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# M26-16

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Math Expert
Joined: 02 Sep 2009
Posts: 58402

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16 Sep 2014, 01:25
00:00

Difficulty:

45% (medium)

Question Stats:

57% (01:22) correct 43% (01:40) wrong based on 153 sessions

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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

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Math Expert
Joined: 02 Sep 2009
Posts: 58402

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16 Sep 2014, 01:25
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 $$n=2)$$.

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Intern
Joined: 26 Jul 2011
Posts: 26

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18 Sep 2014, 14:16
Hi Bunuel,

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
Math Expert
Joined: 02 Sep 2009
Posts: 58402

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19 Sep 2014, 02:14
gabriel87 wrote:
Hi Bunuel,

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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Intern
Joined: 09 Sep 2015
Posts: 5
GMAT 1: 630 Q46 V31
GPA: 3.53
WE: Education (Education)

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25 Jul 2016, 10:41
I think this is a high-quality question.
Intern
Joined: 02 Nov 2015
Posts: 20

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26 Jul 2016, 05:22
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.

Regards
Yash
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Joined: 19 Jul 2016
Posts: 49

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26 Jan 2017, 10:38
hi Bunuel
please elaborate it further. i didn't understand why we are taking/considering n=2

thnx
Math Expert
Joined: 02 Sep 2009
Posts: 58402

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26 Jan 2017, 10:44
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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Joined: 26 Mar 2013
Posts: 2345

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27 Jan 2017, 02:54
4
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

Intern
Joined: 20 Nov 2017
Posts: 16

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25 Feb 2018, 16:30
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
Manager
Joined: 09 Oct 2015
Posts: 226

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08 Aug 2018, 03:48
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
Intern
Joined: 23 Jun 2018
Posts: 24

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08 Aug 2018, 06:40
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
Intern
Joined: 01 May 2017
Posts: 10

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13 Aug 2018, 19:07
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
Intern
Joined: 24 Feb 2014
Posts: 36
Location: United States (GA)
WE: Information Technology (Computer Software)

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26 Sep 2019, 22:15
I think this is a high-quality question and I agree with explanation.
Re M26-16   [#permalink] 26 Sep 2019, 22:15
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# M26-16

Moderators: chetan2u, Bunuel