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M09-36

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Bunuel
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M09-36 [#permalink] New post   16 Sep 2014, 00:41
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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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Bunuel
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Re M09-36 [#permalink] New post   16 Sep 2014, 00:41
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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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luisnavarro
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Re: M09-36 [#permalink] New post   02 Jul 2015, 08:10
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
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Bunuel
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Re: M09-36 [#permalink] New post   02 Jul 2015, 08:37
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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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Re: M09-36 [#permalink] New post   02 Jul 2015, 09:00
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] New post   28 Nov 2015, 11:09
Hi Bunuel

I think the correct choice is D.
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Re: M09-36 [#permalink] New post   28 Nov 2015, 11:18
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sigma wrote:
Hi Bunuel

I think the correct choice is D.


Care to elaborate?
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Re: M09-36 [#permalink] New post   28 Nov 2015, 20:49
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] New post   29 Nov 2015, 06:50
Expert Reply
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.
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Re: M09-36 [#permalink] New post   10 Jan 2016, 10:38
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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Re: M09-36 [#permalink] New post   14 Apr 2016, 17:49
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] New post   17 Aug 2018, 10:18
I think this is a high-quality question and I agree with explanation.
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Re: M09-36 [#permalink] New post   15 Jun 2022, 02:45
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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


Bunuel in similar figures, if k is the scaling factor then it is also the ratio of any 2 corresponding lengths, hence the area changes by k^2.

Keeping this theory in mind, we are given k^2 = 3, Therefore k=3^1/2 and therefore diagonal of square B to that of square A = 1/(3)1^2 .
Is my reasoning correct?

Thanks in adv.
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Re: M09-36 [#permalink]
15 Jun 2022, 02:45
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