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# What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2

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Manager
Joined: 24 May 2016
Posts: 170
What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 [#permalink]

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12 Jul 2016, 01:53
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What is the value of integer n if $$(\sqrt{\frac{16}{10^n}})^2=0.04^2$$

A) 0
B) 1
C) 2
D) 3
E) 4

Please explain in detail your answer.

Thank you.
[Reveal] Spoiler: OA

Last edited by Divyadisha on 09 Aug 2016, 05:53, edited 4 times in total.
Edited the question and the OA.
Manager
Joined: 07 Mar 2015
Posts: 110
Location: India
Concentration: General Management, Operations
GMAT 1: 590 Q46 V25
GPA: 3.84
WE: Engineering (Energy and Utilities)
Re: What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 [#permalink]

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12 Jul 2016, 02:09
I am getting n=4 , I don't know where I am going wrong

EBITDA wrote:
What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2

A) 0
B) 1
C) 2
D) 3
E) 4

Please explain in detail your answer.

Thank you.
Retired Moderator
Joined: 26 Nov 2012
Posts: 600
Re: What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 [#permalink]

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12 Jul 2016, 02:15
EBITDA wrote:
What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2

A) 0
B) 1
C) 2
D) 3
E) 4

Please explain in detail your answer.

Thank you.

Given (√(16/(10^n)))^2 = 0.04^2.

Now on LHS we can get rid of square root due to the square.

Then it becomes

=> (16/(10^n) = 0.0016

16 * 0.0001 = 0.0016

Cancelling 16 on both sides we get the below.

Now it changes to 1/$$10^n$$ = 0.0001

Cross multiplying

1/ 0.0001 = $$10^n$$
$$10^4$$ = $$10^n$$.

So n = 4.

Last edited by msk0657 on 12 Jul 2016, 04:41, edited 2 times in total.
Manager
Joined: 24 May 2016
Posts: 170
Re: What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 [#permalink]

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12 Jul 2016, 03:53
msk0657 wrote:
EBITDA wrote:
What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2

A) 0
B) 1
C) 2
D) 3
E) 4

Please explain in detail your answer.

Thank you.

Given (√(16/(10^n)))^2 = 0.04^2.

Now on LHS we can get rid of square root due to the square.

Then it becomes

=> (16/(10^n) = 0.0016

16 * 0.001 = 0.0016

Cancelling 16 on both sides we get the below.

Now it changes to 1/$$10^n$$ = 0.001

Cross multiplying

1/ 0.001 = $$10^n$$
$$10^3$$ = $$10^n$$.

So n = 3.

Option D is the correct option.

Hi msk0657,

The part of your answer that I have marked in red is wrong.

It should be 16 * 0.0001 = 0.0016

Nonetheless, here is my approach.

First, I eliminate the square root and the square.

16 / (10^n) = (4 / 100)^2 ---> 16 / (10^n) = 16 / 10,000

Then, I eliminate the 16.

1/ (10^n) = 1 / 10,000

This equals:

10,000 = 10^n

Therefore, n = 4.

Could someone please explain where am I making an error?

Thank you so much.
Math Expert
Joined: 02 Sep 2009
Posts: 44351
Re: What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 [#permalink]

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12 Jul 2016, 04:32
EBITDA wrote:
What is the value of integer n if $$(\sqrt{\frac{16}{10^n}})^2=0.04^n$$

A) 0
B) 1
C) 2
D) 3
E) 4

Please explain in detail your answer.

Thank you.

The OA is wrong. The correct answer is 4 (E)
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Joined: 26 Nov 2012
Posts: 600
Re: What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 [#permalink]

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12 Jul 2016, 04:38
EBITDA wrote:
What is the value of integer n if $$(\sqrt{\frac{16}{10^n}})^2=0.04^2$$

A) 0
B) 1
C) 2
D) 3
E) 4

Please explain in detail your answer.

Thank you.

Hi there,

That is typing mistake...I missed it... it has to be 16 * 0.0001 = 0.0016 ( 0.04 * 0.04 )

It looks like you posted wrong option too.. Bunuel edited the question and I edited my previous solution and n will be 4.
Manager
Joined: 24 May 2016
Posts: 170
Re: What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 [#permalink]

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12 Jul 2016, 04:42
msk0657 wrote:
EBITDA wrote:
What is the value of integer n if $$(\sqrt{\frac{16}{10^n}})^2=0.04^2$$

A) 0
B) 1
C) 2
D) 3
E) 4

Please explain in detail your answer.

Thank you.

Hi there,

That is typing mistake...I missed it... it has to be 16 * 0.001 = 0.0016 ( 0.04 * 0.04 )

It looks like you posted wrong option + question too.. Bunuel edited the question and I edited my previous solution and n will be 4.

I was given a wrong official answer. The correct answer is option E, as already stated above.
Manager
Joined: 06 Jun 2014
Posts: 56
Re: What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 [#permalink]

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08 Aug 2016, 14:35
my solution:
1. get rid of the square power on both sides
$$\frac{16}{10^n}=0.0016$$

2. put the unknown variable on left side

$$10^n= \frac{16}{0.0016}$$ and now $$0.0016 = 16*10^(-4)$$ so we get

$$10^n=\frac{16}{16}*10^4$$ switch signs to +4 power when placed from denominator to nominator

3. $$10^n=1*10^4$$ or n=4
Senior Manager
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Posts: 477
Location: India
WE: Information Technology (Computer Software)
Re: What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 [#permalink]

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22 Aug 2017, 10:43
What is the value of integer n if (1610n−−−√)2=0.042(1610n)2=0.042

A) 0
B) 1
C) 2
D) 3
E) 4

Answer:
cancel the squares oon both sides,
then remove the root on 16/10^n
then it is equal 4/10^2/n=.04
then this equal to 100=10^n/2
then n =4

answer =E=4
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Joined: 22 May 2016
Posts: 1424
What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 [#permalink]

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22 Aug 2017, 13:06
EBITDA wrote:
What is the value of integer n if $$(\sqrt{\frac{16}{10^n}})^2=0.04^2$$

A) 0
B) 1
C) 2
D) 3
E) 4

Please explain in detail your answer.

Thank you.

$$(\sqrt{\frac{16}{10^n}})^2=0.04^2$$

$${\frac{16}{10^n}}=0.0016$$

$${\frac{16}{10^n}} = 16 * 10^{-4}$$

$${\frac{16}{10^n}} = {\frac{16}{10^4}}$$

$$n = 4$$

Answer E
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Re: What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 [#permalink]

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24 Aug 2017, 16:11
EBITDA wrote:
What is the value of integer n if $$(\sqrt{\frac{16}{10^n}})^2=0.04^2$$

A) 0
B) 1
C) 2
D) 3
E) 4

We can simplify the given equation and we have:

16/10^n = (4/100)^2

16/10^n = 16/100^2

Since the numerators are equal, the denominators should also be equal:

10^n = 100^2

10^n = (10^2)^2

10^n = 10^4

n = 4

Answer: E
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Re: What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2   [#permalink] 24 Aug 2017, 16:11
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# What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2

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