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

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by Max@Math Revolution » Mon Apr 04, 2016 12:01 am
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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by Brent@GMATPrepNow » Mon Apr 04, 2016 7:58 am
Max@Math Revolution 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.

Answer choice A
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


Answer choice B
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!!

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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If 10^(n-1)< 0.000125 <10^n, what is the value of an i

by Max@Math Revolution » Wed Apr 06, 2016 5:27 am
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
Thus, the answer is B
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