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What is the value of ...

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What is the value of ...  [#permalink]

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New post 14 Nov 2016, 03:51
3
11
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

68% (02:04) correct 32% (02:33) wrong based on 217 sessions

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Intern
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Re: What is the value of ...  [#permalink]

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New post 14 Nov 2016, 16:13
5
1
Bunuel wrote:
What is the value of \(\sqrt{\frac{10}{3\sqrt{11}+10}+30\sqrt{11}}\)

A. \(\sqrt{11}\)

B. \(\sqrt{33}\)

C. 8

D. 10

E. \(30\sqrt{11}\)


IMO Solution is 'D'.

Please see the attached file for detail calculation.
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Re: What is the value of ...  [#permalink]

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New post 14 Nov 2016, 04:13
Bunuel wrote:
What is the value of \(\sqrt{\frac{10}{3\sqrt{11}+10}+30\sqrt{11}}\)

A. \(\sqrt{11}\)

B. \(\sqrt{33}\)

C. 8

D. 10

E. \(30\sqrt{11}\)



IMO D

10/{3(sqrt 11)+10} can be simplified as 100-30(sqrt 11)
sqrt( 100-30(sqrt 11)+30(sqrt 11) ) will yield the answer 10
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Re: What is the value of ...  [#permalink]

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New post 17 Nov 2016, 14:58
Bunuel wrote:
What is the value of \(\sqrt{\frac{10}{3\sqrt{11}+10}+30\sqrt{11}}\)

A. \(\sqrt{11}\)

B. \(\sqrt{33}\)

C. 8

D. 10

E. \(30\sqrt{11}\)


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Re: What is the value of ...  [#permalink]

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New post 18 Nov 2016, 20:18
2
It's D
The easiest approach is if you use estimates - > square-root of 11 is approx 3.5 (you know its between 3 and 4) so
3x(square-root of 11) is ~10
30x(square-root of 11) is ~100
So
10/(3(sqr11)+10) + 30(sqr11)=10/20+100. Square-root of 100 1/2 is approx 10.
Lets look at the responses:
A)sqr11 = ~3.5 can't be
B)sqr30 = ~6 can't be
C)8 can't be
D) 10 thats it
E) 30(sqr11)= ~100 can't be
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New post 08 Dec 2019, 17:05
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Re: What is the value of ...   [#permalink] 08 Dec 2019, 17:05
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