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# If 10^n< 0.000025 <10^{n+1}, what is the value of an integer n?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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If 10^n< 0.000025 <10^{n+1}, what is the value of an integer n? [#permalink]

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15 Aug 2017, 00:32
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If $$10^n< 0.000025 <10^{n+1}$$, what is the value of an integer n?

A. -5
B. -4
C. -3
D. 4
E. 5
[Reveal] Spoiler: OA

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If 10^n< 0.000025 <10^{n+1}, what is the value of an integer n? [#permalink]

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15 Aug 2017, 00:59
To find the exact value of the expression, simplify the expression:
$$0.000025 = 25*10^{-6} = \frac{100*10^{-6}}{4} = \frac{10^{2-6}}{4} = \frac{1}{4}*10^{-4}$$

Since this value must be between the range $$10^n$$ and $$10^{n+1}$$,
n must take the value of -5 as the value is between $$10^{-5}$$ and $$10^{-4}$$ (Option A)
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Re: If 10^n< 0.000025 <10^{n+1}, what is the value of an integer n? [#permalink]

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15 Aug 2017, 01:02
MathRevolution wrote:
If $$10^n< 0.000025 <10^{n+1}$$, what is the value of an integer n?

A. -5
B. -4
C. -3
D. 4
E. 5

0.000025 = 2.5*10^(-5)
also,
1<2.5<10
therefore
10(-5)<2.5*10^(-5)<10^(-4)
On comparing, we get
n = -5
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4908
GPA: 3.82
Re: If 10^n< 0.000025 <10^{n+1}, what is the value of an integer n? [#permalink]

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16 Aug 2017, 23:53
=>$$0.00001 < 0.000025 < 0.0001$$
$$10^{-5} < 0.000025 < 10^{-4}$$

Ans: A
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Re: If 10^n< 0.000025 <10^{n+1}, what is the value of an integer n?   [#permalink] 16 Aug 2017, 23:53
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