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Is the length of the diagonal of the rectangle bigger than root(6) ?

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Is the length of the diagonal of the rectangle bigger than root(6) ?  [#permalink]

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New post 01 Nov 2010, 04:41
2
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A
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D
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Is the length of the diagonal of the rectangle bigger than \(\sqrt{6}\) ?

(1) The shorter side of the rectangle is 2.
(2) The longer side of the rectangle is 3.


Hi,

In Geomtry I, question 3 the DS question is:

Question: The OA assumes sides as integers, otherwise it should be another answer. Why is assuming integers and not decimals?

Thank you,
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Re: Is the length of the diagonal of the rectangle bigger than root(6) ?  [#permalink]

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New post 01 Nov 2010, 05:02
1
You don't need to assume sides as integers.
Statement (1) The shorter side of the rectangle is 2 which means the greater side will be more than 2. Let us say it is just a little more than 2, say 2.01.
The diagonal will be \(\sqrt{{2^2 + (2.01)^2}} = \sqrt{8.04}.\) This is definitely greater than \(\sqrt{6}\). So it doesn't matter what the greater side is, the diagonal will be greater than root 6. Statement (1) is sufficient.
Statement (2) The greater side of the rectangle is 3. The smaller side can be as small as possible, let's say a little more than 0. Still, the diagonal will be \(\sqrt{{3^2 + (0.01)^2}} = \sqrt{9.0001}.\) This is definitely greater than \(\sqrt{6}\). Therefore, statement (2) is sufficient.
Answer (D).
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Re: Is the length of the diagonal of the rectangle bigger than root(6) ?  [#permalink]

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New post 01 Nov 2010, 05:06
VeritasPrepKarishma wrote:
You don't need to assume sides as integers.
Statement (1) The shorter side of the rectangle is 2 which means the greater side will be more than 2. Let us say it is just a little more than 2, say 2.01.
The diagonal will be \(\sqrt{{2^2 + (2.01)^2}} = \sqrt{8.04}.\) This is definitely greater than \(\sqrt{6}\). So it doesn't matter what the greater side is, the diagonal will be greater than root 6. Statement (1) is sufficient.
Statement (2) The greater side of the rectangle is 3. The smaller side can be as small as possible, let's say a little more than 0. Still, the diagonal will be \(\sqrt{{3^2 + (0.01)^2}} = \sqrt{9.0001}.\) This is definitely greater than \(\sqrt{6}\). Therefore, statement (2) is sufficient.
Answer (D).




Hi Karishma,

Once posted, I realized it was talking about the diagonal, while I was thinking in the area.
Apologize for my mistake.

Thanks!
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Re: Is the length of the diagonal of the rectangle bigger than root(6) ?  [#permalink]

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New post 23 Jul 2016, 13:41
Is this really 700+ question?
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Re: Is the length of the diagonal of the rectangle bigger than root(6) ?  [#permalink]

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New post 24 Jul 2016, 00:34
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Konstantin1983 wrote:
Is this really 700+ question?


maybe during exam condition it can be.
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Re: Is the length of the diagonal of the rectangle bigger than root(6) ?  [#permalink]

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New post 24 Jul 2016, 01:24
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Is the length of the diagonal of the rectangle bigger than root(6) ?  [#permalink]

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New post 15 Aug 2017, 14:29
i'm sure it's not a 700 level question. I solved it just by applying logic...

1. if short one is 2, then we can minimize the longer one to be 2 for example too... a^2 + b^2 = c^2. so we have a=2, b=2, and c^2 = 8. c is sqrt(8). we can give only 1 answer so sufficient.
2. if the bigger one is 3, the other one doesn't matter, as 3^2 = 9. and 9+ smth squared will always be bigger than sqrt(6)... sufficient.

D is the answer.
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Re: Is the length of the diagonal of the rectangle bigger than root(6) ?  [#permalink]

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New post 02 Nov 2018, 17:03
vivaslluis wrote:
Is the length of the diagonal of the rectangle bigger than \(\sqrt{6}\) ?

(1) The shorter side of the rectangle is 2.
(2) The longer side of the rectangle is 3.

\(a \ge b > 0\,\,\,\,\,\left[ {{\rm{rectangle}}\,\,{\rm{dimensions}}} \right]\)

\({a^2} + {b^2}\,\,\mathop > \limits^? \,\,6\)


\(\left( 1 \right)\,\,a > b = 2\,\,\,\, \Rightarrow \,\,\,{a^2} + {b^2} > {2^2} + {2^2} = 8\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle\)

\(\left( 2 \right)\,\,3 = a > b > 0\,\,\,\, \Rightarrow \,\,\,{a^2} + {b^2} > {3^2} = 9\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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