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Which of the following is equivalent to 21/6 ?

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Which of the following is equivalent to 21/6 ? [#permalink]

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New post 06 Jun 2017, 10:01
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Which of the following is equivalent to \(\frac{\sqrt{21}}{6}\)?

A. \(\frac{\sqrt{7}}{2}\)

B. 7/12

C. \(\sqrt{\frac{7}{2}}\)

D. \(\sqrt{\frac{7}{12}}\)

E. \(\frac{7\sqrt{3}}{2}\)
[Reveal] Spoiler: OA

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Which of the following is equivalent to 21/6 ? [#permalink]

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\(\frac{\sqrt{21}}{6}\) = \(\frac{\sqrt{7*3}}{6}\)

= \(\frac{\sqrt{7*3}}{\sqrt{36}}\)

= \(\frac{\sqrt{7*3}}{\sqrt{12*3}}\) = \(\sqrt{\frac{7}{12}}\) (Option D)
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Re: Which of the following is equivalent to 21/6 ? [#permalink]

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New post 06 Jun 2017, 11:08
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Bunuel wrote:
Which of the following is equivalent to \(\frac{\sqrt{21}}{6}\)?

A. \(\frac{\sqrt{7}}{2}\)

B. 7/12

C. \(\sqrt{\frac{7}{2}}\)

D. \(\sqrt{\frac{7}{12}}\)

E. \(\frac{7\sqrt{3}}{2}\)


Useful rule: \(\frac{\sqrt{x}}{\sqrt{y}} = {\sqrt{\frac{x}{y}}}\)

So, \(\frac{\sqrt{21}}{6} =\frac{\sqrt{21}}{\sqrt{36}} = {\sqrt{\frac{21}{36}}} = {\sqrt{\frac{7}{12}}}\)

Answer:
[Reveal] Spoiler:
D

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Re: Which of the following is equivalent to 21/6 ? [#permalink]

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New post 27 Jun 2017, 02:41
Why in this case it's wrong to square all and remove the square root?
In this question https://gmatclub.com/forum/2-240047.html I saw that it's feasible... why in this case it isn't?
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Which of the following is equivalent to 21/6 ? [#permalink]

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New post 27 Jun 2017, 03:34
MvArrow wrote:
Why in this case it's wrong to square all and remove the square root?
In this question https://gmatclub.com/forum/2-240047.html I saw that it's feasible... why in this case it isn't?



Let a= \(\frac{\sqrt{21}}{6}\)

If you want to remove the square root, square both sides

\(a^2 =\frac{21}{6^2}\) = \(\frac{21}{36} = \frac{7*3}{12*3} = \frac{7}{12}\)

Taking square root, we get a = \(\sqrt{\frac{7}{12}}\)(Option D)
Hope it helps!
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Re: Which of the following is equivalent to 21/6 ? [#permalink]

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MvArrow wrote:
Which of the following is equivalent to \(\frac{\sqrt{21}}{6}\)?

A. \(\frac{\sqrt{7}}{2}\)

B. 7/12

C. \(\sqrt{\frac{7}{2}}\)

D. \(\sqrt{\frac{7}{12}}\)

E. \(\frac{7\sqrt{3}}{2}\)

Why in this case it's wrong to square all and remove the square root?
In this question https://gmatclub.com/forum/2-240047.html I saw that it's feasible... why in this case it isn't?


You can do this way but you should square the options too to compare apples with apples. When you square, the question becomes: which of the following is equivalent to \((\frac{\sqrt{21}}{6})^2=\frac{21}{36}=\frac{7}{12}\). Option D squared gives exactly this value: \((\sqrt{\frac{7}{12}})^2=\frac{7}{12}\)

Answer: D.

Hope it helps.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Which of the following is equivalent to 21/6 ? [#permalink]

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New post 27 Jun 2017, 03:55
Bunuel wrote:
Which of the following is equivalent to \(\frac{\sqrt{21}}{6}\)?

A. \(\frac{\sqrt{7}}{2}\)

B. 7/12

C. \(\sqrt{\frac{7}{2}}\)

D. \(\sqrt{\frac{7}{12}}\)

E. \(\frac{7\sqrt{3}}{2}\)


\(\frac{\sqrt{21}}{6}\)
\(\frac{\sqrt{7*3}}{\sqrt{3*3*2*2}}\)
\(\frac{\sqrt{7}}{\sqrt{3*2*2}}\)
\(\frac{\sqrt{7}}{\sqrt{12}}\)

Answer D.
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Re: Which of the following is equivalent to 21/6 ? [#permalink]

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New post 27 Jun 2017, 04:16
Bunuel wrote:
MvArrow wrote:
Which of the following is equivalent to \(\frac{\sqrt{21}}{6}\)?

A. \(\frac{\sqrt{7}}{2}\)

B. 7/12

C. \(\sqrt{\frac{7}{2}}\)

D. \(\sqrt{\frac{7}{12}}\)

E. \(\frac{7\sqrt{3}}{2}\)

Why in this case it's wrong to square all and remove the square root?
In this question https://gmatclub.com/forum/2-240047.html I saw that it's feasible... why in this case it isn't?


You can do this way but you should square the options too to compare apples with apples. When you square, the question becomes: which of the following is equivalent to \((\frac{\sqrt{21}}{6})^2=\frac{21}{36}=\frac{7}{12}\). Option D squared gives exactly this value: \((\sqrt{\frac{7}{12}})^2=\frac{7}{12}\)

Answer: D.

Hope it helps.


Great! Thanks! I din't think about it
:oops:
Re: Which of the following is equivalent to 21/6 ?   [#permalink] 27 Jun 2017, 04:16
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