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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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11 Apr 2017, 11:06
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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15 Apr 2018, 11:02
+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, 11:02
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