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Math Expert V
Joined: 02 Sep 2009
Posts: 56261

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Difficulty:   45% (medium)

Question Stats: 65% (01:04) correct 35% (01:16) wrong based on 110 sessions

### HideShow timer Statistics 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

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 56261

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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:
$$\frac{b}{\sqrt{3}b} = \frac{1}{\sqrt{3}} = \frac{1}{3^{\frac{1}{2}}}.$$

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Intern  Joined: 24 Jun 2015
Posts: 46

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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:
$$\frac{b}{\sqrt{3}b} = \frac{1}{\sqrt{3}} = \frac{1}{3^{\frac{1}{2}}}.$$

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 V
Joined: 02 Sep 2009
Posts: 56261

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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:
$$\frac{b}{\sqrt{3}b} = \frac{1}{\sqrt{3}} = \frac{1}{3^{\frac{1}{2}}}.$$

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.
_________________
Intern  Joined: 24 Jun 2015
Posts: 46

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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:
$$\frac{b}{\sqrt{3}b} = \frac{1}{\sqrt{3}} = \frac{1}{3^{\frac{1}{2}}}.$$

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¡¡
Intern  Joined: 26 Aug 2015
Posts: 2

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Hi Bunuel

I think the correct choice is D.
Math Expert V
Joined: 02 Sep 2009
Posts: 56261

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sigma wrote:
Hi Bunuel

I think the correct choice is D.

Care to elaborate?
_________________
Intern  Joined: 26 Aug 2015
Posts: 2

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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.
Math Expert V
Joined: 02 Sep 2009
Posts: 56261

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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.
_________________
Intern  Joined: 17 Oct 2015
Posts: 17

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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:
$$\frac{b}{\sqrt{3}b} = \frac{1}{\sqrt{3}} = \frac{1}{3^{\frac{1}{2}}}.$$

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.
Intern  Joined: 21 Oct 2015
Posts: 46
GMAT 1: 620 Q47 V28 ### Show Tags

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.
Intern  B
Joined: 14 Jul 2018
Posts: 4
Location: United States (AZ)
Concentration: Strategy, Finance
GPA: 3.45
WE: Securities Sales and Trading (Energy and Utilities)

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I think this is a high-quality question and I agree with explanation. Re M09-36   [#permalink] 17 Aug 2018, 10:18
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# M09-36

Moderators: chetan2u, Bunuel  