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Bob plans to draw a square ABCD with a point O on the side AB but is

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Bob plans to draw a square ABCD with a point O on the side AB but is  [#permalink]

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New post Updated on: 25 Aug 2015, 23:45
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Bob plans to draw a square ABCD with a point O on the side AB but is not successful. Why is Bob unable to draw the square?

(1) The length of OD is twice that of OC.

(2) The length of OD is 4 cm.

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Originally posted by VenoMfTw on 25 Aug 2015, 22:44.
Last edited by Bunuel on 25 Aug 2015, 23:45, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Bob plans to draw a square ABCD with a point O on the side AB but is  [#permalink]

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New post 02 Jul 2016, 13:05
Imagine that the point is the point A then ratio of OD to OC would be side : diagonal.
Assume that ABCD is a square, then that ratio comes out the be s:s \sqrt{2} which is 1: \sqrt{2}.
Since diagonal is of maximum length in a square, the max ratio will always be 1: \sqrt{2}.
There is not point on the side of the square which can exceed this ratio if it has to be on the side of square.
1: 2 greater than 1:\sqrt{2}. Therefore, Statement 1 is sufficient to prove that a square cannot be drawn.
Statement 2 does not provide any valuable additional information and hence is insufficient.
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Re: Bob plans to draw a square ABCD with a point O on the side AB but is  [#permalink]

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New post 03 Jul 2016, 00:37
(1) The length of OD is twice that of OC.

the largest distance between any two points within a square is the diagonal.

if the side of the square is A then the diagonal is Aroot2, as per the question though OD=2OC .The square is thus not possible to draw with the given criteria . Thus sufficient

(2) The length of OD is 4 cm.

insufficient.
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Re: Bob plans to draw a square ABCD with a point O on the side AB but is  [#permalink]

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New post 15 Mar 2017, 19:56
I got this question right through intuition but can someone diagram it for me? I don't actually understand the logic behind this question.
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Re: Bob plans to draw a square ABCD with a point O on the side AB but is  [#permalink]

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New post 03 Aug 2017, 07:49
The longest line we can inscribe in a square is its diagnol(BD). let length of a side of square is a. Then diagnol (BD) = aroot2 (45-45-90).
Now lets draw point O near to B making OC approximately equal to BC (OC=a). Now according to question OD=2OC but we know that BD is the longest and its value is just aroot 2. So a square cannot be drawn.
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Re: Bob plans to draw a square ABCD with a point O on the side AB but is  [#permalink]

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New post 08 May 2018, 03:43
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what if the point is between A and B but not on A/B. since question states Point O is on side of AB. So the location is not clarified.

if that's the case, 1 is insufficient.

Even 2 is insufficient and ofcourse both are still insufficient. In my view answer is E. Can someone advice on my approach?
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Re: Bob plans to draw a square ABCD with a point O on the side AB but is  [#permalink]

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New post 08 May 2018, 04:48
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[quote="bhargavasrikantha"]what if the point is between A and B but not on A/B. since question states Point O is on side of AB. So the location is not clarified.

if that's the case, 1 is insufficient.

Even 2 is insufficient and ofcourse both are still insufficient. In my view answer is E. Can someone advice on my approach?[/quote]

Hello

The MAX ratio of OD to OC you will get will be when point O coincides with point B. Because in that case OD will be diagonal and OC will be the side, and thus the required ratio will be √2 : 1.

If instead you take point somewhere else between A and B then OD : OC will be less than √2 : 1.

So if the Max possible ratio in this case of a square is √2 : 1,then it can never be 2:1.

That's why statement 1 is sufficient

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Re: Bob plans to draw a square ABCD with a point O on the side AB but is &nbs [#permalink] 08 May 2018, 04:48
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