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

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12 Jul 2016, 00:53
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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.

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Last edited by

Divyadisha on 09 Aug 2016, 04:53, edited 4 times in total.

Edited the question and the OA.

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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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12 Jul 2016, 01:09

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.

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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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12 Jul 2016, 01:15

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, 03:41, edited 2 times in total.

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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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12 Jul 2016, 02:53

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.

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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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12 Jul 2016, 03:32
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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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12 Jul 2016, 03:38

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.

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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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12 Jul 2016, 03:42

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.

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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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08 Aug 2016, 13:35

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

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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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22 Aug 2017, 02:12

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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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22 Aug 2017, 09:43

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

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22 Aug 2017, 12:06

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, 15:11
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
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24 Aug 2017, 15:11