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M09-36

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M09-36  [#permalink]

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New post 15 Sep 2014, 23:41
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If the area of square \(A\) is three times the area of square \(B\), what is the ratio of the diagonal of square \(B\) to that of square \(A\)?

A. \(\frac{1}{3^{(\frac{1}{2})}}\)
B. \(\frac{1}{3^{(\frac{1}{3})}}\)
C. \(3^{(\frac{1}{3})}\)
D. \(3^{(\frac{1}{2})}\)
E. 3

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Re M09-36  [#permalink]

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New post 15 Sep 2014, 23:41
2
Official Solution:

If the area of square \(A\) is three times the area of square \(B\), what is the ratio of the diagonal of square \(B\) to that of square \(A\)?

A. \(\frac{1}{3^{(\frac{1}{2})}}\)
B. \(\frac{1}{3^{(\frac{1}{3})}}\)
C. \(3^{(\frac{1}{3})}\)
D. \(3^{(\frac{1}{2})}\)
E. 3


The ratio of the diagonals is the same as the ratio of the sides. If the side of \(B\) is \(b\), then the side of \(A\) must be \(\sqrt{3}b\). The required ratio is:
\(\frac{b}{\sqrt{3}b} = \frac{1}{\sqrt{3}} = \frac{1}{3^{\frac{1}{2}}}.\)


Answer: A
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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

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Re: M09-36  [#permalink]

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New post 02 Jul 2015, 07:10
Bunuel wrote:
Official Solution:

If the area of square \(A\) is three times the area of square \(B\), what is the ratio of the diagonal of square \(B\) to that of square \(A\)?

A. \(\frac{1}{3^{(\frac{1}{2})}}\)
B. \(\frac{1}{3^{(\frac{1}{3})}}\)
C. \(3^{(\frac{1}{3})}\)
D. \(3^{(\frac{1}{2})}\)
E. 3


The ratio of the diagonals is the same as the ratio of the sides. If the side of \(B\) is \(b\), then the side of \(A\) must be \(\sqrt{3}b\). The required ratio is:
\(\frac{b}{\sqrt{3}b} = \frac{1}{\sqrt{3}} = \frac{1}{3^{\frac{1}{2}}}.\)


Answer: A


Hi,
I answer correctly, but it would help me if you explain in a little more detail the conclusion in order to answer quickly: The ratio of the diagonals is the same as the ratio of the sides. If the side of B is b, then the side of A must be 3√b

Thanks a lot.

Regards,

Luis Navarro
Looking for 700
Math Expert
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Joined: 02 Sep 2009
Posts: 51035
Re: M09-36  [#permalink]

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New post 02 Jul 2015, 07:37
1
luisnavarro wrote:
Bunuel wrote:
Official Solution:

If the area of square \(A\) is three times the area of square \(B\), what is the ratio of the diagonal of square \(B\) to that of square \(A\)?

A. \(\frac{1}{3^{(\frac{1}{2})}}\)
B. \(\frac{1}{3^{(\frac{1}{3})}}\)
C. \(3^{(\frac{1}{3})}\)
D. \(3^{(\frac{1}{2})}\)
E. 3


The ratio of the diagonals is the same as the ratio of the sides. If the side of \(B\) is \(b\), then the side of \(A\) must be \(\sqrt{3}b\). The required ratio is:
\(\frac{b}{\sqrt{3}b} = \frac{1}{\sqrt{3}} = \frac{1}{3^{\frac{1}{2}}}.\)


Answer: A


Hi,
I answer correctly, but it would help me if you explain in a little more detail the conclusion in order to answer quickly: The ratio of the diagonals is the same as the ratio of the sides. If the side of B is b, then the side of A must be 3√b

Thanks a lot.

Regards,

Luis Navarro
Looking for 700


Check here: if-the-area-of-square-a-is-three-times-the-area-of-square-b-85808.html

Hope it helps.
_________________

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Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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: M09-36  [#permalink]

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New post 02 Jul 2015, 08:00
Bunuel wrote:
luisnavarro wrote:
Bunuel wrote:
Official Solution:

If the area of square \(A\) is three times the area of square \(B\), what is the ratio of the diagonal of square \(B\) to that of square \(A\)?

A. \(\frac{1}{3^{(\frac{1}{2})}}\)
B. \(\frac{1}{3^{(\frac{1}{3})}}\)
C. \(3^{(\frac{1}{3})}\)
D. \(3^{(\frac{1}{2})}\)
E. 3


The ratio of the diagonals is the same as the ratio of the sides. If the side of \(B\) is \(b\), then the side of \(A\) must be \(\sqrt{3}b\). The required ratio is:
\(\frac{b}{\sqrt{3}b} = \frac{1}{\sqrt{3}} = \frac{1}{3^{\frac{1}{2}}}.\)


Answer: A


Hi,
I answer correctly, but it would help me if you explain in a little more detail the conclusion in order to answer quickly: The ratio of the diagonals is the same as the ratio of the sides. If the side of B is b, then the side of A must be 3√b

Thanks a lot.

Regards,

Luis Navarro
Looking for 700


Check here: if-the-area-of-square-a-is-three-times-the-area-of-square-b-85808.html

Hope it helps.


Thanks a lot¡¡
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Re: M09-36  [#permalink]

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New post 28 Nov 2015, 10:09
Hi Bunuel

I think the correct choice is D.
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Re: M09-36  [#permalink]

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New post 28 Nov 2015, 10:18
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Re: M09-36  [#permalink]

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New post 28 Nov 2015, 19:49
Bunuel wrote:
sigma wrote:
Hi Bunuel

I think the correct choice is D.


Care to elaborate?


Oh, I had put in the link mentioned by you at the top but it didn't go through.

The correct choice is root 3, even as per the link that you have given on the top you can see in your earlier post you have mentioned it as root 3.
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Re: M09-36  [#permalink]

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New post 29 Nov 2015, 05:50
sigma wrote:
Bunuel wrote:
sigma wrote:
Hi Bunuel

I think the correct choice is D.


Care to elaborate?


Oh, I had put in the link mentioned by you at the top but it didn't go through.

The correct choice is root 3, even as per the link that you have given on the top you can see in your earlier post you have mentioned it as root 3.


You should read the questions more carefully. The question above asks about the ratio of the diagonal of square B to that of square A, while the question from the link asks about the ratio of the diagonal of square A to that of square B.

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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: M09-36  [#permalink]

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New post 10 Jan 2016, 09:38
Hi!

I'm trying to solve using the diagonal, but my answer is not matching....
Area of A: 12
Area of B: 4

Diagonal of A: \(\sqrt{24}\)
Diagonal of B: \(\sqrt{8}\)

Ratio:
\(\sqrt{24}\) / \(\sqrt{8}\) -> \(\sqrt{2}\) / \(\sqrt{6}\)

Could someone help? :)

Bunuel wrote:
luisnavarro wrote:
Bunuel wrote:
Official Solution:

If the area of square \(A\) is three times the area of square \(B\), what is the ratio of the diagonal of square \(B\) to that of square \(A\)?

A. \(\frac{1}{3^{(\frac{1}{2})}}\)
B. \(\frac{1}{3^{(\frac{1}{3})}}\)
C. \(3^{(\frac{1}{3})}\)
D. \(3^{(\frac{1}{2})}\)
E. 3


The ratio of the diagonals is the same as the ratio of the sides. If the side of \(B\) is \(b\), then the side of \(A\) must be \(\sqrt{3}b\). The required ratio is:
\(\frac{b}{\sqrt{3}b} = \frac{1}{\sqrt{3}} = \frac{1}{3^{\frac{1}{2}}}.\)


Answer: A


Hi,
I answer correctly, but it would help me if you explain in a little more detail the conclusion in order to answer quickly: The ratio of the diagonals is the same as the ratio of the sides. If the side of B is b, then the side of A must be 3√b

Thanks a lot.

Regards,

Luis Navarro
Looking for 700


Check here: if-the-area-of-square-a-is-three-times-the-area-of-square-b-85808.html

Hope it helps.
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M09-36  [#permalink]

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New post 14 Apr 2016, 16:49
Though it is often advised not to rely too much on math formula on GMAT but this problem is best suited if you remember below :

Area of Square = (Diagonal^2)/2 --> Square of diagonal divided by 2.

Let's apply the same formula here -
(A^2)/2 = (3)(B^2)/2 -->Where A is the diagonal of SquareA and B is the diagonal of SquareB.
Simplifying the formula,
B/A = 1/Sqrt(3). Ans A.

It is little easy in this case as we have a direct formula which links Area of a square to its diagonal. Hope it makes sense.
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Re M09-36  [#permalink]

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New post 17 Aug 2018, 09:18
I think this is a high-quality question and I agree with explanation.
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Re M09-36 &nbs [#permalink] 17 Aug 2018, 09:18
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