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If 10^n< 0.003456 <10^{n+1}, what is the value of the

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by Max@Math Revolution » Wed May 16, 2018 2:08 am

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[GMAT math practice question]

If 10^n< 0.003456 <10^{n+1}, what is the value of the integer n?

A. -4
B. -3
C. -2
D. -1
E. 0
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by Jeff@TargetTestPrep » Thu May 17, 2018 5:18 pm
Max@Math Revolution wrote:
If 10^n< 0.003456 <10^{n+1}, what is the value of the integer n?

A. -4
B. -3
C. -2
D. -1
E. 0
Simplifying, we have:

10^n < 3.456 x 10^-3 < 10^(n+1)

We see that if n = -3, then:

10^-3 < 10^-3 x 3.456 < 10^-2

Answer: B

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by Max@Math Revolution » Fri May 18, 2018 12:38 am
=>

When we multiply all sides of the inequality by 10^6, we obtain 10^{n*}10^6 < 3,456 < 10^{n+1}*10^6 or 10^{n+6} < 3,456 < 10^{n+7}..
Since 1,000 < 3,456 < 10,000, 10^{n+6}=1,000=103 and n+6=3. So, n=-3.


Therefore, the answer is B.

Answer: B
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