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M26-16

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M26-16  [#permalink]

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New post 16 Sep 2014, 00:25
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

58% (00:51) correct 42% (01:08) wrong based on 236 sessions

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Re M26-16  [#permalink]

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New post 16 Sep 2014, 00:25
1
2
Official Solution:

If \(n\) is an integer and \(\frac{1}{10^{n+1}} \lt 0.00737 \lt \frac{1}{10^n}\), then what is the value of \(n\)?

A. 1
B. 2
C. 3
D. 4
E. 5


There is no need for algebraic manipulation to solve this question.

\(\frac{1}{10^{n+1}}\) is 10 times less than \(\frac{1}{10^n}\), and both when expressed as decimals are of a type 0.001 (some number of zeros before 1). Which means that the given expression to hold true we should have: \(0.001 \lt 0.00737 \lt 0.01\), which means that \(n=2\) \((\frac{1}{10^n}=0.01\), so \(n=2)\).


Answer: B
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Re: M26-16  [#permalink]

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New post 18 Sep 2014, 13:16
Hi Bunuel,

I am unable to understand the explanation. Please help me on this.

This is how is approached, but got stuck.

\(\frac{1}{10^{n+1}} \lt \frac{737}{10^5} \lt \frac{1}{10^n}\)

Approximate 737 to 1000

\(\frac{1}{10^{n+1}} \lt \frac{10^3}{10^5} \lt \frac{1}{10^n}\)

\(\frac{1}{10^{n+1}} \lt \frac{1}{10^2} \lt \frac{1}{10^n}\)

Thanks,
Gabriel
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Re: M26-16  [#permalink]

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New post 19 Sep 2014, 01:14
gabriel87 wrote:
Hi Bunuel,

I am unable to understand the explanation. Please help me on this.

This is how is approached, but got stuck.

\(\frac{1}{10^{n+1}} \lt \frac{737}{10^5} \lt \frac{1}{10^n}\)

Approximate 737 to 1000

\(\frac{1}{10^{n+1}} \lt \frac{10^3}{10^5} \lt \frac{1}{10^n}\)

\(\frac{1}{10^{n+1}} \lt \frac{1}{10^2} \lt \frac{1}{10^n}\)

Thanks,
Gabriel


For alternative solutions go through this topic: 12-easy-pieces-or-not-126366.html

As for your solution you cannot approximate the way you did, it won't give you a correct answer.
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Re M26-16  [#permalink]

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New post 25 Jul 2016, 09:41
I think this is a high-quality question.
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Re: M26-16  [#permalink]

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New post 26 Jul 2016, 04:22
What I did-

Approximate 737 to 700= 7 X 100.

Doing so will give you power of 3 to 10 in denominator. Now, this inequality becomes very simple as we need to have smaller powers than 3 (of 10) in denominator for the right most expression to have greater value. Also, please remember that you can not have n=1, else the left most expression would attain greater value than the middle expression

I hope this helps.

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Re: M26-16  [#permalink]

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New post 26 Jan 2017, 09:38
hi Bunuel
please elaborate it further. i didn't understand why we are taking/considering n=2



thnx
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Re: M26-16  [#permalink]

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New post 26 Jan 2017, 09:44
gupta87 wrote:
hi Bunuel
please elaborate it further. i didn't understand why we are taking/considering n=2



thnx


Basically it was done by plugging options after realising that both \(\frac{1}{10^{n+1}}\) and \(\frac{1}{10^n}\), are of the form 0.001 (some number of zeros before 1).
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Re: M26-16  [#permalink]

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New post 27 Jan 2017, 01:54
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The number is scary 0.00737. So try be simple. Put it as 0.007

Plugging in numbers: 0.001< 0.007 < 0.01..........n=2

Answer; B
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Re: M26-16  [#permalink]

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New post 25 Feb 2018, 15:30
Hi Bunuel,

I solved this problem by multiplying the entire inequality by 10^5 and solved it. This should work all the time with such questions, am I right?

Thank you
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Re: M26-16  [#permalink]

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New post 08 Aug 2018, 02:48
2
multiply every side by 10^5

As the number is positive, no change in sign will occur

10^4-n < 737 < 10^5-n

only n = 2 satisfies this
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Re: M26-16  [#permalink]

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New post 08 Aug 2018, 05:40
1
Bunuel wrote:
If \(n\) is an integer and \(\frac{1}{10^{n+1}} \lt 0.00737 \lt \frac{1}{10^n}\), then what is the value of \(n\)?

A. 1
B. 2
C. 3
D. 4
E. 5


We can plug in the values and solve this question

When it comes to plugging in, i generally pick the middle option (option 3)

when n = 3

1/10^(3+1) = 1/10^4 = 0.0001. This is not less than 0.007.

Now, lets consider n=2
1/10^3 = 0.001 and 1/10^2 = 0.01
0.001< 0.007<0.01

Hence, option B
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Re M26-16  [#permalink]

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New post 13 Aug 2018, 18:07
I think this is a high-quality question and I agree with explanation. Multiplied the entire inequality by 10^3 which makes the middle # 7.37. N = 2 will put the inequality between 1 and 10
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Re M26-16 &nbs [#permalink] 13 Aug 2018, 18:07
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