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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8149
GMAT 1: 760 Q51 V42 GPA: 3.82
If 10^(n-1)< 0.000125 <10^n, what is the value of an integer n?  [#permalink]

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12 00:00

Difficulty:   65% (hard)

Question Stats: 58% (02:02) correct 42% (02:10) wrong based on 204 sessions

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If 10^(n-1)< 0.000125 <10^n, what is the value of an integer n?

A. -4
B. -3
C. -2
D. 3
E. 4

* A solution will be posted in two days.

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Math Expert V
Joined: 02 Aug 2009
Posts: 8187
If 10^(n-1)< 0.000125 <10^n, what is the value of an integer n?  [#permalink]

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2
MathRevolution wrote:
If 10^(n-1)< 0.000125 <10^n, what is the value of an integer n?

A. -4
B. -3
C. -2
D. 3
E. 4

* A solution will be posted in two days.

Hi,
$$10^{n-1}< 0.000125 <10^n$$...
or $$10^{n-1}< 0.000125*\frac{1000}{1000}<10^n$$...
or $$10^{n-1}< \frac{0.125}{1000}<10^n$$...
or $$10^{n-1}*1000<0.125 <10^n*1000$$...
or $$10^{n+2}< 0.125<10^{n+3}$$...
$$10^0=1$$, which >.125
so $$n+3=0$$..$$n=-3$$
B
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Posts: 4065
Re: If 10^(n-1)< 0.000125 <10^n, what is the value of an integer n?  [#permalink]

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3
1
MathRevolution wrote:
If 10^(n-1)< 0.000125 <10^n, what is the value of an integer n?

A. -4
B. -3
C. -2
D. 3
E. 4

* A solution will be posted in two days.

Let's TEST some values.

If n = -4, when we get: 10^(-4-1)< 0.000125 < 10^(-4)
Simplify to get: 10^(-5) < 0.000125 < 10^(-4)
Or we can say: 1/100,000 < 0.000125 < 1/10,0000
Rewrite as decimals to get: 0.00001 < 0.000125 < 0.0001
This is NO GOOD, because 0.000125 is GREATER than 0.0001
ELIMINATE A

If n = -3, when we get: 10^(-3-1)< 0.000125 < 10^(-3)
Rewrite as decimals to get: 0.0001 < 0.000125 < 0.001
PERFECT!!

Cheers,
Brent
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Math Revolution GMAT Instructor V
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GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If 10^(n-1)< 0.000125 <10^n, what is the value of an integer n?  [#permalink]

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If 10^(n-1)< 0.000125 <10^n, what is the value of an integer n?

A. -4
B. -3
C. -2
D. 3
E. 4

-> Multiply 10^6- > (10^6){10^(n-1)}<125<(10^6)(10^n) -> 125 is bigger than 100
-> (10^6)(10^(n-1))=100 -> 10^(6+n-1)=10^2, n+5=2 -> n=-3
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Re: If 10^(n-1)< 0.000125 <10^n, what is the value of an integer n?  [#permalink]

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wouldn't 10^-4 be .0010 since you move the decimal places 4 units to the right. Do we disregard the 0 next to the 10?
Manager  Joined: 09 Jul 2013
Posts: 107
Re: If 10^(n-1)< 0.000125 <10^n, what is the value of an integer n?  [#permalink]

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bullfromist wrote:
wouldn't 10^-4 be .0010 since you move the decimal places 4 units to the right. Do we disregard the 0 next to the 10?

You are right that the decimal moves 4 places, but this is actually scientific notation, and what is omitted from the way it is written above is the 1* in front of the $$10^{-4}$$. So when you see $$10^{-1}$$, what you should be reading is $$1*10^{-4}$$. The decimal is moved for the 1, not the 10. Similarly, what do you do if you have $$876.38*10^{-3}$$ ? You move the decimal on the 876.38 to the left 3 places. $$876.38*10^{-3} = 0.87638$$

You can prove it to yourself in another way:
$$10^{-1} = \frac{1}{10} = 0.1$$
$$10^{-2} = \frac{1}{10^2} = 0.01$$
$$10^{-3} = \frac{1}{10^3} = 0.001$$
$$10^{-4} = \frac{1}{10^4} = 0.0001$$

so $$10^{-4}$$ is a shorthand way of saying "divide by 10000". But what are we dividing by 10000? Whatever is multiplied in front of $$10^{-4}$$. If there's nothing written in front, then it's the same as multiplying by 1, and we typically don't write it when things are multiplied by 1.

I hope that clears up the confusion

Cheers
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GRE 1: Q169 V154 Re: If 10^(n-1)< 0.000125 <10^n, what is the value of an integer n?  [#permalink]

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Multiply all the sides by 10^6 and we can say that N must be -3
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Re: If 10^(n-1)< 0.000125 <10^n, what is the value of an integer n?  [#permalink]

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Hi!
Expert, i tried solving this question but still unable to comprehend using values substitution method.
kindly help with some other way out please..
chetan4u i do appreciate your method but do help me with understanding that once or something different which can be recalled while following same pattern question.
thanks
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Re: If 10^(n-1)< 0.000125 <10^n, what is the value of an integer n?  [#permalink]

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Celestial09 wrote:
Hi!
Expert, i tried solving this question but still unable to comprehend using values substitution method.
kindly help with some other way out please..
chetan4u i do appreciate your method but do help me with understanding that once or something different which can be recalled while following same pattern question.
thanks

Question Says 10^(n-1)< 125*10^-6<10^n

so, if we multiply the above inequality with 10^6, we will get

10^(n-1+6)<125 *10^(-6+6)<10^(n+6)

=> 10^(n+5)<125<10^(n+6)

Now, we have 100 less than 125 and 1000 greater than 125.

So, if we put n+5=2 , we will get n=-3, which will make the above inequality as

100<125<1000.

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Re: If 10^(n-1)< 0.000125 <10^n, what is the value of an integer n?  [#permalink]

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MathRevolution wrote:
If 10^(n-1)< 0.000125 <10^n, what is the value of an integer n?

A. -4
B. -3
C. -2
D. 3
E. 4

* A solution will be posted in two days.

$$10^{(n-1)} < 0.000125 < 10^n$$

$$0.000125 = 0.0001 + 0.000025 = 10^{-4} + 0.000025$$

so $$0.000125$$ = a number slightly more than $$10^{-4}$$ but still less than $$10^{-3}$$

Hence $$n = -3$$

Thanks,
GyM
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Re: If 10^(n-1)< 0.000125 <10^n, what is the value of an integer n?  [#permalink]

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_________________ Re: If 10^(n-1)< 0.000125 <10^n, what is the value of an integer n?   [#permalink] 15 Oct 2019, 14:19
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