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# If 0 < 10^n < 1,000,000, where n is a non-negative integer, what is

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If 0 < 10^n < 1,000,000, where n is a non-negative integer, what is  [#permalink]

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01 Aug 2017, 00:03
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If $$0 < 10^n < 1,000,000$$, where n is a non-negative integer, what is the greatest value of $$\frac{1}{2^n}$$?

A. 1/2
B. 1
C. 5
D. 32
E. 64

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If 0 < 10^n < 1,000,000, where n is a non-negative integer, what is  [#permalink]

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01 Aug 2017, 00:10
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Bunuel wrote:
If $$0 < 10^n < 1,000,000$$, where n is a non-negative integer, what is the greatest value of $$\frac{1}{2^n}$$?

A. 1/2
B. 1
C. 5
D. 32
E. 64

Since n is a non-negative integer n can take 0,1,2,3,4,5

Greatest value in a fraction means n should be smallest i.e. 0
$$1/2^0$$ = 1

B
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Re: If 0 < 10^n < 1,000,000, where n is a non-negative integer, what is  [#permalink]

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01 Aug 2017, 00:15
n is a non-negative integer = N is 0 and all positive integer

0<10n<1,000,000 means Power n can have max value as 5 which will give 100,000

and n can have minimum value as 0 which will make 10n = 1.

So n can be 0,1,2,3,4 and 5

So what value can be taken to make 1/2n (Power N)as max value. So minimum can be taken to make 1/2n max ..which is Zero can be taken.

So Answer will be 1/1 = 1 == Option (B)
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If 0 < 10^n < 1,000,000, where n is a non-negative integer, what is  [#permalink]

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05 Aug 2017, 08:07
Bunuel wrote:
If $$0 < 10^n < 1,000,000$$, where n is a non-negative integer, what is the greatest value of $$\frac{1}{2^n}$$?

A. 1/2
B. 1
C. 5
D. 32
E. 64

$$0 < 10^n < 1,000,000$$

0 < 10^n < 10^6

So, n could be 0,1,2,3,4,5 since n is a non-negative integer.

The greatest value of $$\frac{1}{2^n}$$ could be achieved if 2^n is the smallest, i.e. for n = 0 at which the fraction becomes 1/2^0
or 1/1 = 1.

Ans B) 1
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Re: If 0 < 10^n < 1,000,000, where n is a non-negative integer, what is  [#permalink]

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02 Apr 2020, 08:09
0<10^n<1,000,0000
since , n is a non negative integer , n = 0,1,2,3,4,5
to get max of 1/2^n , n must be 0 (min value )
so, the required value = 1/2^0 = 1
Re: If 0 < 10^n < 1,000,000, where n is a non-negative integer, what is   [#permalink] 02 Apr 2020, 08:09