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5√2 percent of 1/√200 =

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5√2 percent of 1/√200 =  [#permalink]

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New post 18 Oct 2018, 01:14
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

72% (00:45) correct 28% (00:31) wrong based on 47 sessions

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5√2 percent of 1/√200 =  [#permalink]

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New post 18 Oct 2018, 05:48
(5\sqrt{2})/100) * 1/(10*\sqrt{2}) = 0.005

Option A
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Re: 5√2 percent of 1/√200 =  [#permalink]

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New post 19 Oct 2018, 06:56
Top Contributor
Bunuel wrote:
\(5√2\) percent of \(\frac{1}{√200} =\)


A. 0.005
B. 0.02
C. 0.05
D. 0.2
E. 0.5


p percent = p/100
For example, 19% = 19/100
So, 5√2 percent = (5√2)/100

√200 = (√100)(√2) = 10√2

So, 5√2 percent of 1/√200 = [(5√2)/100][1/10√2]
= [5/100][1/10] [the √2's cancel out]
= 5/1000
= 0.005

Answer: A

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Brent
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5√2 percent of 1/√200 =  [#permalink]

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New post 19 Oct 2018, 09:30
Bunuel wrote:
\(5√2\) percent of \(\frac{1}{√200} =\)


A. 0.005
B. 0.02
C. 0.05
D. 0.2
E. 0.5

I. Arithmetic
Change the denominator either initially* or while solving, as here

Setup: 10 percent of \(\frac{1}{2}=\)
LHS: \((\frac{10}{100}*\frac{1}{2})\)

\(5√2\) percent of \(\frac{1}{√200}\):

\((\frac{5\sqrt{2}}{100}*\frac{1}{\sqrt{200}})=\frac{5\sqrt{2}}{100*\sqrt{200}}=\)

\(\frac{5\sqrt{2}}{100*\sqrt{100*2}}=\)

\(\frac{5\sqrt{2}}{100*10\sqrt{2}}=\)

\(\frac{5}{100*10}=\frac{1}{100*2}=\frac{1}{200}=\)

\(0.005\)

Answer A

II. Approximate in pieces

\(5√2\) percent of \(\frac{1}{√200}\)?

(1) \(5\sqrt{2}\approx{(5*1.4)}\approx{7}\)

\(7\) percent =\(0.07\)

(2) \(\frac{1}{\sqrt{200}}\):
the denominator is between 14 and 15. \(14^2=196\), and \(15^2=225\)

\(\sqrt{196}<\sqrt{200}<\sqrt{225}\)

\(\sqrt{200}\) is closer to 14:
\(\frac{1}{\sqrt{200}}\approx{\frac{1}{14}}\approx{0.07}\)

(3) Together: 7 percent of 0.07 =

\((0.07*0.07)=0.0049\)

\(\approx{0.005}\)

Answer A

*\(\frac{1}{\sqrt{200}}\)
Change the denominator
\(\sqrt{200}=\sqrt{100*2}=10\sqrt{2}=>\)
\(\frac{1}{\sqrt{200}}=
\frac{1}{10\sqrt{2}}\)
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Re: 5√2 percent of 1/√200 =  [#permalink]

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New post 19 Oct 2018, 14:21
Bunuel wrote:
\(5√2\) percent of \(\frac{1}{√200} =\)


A. 0.005
B. 0.02
C. 0.05
D. 0.2
E. 0.5


We can express 5√2 percent as 5√2/100. Thus, we have:

(5√2)/100 x (1/√200) = (5√2)/(100√200) =1/(20 x 10) = 1/200 = 0.005

Answer: A
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Re: 5√2 percent of 1/√200 = &nbs [#permalink] 19 Oct 2018, 14:21
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