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# If the area of square A is three times the area of square B

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Intern
Joined: 18 Oct 2009
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Schools: Kellogg
If the area of square A is three times the area of square B  [#permalink]

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Updated on: 30 Jan 2014, 21:44
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55% (hard)

Question Stats:

68% (01:34) correct 32% (01:57) wrong based on 366 sessions

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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 A to that of square B?

A. $$\frac{1}{\sqrt{3}}$$

B. $$\frac{1}{\sqrt[3]{3}}$$

C. $$\sqrt[3]{3}$$

D. $$\sqrt{3}$$

E. 3

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Originally posted by slingfox on 25 Oct 2009, 21:22.
Last edited by Bunuel on 30 Jan 2014, 21:44, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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Re: Ratio of Triangle Measurements  [#permalink]

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25 Oct 2009, 22:32
1
slingfox wrote:
If the area of square Q is three times the area of square P, what is the ratio of the diagonal of square Q to that of square?

A. 1/Sqrt(3)
B. 1/Third Root(3)
C. Third Root(3)
D. Sqrt(3)
E. 3

Area of small square-P = s^2
Side of small square-P = s
Diagonal of a small square-P = s (sqrt2)

Area of large square-Q = 3s^2
Side of large square-Q = s {sqrt(3)}
Diagonal of a large square-Q = s (sqrt6)

Diagonal of a large square-Q / Diagonal of a small square-P = s (sqrt6) / s (sqrt2) = sqrt3
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Joined: 15 Sep 2009
Posts: 115
Re: Ratio of Triangle Measurements  [#permalink]

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26 Oct 2009, 05:07
Area Q = 3a^2

Area P = 3b^2.

3a^2 = 3b^2.

a = sqrt(3)*b.

diagonal of Q = sqrt(2) * a

diagonal of P = sqrt(2) * b.

Ratio of Q/P = a/b = sqrt(3) * b/b = sqrt(3).

I will go with option D
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Re: Ratio of Triangle Measurements  [#permalink]

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26 Oct 2009, 08:29
3
I wouldn't waste time calculating the ratio of the diagonals, calculating the ratio of the sides would suffice as it equals the ratio of the diagonals.
i.e. a/b = sqrt2*a/sqrt2*b.
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Re: Ratio of Triangle Measurements  [#permalink]

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26 Oct 2009, 08:35
true, we just need to calculate ratio of sides ps to qs (as the ratio of diagonals is same as ratio of sides because diagonal is always $$sqrt2$$ times side)

given that $$p^2/q^2=3 ==> p/q=sqrt3$$
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Re: Ratio of Triangle Measurements  [#permalink]

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30 Oct 2009, 20:33
sqr(e1)/sqr(e2) = 3/1

e1/e2 = sqrt(3)

D
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Re: Ratio of Triangle Measurements  [#permalink]

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30 Oct 2009, 21:02
nice approach atish. diagonal is $$sqrt(2)$$ x side
In test conditions, these things never comes to mind
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Joined: 02 Sep 2009
Posts: 52288
Re: If the area of square A is three times the area of square B  [#permalink]

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30 Jan 2014, 21:49
1
slingfox wrote:
If the area of square A is three times the area of square B, what is the ratio of the diagonal of square A to that of square B?

A. $$\frac{1}{\sqrt{3}}$$

B. $$\frac{1}{\sqrt[3]{3}}$$

C. $$\sqrt[3]{3}$$

D. $$\sqrt{3}$$

E. 3

The area of a square is $$\frac{diagonal^2}{2}$$.

Hence we are given that $$\frac{D^2}{2}=3*\frac{d^2}{2}$$ --> $$\frac{D}{d}=\sqrt{3}$$.

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Re: If the area of square A is three times the area of square B  [#permalink]

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30 Jan 2014, 22:19
slingfox wrote:
If the area of square A is three times the area of square B, what is the ratio of the diagonal of square A to that of square B?

A. $$\frac{1}{\sqrt{3}}$$

B. $$\frac{1}{\sqrt[3]{3}}$$

C. $$\sqrt[3]{3}$$

D. $$\sqrt{3}$$

E. 3

Let us say that area of A is 12 and area of B is 4.
Side of A = 2(3)^1/2
Side of B = 2
Diagonal of A/Diagonal of B = (Side of A)/(Side of B) = (3^1/2)/1

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Re: If the area of square A is three times the area of square B  [#permalink]

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09 Mar 2014, 21:01
3
Say area of Square B = 1 (Each side = 1), then
Area of Square A = 3 (Each side = $$\sqrt{3}$$)

Diagonal of Square A = $$\sqrt{6}$$

Diagonal of Square B = $$\sqrt{2}$$

Ratio = $$\sqrt{3}$$

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Re: If the area of square A is three times the area of square B  [#permalink]

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20 May 2014, 11:18
Am I going crazy or is there something wrong with this GMATClub CAT question? I don't think the correct answer is listed.

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Re: If the area of square A is three times the area of square B  [#permalink]

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20 May 2014, 11:42
Kenny537 wrote:
Am I going crazy or is there something wrong with this GMATClub CAT question? I don't think the correct answer is listed.

Just realized the answer is meant to be (1/sqrt of 3) rather than (1/3.5). Now it makes sense. Hard to tell.
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Re: If the area of square A is three times the area of square B  [#permalink]

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20 May 2014, 23:59
Dear Kenny537,
Problem at gmat club is asking for the ratio of the diagonal of square A to that of square B while in the image attached by you, the ratio of the diagonal of square B to that of square A is being asked.

Accordingly, answer is right in both the questions because both are asking different ratios.
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Re: If the area of square A is three times the area of square B  [#permalink]

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21 May 2014, 06:23
kundankshrivastava wrote:
Dear Kenny537,
Problem at gmat club is asking for the ratio of the diagonal of square A to that of square B while in the image attached by you, the ratio of the diagonal of square B to that of square A is being asked.

Accordingly, answer is right in both the questions because both are asking different ratios.

I am aware that it is a different question. I just didn't feel like creating a thread for the question and thought this was a similar enough question.
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Re: If the area of square A is three times the area of square B  [#permalink]

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20 Feb 2016, 03:39
A square is a rhombus. The area of a rhombus is 1/2 * d1 * d2. For a square, d1 = d2 (=d). Thus area = $$1/2 * d^2$$
If area is 3 times the other, the diagonal should be \sqrt{3} times the other.
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Re: If the area of square A is three times the area of square B  [#permalink]

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22 Sep 2018, 18:41
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If the area of square A is three times the area of square B &nbs [#permalink] 22 Sep 2018, 18:41
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